juliatest.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-7.5652184538256755, 3.4042678600205263]\n",
      "4.1588830833596715\n",
      "32954.979192520936\n",
      "Union{Missing, Float64}[10.402897642095965]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Plots\n",
    "using GLM\n",
    "using DataFrames\n",
    "\n",
    "x = [9,16,25,36,49]\n",
    "y = [0.7,8.83,39.276,82.506,268.672]\n",
    "lx = log.(x)\n",
    "ly = log.(y)\n",
    "scatter(log.(x), log.(y))\n",
    "data = DataFrame(x = lx, y = ly)\n",
    "model = lm(@formula(y ~ 1 + x), data)\n",
    "\n",
    "# Print model summary\n",
    "println(coef(model))  # Print coefficients (intercept and slope)\n",
    "\n",
    "# Plot\n",
    "scatter(lx, ly, label=\"Data\", title=\"Linear Regression\", xlabel=\"x\", ylabel=\"y\")\n",
    "\n",
    "# Create fitted line based on the model\n",
    "x_fit = range(minimum(lx), stop=maximum(lx), length=100)\n",
    "y_fit = predict(model, DataFrame(x=x_fit))\n",
    "# println(log(64))\n",
    "# println(exp(10.402897642095965))\n",
    "# println(predict(model, DataFrame(x = log(196))))\n",
    "\n",
    "# Add regression line to the plot\n",
    "plot!(x_fit, y_fit, label=\"Fit\", linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Vector{Int64}}:\n",
       " [1, 4]\n",
       " [2, 5]\n",
       " [3, 6]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a sample matrix\n",
    "matrix = [1 2 3; 4 5 6]\n",
    "vector_of_vectors = [matrix[:, i] for i in 1:size(matrix, 2)]\n",
    "vector_of_vectors\n",
    "\n",
    "# Flatten the matrix into a vector\n",
    "# vec_matrix = vec(matrix)\n",
    "# println(typeof(vec_matrix))\n",
    "# vec_matrix\n",
    "\n",
    "# # Convert elements of the vector to Int64\n",
    "# vec_int64 = Int64.(vec_matrix)\n",
    "\n",
    "# # Display the result\n",
    "# println(vec_int64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Vector{DitStr{2, 10, Int64}}:\n",
       " 1101000100 ₍₂₎\n",
       " 1101010000 ₍₂₎\n",
       " 0100000001 ₍₂₎\n",
       " 1001111111 ₍₂₎"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao\n",
    "\n",
    "layers = 5\n",
    "N = 10\n",
    "g = chain(N)\n",
    "for _ in 1:layers\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:N\n",
    "        push!(g, put(N, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "p = rand(nparameters(g)) .* 2π\n",
    "dispatch!(g, p)\n",
    "reg = Yao.zero_state(N)\n",
    "measure(apply(reg, g), nshots = 4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original data_train[1]: Bool[1, 0, 1]\n",
      "Converted data_train[1]: Bool[1, 0, 1]\n"
     ]
    }
   ],
   "source": [
    "data_train = [\n",
    "    [true, false, true],  # boolean array\n",
    "    [false, true, false],\n",
    "    [true, true, false]\n",
    "]\n",
    "\n",
    "println(\"Original data_train[1]: \", data_train[1])\n",
    "\n",
    "# Convert the boolean array to an integer array\n",
    "data_train[1] = Int.(data_train[1])\n",
    "\n",
    "println(\"Converted data_train[1]: \", data_train[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constructs a quantum circuit g with parameters θ, then differentiates the recursive algorithm given in Section 5.1 of https://arxiv.org/abs/1112.2184 to obtain the gradient of p_θ(x) wrt θ, where x is a measurement of g|0>. The differentiation takes polynomial time due to memoization.\n",
    "# We then compare our results to the finite difference gradient\n",
    "\n",
    "using Yao, FLOYao\n",
    "using LinearAlgebra\n",
    "\n",
    "nq = 15 #Number of qubits\n",
    "layers = 2 #Number of brick-wall layers in the circuit\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Nearest-neighbor XX rotation gates\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.)) #Nearest-neighbor XY rotation gates\n",
    "    end\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.))) #Single qubit Z rotation gates\n",
    "    end\n",
    "end\n",
    "\n",
    "#Set g to have random parameters\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "println(\"number of parameters: \", nparams)\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, assuming that i≠j\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = 1\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= 1\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= -1\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    if i > j\n",
    "        c *= -1\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j) #Returns [γ_i,γ_j]=2γ_iγ_j, due to the anti-commutation of Majorana operators. It needs to be an 'Add' object so that the Yao.expect' function can take it in as input.\n",
    "    return Add(majoranaindices2kron(nq, i, j)) \n",
    "end\n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            ni = b[i-1]\n",
    "            cur_prob = probabilities[i-1]\n",
    "            cur_grad_prob = grad_probabilities[:, i-1]\n",
    "            cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "            cur_grad_prefactor = (-1)^ni / (2*cur_prob^2)\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[:,p,q] .-= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,p]*temp_m[2*(i-1),q] .+ temp_m[2*(i-1)-1,p] * temp_grad_m[:,2*(i-1),q])))\n",
    "                    temp_grad_m[:,p,q] .+= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,q]*temp_m[2*(i-1),p] .+ temp_m[2*(i-1)-1,q] * temp_grad_m[:,2*(i-1),p])))\n",
    "                end\n",
    "            end\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= cur_prefactor * (temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q])\n",
    "                    temp_m[p,q] += cur_prefactor * (temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p])\n",
    "                end\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            temp_m = covariance_matrix(apply(reg, g))\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[:,p,q] = expect'(ham, reg => g)[2]\n",
    "                end\n",
    "            end\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        end\n",
    "        diff = (time() - t) * 10^6\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function log_grad_opt(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities) #Returns ∇_θlog(p_θ(b)), evaluated at 'theta' (parameters of circuit) and 'b' (measurement result); 'reg' is the initial register and must be of type MajoranaReg (e.g. FLOYao.zero_state(nq)). This uses the optimal updating function which is more efficient but still outputs the same thing as the original update! function.\n",
    "    update_opt!(reg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[:, i] / probabilities[i]\n",
    "    end\n",
    "    optimized_prob = probabilities\n",
    "    return optimized_prob, s\n",
    "end\n",
    "\n",
    "reg = apply(FLOYao.zero_state(nq), g)\n",
    "bitstr = measure(reg, nshots = 1)[1] #Random measurement of g|0>\n",
    "println(\"measured outcome: $bitstr\")\n",
    "println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr)) #Uses FLOYao.bitstring_probability(reg, bitstr) which is known to be correct. We check this number against our algorithm output, to verify correctness.\n",
    "\n",
    "T = Float64 #Can also be BigFloat, may experiment with other data types later\n",
    "println(\"data type used in calculations: $T\") \n",
    "println(\"note: the time (μs) taken for 'iteration i' refers to the time required for the algorithm to compute p_θ(x_i|x_1,...x_{i-1}) and ∇_θ(p_θ(x_i|x_1,...x_{i-1}))\")\n",
    "\n",
    "#Initializing temporary matrices and vectors.\n",
    "temp_m = Matrix{T}(undef, dim, dim)\n",
    "temp_grad_m = Array{T}(undef, nparams, dim, dim)\n",
    "probabilities = Vector{T}(undef, nq)\n",
    "grad_probabilities = Matrix{T}(undef, nparams, nq)\n",
    "\n",
    "optimized_prob, optimized = log_grad_opt(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "println(\"The ith entry in the following vector is p_θ(x_i|x_1,...x_{i-1})\")\n",
    "println(optimized_prob)\n",
    "println(\"the product of all entries in the above vector, should match the earlier probability computed using FLOYao.bitstring_probability: \", prod(optimized_prob))\n",
    "println(\"The following vector is ∇_θ(log(p_θ(x))), evaluated at x = measured outcome\")\n",
    "optimized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp_m = Matrix{T}(undef, dim, dim)\n",
    "temp_grad_m = Array{T}(undef, nparams, dim, dim)\n",
    "probabilities = Vector{T}(undef, nq)\n",
    "grad_probabilities = Matrix{T}(undef, nparams, nq)\n",
    "\n",
    "dispatch!(g, p)\n",
    "temp_m = covariance_matrix(apply(reg, g))\n",
    "i = 1\n",
    "ni = bitstr[i]\n",
    "probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "for p in 1:dim\n",
    "    for q in p+1:dim\n",
    "        ham = majorana_commutator(nq, p, q)\n",
    "        temp_grad_m[:,p,q] = expect'(ham, reg => g)[2]\n",
    "    end\n",
    "end\n",
    "grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "\n",
    "function helper!(temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    ni = b[i-1]\n",
    "    cur_prob = probabilities[i-1]\n",
    "    cur_grad_prob = grad_probabilities[:, i-1]\n",
    "    cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "    cur_grad_prefactor = (-1)^ni / (2*cur_prob^2)\n",
    "    for p in 2*(i-1)+1:dim\n",
    "        for q in p+1:dim\n",
    "            temp_grad_m[:,p,q] .-= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,p]*temp_m[2*(i-1),q] .+ temp_m[2*(i-1)-1,p] * temp_grad_m[:,2*(i-1),q])))\n",
    "            temp_grad_m[:,p,q] .+= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,q]*temp_m[2*(i-1),p] .+ temp_m[2*(i-1)-1,q] * temp_grad_m[:,2*(i-1),p])))\n",
    "        end\n",
    "    end\n",
    "    for p in 2*(i-1)+1:dim\n",
    "        for q in p+1:dim\n",
    "            temp_m[p,q] -= cur_prefactor * (temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q])\n",
    "            temp_m[p,q] += cur_prefactor * (temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p])\n",
    "        end\n",
    "    end\n",
    "    ni = b[i]\n",
    "    probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "    grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "end\n",
    "\n",
    "@benchmark helper!(temp_m, temp_grad_m, probabilities, grad_probabilities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3; 8 10 12; 21 24 27]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3×1 Matrix{Float64}:\n",
       "  2.0\n",
       " 10.0\n",
       " 24.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vv = [1,2,3]\n",
    "m = [1 2 3;4 5 6;7 8 9]\n",
    "\n",
    "println(vv.*m)\n",
    "M = vv.*m\n",
    "mean(M, dims=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[36mnqubits: 2\u001b[39m\n",
      "\u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
      "└─ rot(\u001b[36mnqubits: 2\u001b[39m\n",
      "\u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
      "├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>X\n",
      "└─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>X, 0.0)\n",
      "\u001b[36mnqubits: 2\u001b[39m\n",
      "\u001b[34m\u001b[1mchain\u001b[22m\u001b[39m\n",
      "└─ rot(\u001b[36mnqubits: 2\u001b[39m\n",
      "\u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
      "├─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>X\n",
      "└─ \u001b[37m\u001b[1m2\u001b[22m\u001b[39m=>X, 2.4543939193017965)\n",
      "2.4543939193017965\n",
      "0.33687824474746414\n",
      "-0.9415482187418059\n",
      "ComplexF64[0.33687824474746414 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 - 0.9415482187418059im]\n",
      "\u001b[36mnqubits: 2\u001b[39m\n",
      "\u001b[36m\u001b[1mkron\u001b[22m\u001b[39m\n",
      "└─ \u001b[37m\u001b[1m1\u001b[22m\u001b[39m=>Z\n",
      "-0.7730260964317354\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-0.7730260964317353"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "nq = 2\n",
    "circuit = chain(nq)\n",
    "push!(circuit, rot(kron(nq, 1 => X, 2 => X), 0.))\n",
    "println(circuit)\n",
    "param = rand()*2π \n",
    "dispatch!(circuit, param)\n",
    "println(circuit)\n",
    "println(param)\n",
    "println(cos(param/2))\n",
    "println(-sin(param/2))\n",
    "r = Yao.zero_state(nq) |> circuit \n",
    "r |> statevec |> println\n",
    "ham = kron(nq, 1 => Z)\n",
    "println(ham)\n",
    "println(cos(param))\n",
    "expect(ham, r)\n",
    "function f(reg)\n",
    "    return expect'(ham, reg => g)[2]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{ZGate}}}}}}\n",
      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
      "KronBlock{2, 1, Tuple{Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{ZGate}}}}}}}}\n"
     ]
    },
    {
     "ename": "FLOYao.NonFLOException",
     "evalue": "NonFLOException: (nqubits: 10\n[-] kron\n   └─ 1:10=>[-] kron\n         └─ 1=>Z\n,) acting on (1:10,) is not FLO",
     "output_type": "error",
     "traceback": [
      "NonFLOException: (nqubits: 10\n",
      "[-] kron\n",
      "   └─ 1:10=>[-] kron\n",
      "         └─ 1=>Z\n",
      ",) acting on (1:10,) is not FLO\n",
      "\n",
      "Stacktrace:\n",
      " [1] kron2majoranaindices(k::KronBlock{2, 1, Tuple{Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{Scale{Val{-1}, 2, KronBlock{2, 1, Tuple{ZGate}}}}}}}})\n",
      "   @ FLOYao ~/.julia/packages/FLOYao/EsxyP/src/utils.jl:218\n",
      " [2] top-level scope\n",
      "   @ ~/Desktop/Desktop - Peter’s MacBook Air/Harvard/2.5/PRISE/Project/MatchgateGAN/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_Y122sZmlsZQ==.jl:9"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "blk = kron(-kron(-kron(nq,1=>Z)))\n",
    "locs = collect(Iterators.flatten(blk.locs))\n",
    "perm = sortperm(locs)\n",
    "println(blk.blocks[1] |> typeof)\n",
    "println(perm)\n",
    "println(blk |> typeof)\n",
    "FLOYao.kron2majoranaindices(blk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "ename": "FLOYao.NonFLOException",
     "evalue": "NonFLOException: ([-] Z,) acting on (1:1,) is not FLO",
     "output_type": "error",
     "traceback": [
      "NonFLOException: ([-] Z,) acting on (1:1,) is not FLO\n",
      "\n",
      "Stacktrace:\n",
      " [1] kron2majoranaindices(k::KronBlock{2, 1, Tuple{Scale{Int64, 2, ZGate}}})\n",
      "   @ FLOYao ~/.julia/packages/FLOYao/EsxyP/src/utils.jl:218\n",
      " [2] top-level scope\n",
      "   @ ~/Desktop/Desktop - Peter’s MacBook Air/Harvard/2.5/PRISE/Project/MatchgateGAN/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_Y121sZmlsZQ==.jl:41"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao, LinearAlgebra\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    #it's fine, this outputs an Add object now so i can pass it through expect'\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = 1\n",
    "        push!(p, first => -Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= 1\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= -1\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "blk = kron(majoranaindices2kron(4,1,2))\n",
    "blk\n",
    "FLOYao.kron2majoranaindices(blk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of parameters: 56\n",
      "measured outcome: 1011000001 ₍₂₎\n",
      "probability of measuring the above outcome: 0.002515503462413642488555028511800403689413551674951671089462360038403364608074197\n",
      "iteration 2 : 27250.051498413086\n"
     ]
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "using Yao, FLOYao\n",
    "using LinearAlgebra\n",
    "\n",
    "N = 10\n",
    "\n",
    "nq = 10\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.))\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function huh!(b, temp_m, probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = N\n",
    "    dim = 2*nq\n",
    "    for i in 2:nq\n",
    "        i1 = 2*(i-1)\n",
    "        ni = b[i-1]\n",
    "        cur_prob = probabilities[i-1]\n",
    "        cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "        for p in 2*(i-1)+1:dim\n",
    "            for q in p+1:dim\n",
    "                temp_m[p,q] -= cur_prefactor * (temp_m[i1-1,p] * temp_m[i1,q])\n",
    "                temp_m[p,q] += cur_prefactor * (temp_m[i1-1,q] * temp_m[i1,p])\n",
    "            end\n",
    "        end\n",
    "        ni = b[i]\n",
    "        probabilities[i] = (1+(-1)^ni * temp_m[i1+1, i1+2]) / 2\n",
    "    end\n",
    "end\n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:2\n",
    "        if i > 1\n",
    "            t = time()\n",
    "            huh!(b, temp_m, probabilities)\n",
    "            diff = (time() - t) * 10^6\n",
    "            println(\"iteration $i : $diff\")\n",
    "        else\n",
    "            i1 = 0\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[i1+1, i1+2]) / 2\n",
    "        end\n",
    "        # diff = (time() - t) * 10^6\n",
    "        # t_tot += diff\n",
    "        # println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    # println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "bitstr = rand(Bool, N)\n",
    "prob = Vector{Float64}(undef, N)\n",
    "prob[1] = rand() #JUST TESTING huh!, this represents the probabilities vector, not the params of g\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "println(\"number of parameters: \", nparameters(g))\n",
    "reg = FLOYao.zero_state(nq) |> g\n",
    "results = measure(reg, nshots = 1)\n",
    "bitstr = results[1]\n",
    "println(\"measured outcome: $bitstr\")\n",
    "println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr))\n",
    "\n",
    "dim = 2*nq\n",
    "temp_m = Matrix{Float64}(undef, dim, dim)\n",
    "probabilities = Vector{Float64}(undef, nq)\n",
    "# prob(FLOYao.zero_state(nq), p, bitstr, temp_m, probabilities)\n",
    "# update_opt!(FLOYao.zero_state(nq), p, bitstr, temp_m, probabilities)\n",
    "# @benchmark huh!(bitstr, rand(dim, dim), prob) #800 microsec\n",
    "# update_opt!(FLOYao.zero_state(N), p, bitstr, temp_m, probabilities)\n",
    "update_opt!(FLOYao.zero_state(N), p, bitstr, temp_m, probabilities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of parameters: 56\n",
    "# measured outcome: 1010101101 ₍₂₎\n",
    "# probability of measuring the above outcome: 0.002360660013418328876523065726568606080691889830618951769765871877112546743484876\n",
    "# iteration 1: 8805.990219116211\n",
    "# iteration 2: 22840.023040771484\n",
    "# total time: 31646.013259887695"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m229.125 μs\u001b[22m\u001b[39m … \u001b[35m  5.128 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 94.39%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m233.125 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m243.442 μs\u001b[22m\u001b[39m ± \u001b[32m121.536 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m2.53% ±  4.84%\n",
       "\n",
       "  \u001b[39m▂\u001b[39m▂\u001b[39m \u001b[39m▇\u001b[39m█\u001b[34m▅\u001b[39m\u001b[39m▄\u001b[39m▅\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[32m▃\u001b[39m\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▄\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▅\u001b[39m▂\u001b[39m▄\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▂\u001b[39m▅\u001b[39m \u001b[39m█\n",
       "  229 μs\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m        279 μs \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m137.16 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m8064\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "\n",
    "a = rand(20, 20)\n",
    "\n",
    "function gg(i, a)\n",
    "    i1 = 2*(i-1)\n",
    "    cur_prefactor = -1/(2*rand())\n",
    "    for p in 2*(i-1)+1:dim\n",
    "        for q in p+1:dim\n",
    "            a[p,q] -= cur_prefactor * (a[i1-1,p] * a[i1,q])\n",
    "            a[p,q] += cur_prefactor * (a[i1-1,q] * a[i1,p])\n",
    "        end\n",
    "    end\n",
    "    return a\n",
    "end\n",
    "\n",
    "function ggg(a)\n",
    "    for i in 2:10\n",
    "        gg(i, a)\n",
    "    end\n",
    "    return a\n",
    "end\n",
    "\n",
    "@benchmark ggg(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of parameters: 56\n",
      "measured outcome: 1000000001 ₍₂₎\n",
      "probability of measuring the above outcome: 0.01045388618801599602654681368141880519085148814234172450423362156621319723598039\n",
      "type: Float64\n",
      "iteration 1: 281584.0244293213\n",
      "iteration 2: 355.9589385986328\n",
      "iteration 3: 195.98007202148438\n",
      "iteration 4: 150.91896057128906\n",
      "iteration 5: 109.91096496582031\n",
      "iteration 6: 74.86343383789062\n",
      "iteration 7: 46.96846008300781\n",
      "iteration 8: 27.179718017578125\n",
      "iteration 9: 12.874603271484375\n",
      "iteration 10: 3.814697265625\n",
      "total time: 282562.4942779541\n"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao, BenchmarkTools, LinearAlgebra\n",
    "\n",
    "nq = 10\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.))\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        i1 = 2*(i-1)\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            ni = b[i-1]\n",
    "            cur_prob = probabilities[i-1]\n",
    "            cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "            t = time()\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= cur_prefactor * (temp_m[i1-1,p] * temp_m[i1,q])\n",
    "                    temp_m[p,q] += cur_prefactor * (temp_m[i1-1,q] * temp_m[i1,p])\n",
    "                end\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[i1+1, i1+2]) / 2\n",
    "        else\n",
    "            t = time()\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[i1+1, i1+2]) / 2\n",
    "        end\n",
    "        diff = (time() - t) * 10^6\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function prob(reg::MajoranaReg, theta, b, temp_m, probabilities)\n",
    "    nq = nqubits(reg)\n",
    "    update_opt!(reg, theta, b, temp_m, probabilities)\n",
    "    return prod(probabilities)\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "println(\"number of parameters: \", nparameters(g))\n",
    "reg = FLOYao.zero_state(nq) |> g\n",
    "results = measure(reg, nshots = iters)\n",
    "bitstr = results[1]\n",
    "println(\"measured outcome: $bitstr\")\n",
    "println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr))\n",
    "T = Float64\n",
    "\n",
    "println(\"type: $T\")\n",
    "dim = 2*nq\n",
    "temp_m = Matrix{T}(undef, dim, dim)\n",
    "probabilities = Vector{T}(undef, nq)\n",
    "# prob(FLOYao.zero_state(nq), p, bitstr, temp_m, probabilities)\n",
    "update_opt!(FLOYao.zero_state(nq), p, bitstr, temp_m, probabilities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 10 evaluations.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m1.371 μs\u001b[22m\u001b[39m … \u001b[35m191.071 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 96.29%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m1.462 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m1.705 μs\u001b[22m\u001b[39m ± \u001b[32m  4.409 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m8.04% ±  3.18%\n",
       "\n",
       "  \u001b[39m▃\u001b[39m█\u001b[39m█\u001b[34m▇\u001b[39m\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▄\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▅\u001b[39m▄\u001b[39m▅\u001b[39m▄\u001b[39m▅\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m \u001b[39m█\n",
       "  1.37 μs\u001b[90m      \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m      3.24 μs \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m5.00 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m19\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "\n",
    "N = 56\n",
    "c = rand()\n",
    "a = rand(5)\n",
    "b = rand(N)\n",
    "d = rand(N)\n",
    "e = rand(N)\n",
    "print(a)\n",
    "@benchmark $c * ((-b * a[2] * a[3]) .+ (a[4] * (d * a[3] .+ a[2] * e)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 883 evaluations.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m130.144 ns\u001b[22m\u001b[39m … \u001b[35m 10.812 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m133.069 ns               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m140.220 ns\u001b[22m\u001b[39m ± \u001b[32m160.660 ns\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m1.16% ± 2.98%\n",
       "\n",
       "  \u001b[39m▂\u001b[39m▁\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[34m▇\u001b[39m\u001b[39m▅\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[32m▂\u001b[39m\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▇\u001b[39m▆\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m \u001b[39m█\n",
       "  130 ns\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m        166 ns \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m64 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m4\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cur_prefactor = (-1)^ni / (2*rand())\n",
    "temp_m = rand(30,30)\n",
    "@benchmark cur_prefactor * (temp_m[18,21] * temp_m[19,20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 10\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    #it's fine, this outputs an Add object now so i can pass it through expect'\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return im*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end \n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK WELL...)\n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            ni = b[i-1]\n",
    "            cur_prob = probabilities[i-1]\n",
    "            cur_grad_prob = grad_probabilities[:, i-1]\n",
    "            cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "            cur_grad_prefactor = cur_prefactor / cur_prob\n",
    "            i1 = 2*(i-1)-1\n",
    "            i2 = i1+1\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    record = (p == dim - 1) && (q == dim)\n",
    "                    if record\n",
    "                        tt = time()\n",
    "                    end\n",
    "                    k1 = temp_m[i1,p]\n",
    "                    k2 = temp_m[i2,q]\n",
    "                    k3 = temp_m[i1,q]\n",
    "                    k4 = temp_m[i2,p]\n",
    "                    v1 = temp_grad_m[:,i1,p]\n",
    "                    v2 = temp_grad_m[:,i2,q]\n",
    "                    v3 = temp_grad_m[:,i1,q]\n",
    "                    v4 = temp_grad_m[:,i2,p]\n",
    "                    if record\n",
    "                        diff = time() - tt\n",
    "                        # println(\"memory access time: $diff\")\n",
    "                        tt = time()\n",
    "                    end\n",
    "                    temp_grad_m[:,p,q] .-= cur_grad_prefactor * ((cur_grad_prob * k1 * k2) .+ (cur_prob * (v1 * k2 .+ k1 * v2)))\n",
    "                    temp_grad_m[:,p,q] .+= cur_grad_prefactor * ((cur_grad_prob * k3 * k4) .+ (cur_prob * (v3 * k4 .+ k3 * v4)))\n",
    "                    if record\n",
    "                        diff = time() - tt\n",
    "                        # println(\"calculation time: $diff\")\n",
    "                    end   \n",
    "                end\n",
    "            end\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= cur_prefactor * (temp_m[i1,p] * temp_m[i2,q]) \n",
    "                    temp_m[p,q] += cur_prefactor * (temp_m[i1,q] * temp_m[i2,p])\n",
    "                end\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[:,p,q] = expect'(ham, reg => g)[2]\n",
    "                end\n",
    "            end\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        end\n",
    "        diff = time() - t\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function log_grad_opt(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    nq = nqubits(reg)\n",
    "    update_opt!(reg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[:, i] / probabilities[i]\n",
    "    end\n",
    "    optimized_prob = probabilities\n",
    "    return optimized_prob, s\n",
    "end\n",
    "\n",
    "# iters = 1\n",
    "# p = rand(nparameters(g)).*2π\n",
    "# dispatch!(g, p)\n",
    "# reg = FLOYao.zero_state(nq) |> g\n",
    "# results = measure(reg, nshots = iters)\n",
    "# bitstr = results[1]\n",
    "# println(\"measured outcome: $bitstr\")\n",
    "# println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr))\n",
    "\n",
    "T = Float64\n",
    "println(\"type: $T\")\n",
    "temp_m = Matrix{T}(undef, dim, dim)\n",
    "temp_grad_m = Array{T}(undef, nparams, dim, dim)\n",
    "probabilities = Vector{T}(undef, nq)\n",
    "grad_probabilities = Matrix{T}(undef, nparams, nq)\n",
    "optimized_prob, optimized = log_grad_opt(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "optimized;\n",
    "println(\"probabilities equal? \", basic_prob == optimized_prob)\n",
    "println(\"grad(log p) equal? \", basic == optimized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using SparseArrays\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 3\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -2*im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return -2*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK)\n",
    "\n",
    "function update!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    for i in 1:nq\n",
    "        ni = b[i]\n",
    "        if stored > 0\n",
    "            cur_m = temp_m\n",
    "            cur_grad_m = temp_grad_m\n",
    "            cur_prob = probabilities[i]\n",
    "            cur_grad_prob = grad_probabilities[i, :]\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= (-1)^ni * (cur_m[2*i-1,p] * cur_m[2*i,q]) / (2*cur_prob)\n",
    "                    temp_m[p,q] += (-1)^ni * (cur_m[2*i-1,q] * cur_m[2*i,p]) / (2*cur_prob)\n",
    "                    temp_m[q,p] = -temp_m[p,q]\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_m[p,p] = 0.0 #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[p,q] .-= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,p] * cur_m[2*i,q]) .+ (cur_prob * (cur_grad_m[2*i-1,p]*cur_m[2*i,q] .+ cur_m[2*i-1,p] * cur_grad_m[2*i,q]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[p,q] .+= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,q] * cur_m[2*i,p]) .+ (cur_prob * (cur_grad_m[2*i-1,q]*cur_m[2*i,p] .+ cur_m[2*i-1,q] * cur_grad_m[2*i,p]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q) + 0*kron(nq, 1 => Z) #Need to do the commutator, not just γ_iγ_j... (whatever, fix this later)\n",
    "                    #Adding the 0*kron(nq, 1 => Z) just turns it into something that i can pass into expect'\n",
    "                    temp_grad_m[p,q] = expect'(ham, reg => g)[2]\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "function log_grad(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Returns ∇_θlog(p_theta(X)), evaluated at theta (parameters of circuit) and b (measurement result); reg is the initial register (e.g. FLOYao.zero_state(nq))\n",
    "    nq = nqubits(reg)\n",
    "    update!(reg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[i, :] / probabilities[i]\n",
    "    end\n",
    "    return s\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "results = measure(FLOYao.zero_state(nq) |> g, nshots = iters)\n",
    "bitstr = results[1]\n",
    "\n",
    "# FLOYao.bitstring_probability(FLOYao.zero_state(nq) |> g, bitstr)\n",
    "temp_m = Matrix{BigFloat}(undef, dim, dim)\n",
    "temp_grad_m = Matrix{Vector{BigFloat}}(undef, dim, dim)\n",
    "cur_m = Matrix{BigFloat}(undef, dim, dim)\n",
    "cur_grad_m = Matrix{Vector{BigFloat}}(undef, dim, dim)\n",
    "probabilities = Vector{BigFloat}(undef, nq)\n",
    "grad_probabilities = Matrix{BigFloat}(undef, nq, nparams)\n",
    "log_grad(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.196152422706632"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using SparseArrays\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "using Printf\n",
    "\n",
    "nq = 10\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    #it's fine, this outputs an Add object now so i can pass it through expect'\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return im*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "function print_matrix(A)\n",
    "    for i in 1:size(A, 1)\n",
    "        for j in 1:size(A, 2)\n",
    "            @printf(\"%6.2f \", A[i, j])  # Prints each element with 4 decimal places, padded to 6 characters\n",
    "        end\n",
    "        println()  # Move to the next line after each row\n",
    "    end\n",
    "end\n",
    "\n",
    "function print_vec_matrix(A)\n",
    "    for i in 1:size(A, 1)\n",
    "        for j in 1:size(A, 2)\n",
    "            for element in A[i, j]\n",
    "                @printf(\"%.2f \", element)\n",
    "            end\n",
    "            println()\n",
    "        end\n",
    "        println()\n",
    "    end\n",
    "end\n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK WELL...)\n",
    "\n",
    "function update!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            cur_m = deepcopy(temp_m)\n",
    "            cur_grad_m = deepcopy(temp_grad_m)\n",
    "            cur_prob = deepcopy(probabilities[i-1])\n",
    "            cur_grad_prob = deepcopy(grad_probabilities[i-1, :])\n",
    "            ni = b[i-1]\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[p,q] .-= (-1)^ni * ((-cur_grad_prob * cur_m[2*(i-1)-1,p] * cur_m[2*(i-1),q]) .+ (cur_prob * (cur_grad_m[2*(i-1)-1,p]*cur_m[2*(i-1),q] .+ cur_m[2*(i-1)-1,p] * cur_grad_m[2*(i-1),q]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[p,q] .+= (-1)^ni * ((-cur_grad_prob * cur_m[2*(i-1)-1,q] * cur_m[2*(i-1),p]) .+ (cur_prob * (cur_grad_m[2*(i-1)-1,q]*cur_m[2*(i-1),p] .+ cur_m[2*(i-1)-1,q] * cur_grad_m[2*(i-1),p]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                    # println(\"$p $q\")\n",
    "                    # println(temp_grad_m[p,q])\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= (-1)^ni * (cur_m[2*(i-1)-1,p] * cur_m[2*(i-1),q]) / (2*cur_prob)\n",
    "                    temp_m[p,q] += (-1)^ni * (cur_m[2*(i-1)-1,q] * cur_m[2*(i-1),p]) / (2*cur_prob)\n",
    "                    temp_m[q,p] = -temp_m[p,q]\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_m[p,p] = 0.0 #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[p,q] = expect'(ham, reg => g)[2]\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        end\n",
    "        diff = time() - t\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end \n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            ni = b[i-1]\n",
    "            cur_prob = probabilities[i-1]\n",
    "            cur_grad_prob = grad_probabilities[:, i-1]\n",
    "            cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "            cur_grad_prefactor = (-1)^ni / (2*cur_prob^2)\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[:,p,q] .-= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,p]*temp_m[2*(i-1),q] .+ temp_m[2*(i-1)-1,p] * temp_grad_m[:,2*(i-1),q])))\n",
    "                    temp_grad_m[:,p,q] .+= cur_grad_prefactor * ((-cur_grad_prob * temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,q]*temp_m[2*(i-1),p] .+ temp_m[2*(i-1)-1,q] * temp_grad_m[:,2*(i-1),p])))\n",
    "                end\n",
    "            end\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= cur_prefactor * (temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q])\n",
    "                    temp_m[p,q] += cur_prefactor * (temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p])\n",
    "                end\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[:,p,q] = expect'(ham, reg => g)[2]\n",
    "                end\n",
    "            end\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        end\n",
    "        diff = time() - t\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function log_grad(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Returns ∇_θlog(p_theta(X)), evaluated at theta (parameters of circuit) and b (measurement result); reg is the initial register (e.g. FLOYao.zero_state(nq))\n",
    "    nq = nqubits(reg)\n",
    "    update!(reg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[i, :] / probabilities[i]\n",
    "    end\n",
    "    # print_matrix(grad_probabilities)\n",
    "    # println(probabilities)\n",
    "    # println(prod(probabilities), \" should match first number\")\n",
    "    basic_prob = probabilities\n",
    "    return basic_prob, s\n",
    "end\n",
    "\n",
    "function log_grad_opt(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    nq = nqubits(reg)\n",
    "    update_opt!(reg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[:, i] / probabilities[i]\n",
    "    end\n",
    "    # print_matrix(grad_probabilities)\n",
    "    # println(probabilities)\n",
    "    # println(prod(probabilities), \" should match first number\")\n",
    "    optimized_prob = probabilities\n",
    "    return optimized_prob, s\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "println(\"number of parameters: \", nparameters(g))\n",
    "reg = FLOYao.zero_state(nq) |> g\n",
    "results = measure(reg, nshots = iters)\n",
    "bitstr = results[1]\n",
    "println(\"measured outcome: $bitstr\")\n",
    "println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr))\n",
    "\n",
    "T = Float64\n",
    "println(\"type: $T\")\n",
    "temp_m = Matrix{T}(undef, dim, dim)\n",
    "temp_grad_m = Matrix{Vector{T}}(undef, dim, dim)\n",
    "cur_m = Matrix{T}(undef, dim, dim)\n",
    "cur_grad_m = Matrix{Vector{T}}(undef, dim, dim)\n",
    "probabilities = Vector{T}(undef, nq)\n",
    "grad_probabilities = Matrix{T}(undef, nq, nparams)\n",
    "basic_prob, basic = log_grad(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "basic;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5838855120869042\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "probabilities = rand(20)\n",
    "println(probabilities[18])\n",
    "i = 18\n",
    "ni = 1\n",
    "cur_prob = probabilities[i-1]\n",
    "cur_prefactor = (-1)^ni / (2*cur_prob)\n",
    "cur_grad_prefactor = cur_prefactor / cur_prob\n",
    "cur_prefactor / cur_prob == (-1)^ni / (2*cur_prob^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "measured outcome: 1100000101 ₍₂₎\n",
      "probability of measuring the above outcome: 0.0008600164105701754434095443385810866294273352652446426503674724845482649699819314\n",
      "iteration 1: 0.09096598625183105\n",
      "iteration 2: 0.03353309631347656\n",
      "iteration 3: 0.023656129837036133\n",
      "iteration 4: 0.01830291748046875\n",
      "iteration 5: 0.014895200729370117\n",
      "iteration 6: 0.022277116775512695\n",
      "iteration 7: 0.005960941314697266\n",
      "iteration 8: 0.003259897232055664\n",
      "iteration 9: 0.0012691020965576172\n",
      "iteration 10: 0.00022101402282714844\n",
      "total time: 0.214341402053833\n"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 30\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    #it's fine, this outputs an Add object now so i can pass it through expect'\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return im*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end \n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK WELL...)\n",
    "\n",
    "function update_opt!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place and optimally\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        if i > 1\n",
    "            ni = b[i-1]\n",
    "            cur_prob = probabilities[i-1]\n",
    "            cur_grad_prob = grad_probabilities[:, i-1]\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[:,p,q] .-= (-1)^ni * ((cur_grad_prob * temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,p]*temp_m[2*(i-1),q] .+ temp_m[2*(i-1)-1,p] * temp_grad_m[:,2*(i-1),q]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[:,p,q] .+= (-1)^ni * ((cur_grad_prob * temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p]) .+ (cur_prob * (temp_grad_m[:,2*(i-1)-1,q]*temp_m[2*(i-1),p] .+ temp_m[2*(i-1)-1,q] * temp_grad_m[:,2*(i-1),p]))) / (2*cur_prob^2)\n",
    "                end\n",
    "            end\n",
    "            for p in 2*(i-1)+1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= (-1)^ni * (temp_m[2*(i-1)-1,p] * temp_m[2*(i-1),q]) / (2*cur_prob)\n",
    "                    temp_m[p,q] += (-1)^ni * (temp_m[2*(i-1)-1,q] * temp_m[2*(i-1),p]) / (2*cur_prob)\n",
    "                end\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[:,p,q] = expect'(ham, reg => g)[2]\n",
    "                end\n",
    "            end\n",
    "            grad_probabilities[:, i] = (-1)^ni * temp_grad_m[:,2*i-1, 2*i] / 2\n",
    "        end\n",
    "        diff = time() - t\n",
    "        t_tot += diff\n",
    "        println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function log_grad_opt(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    nq = nqubits(reg)\n",
    "    update_opt!(reg, theta, b, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[:, i] / probabilities[i]\n",
    "    end\n",
    "    optimized_prob = probabilities\n",
    "    return optimized_prob, s\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "reg = FLOYao.zero_state(nq) |> g\n",
    "results = measure(reg, nshots = iters)\n",
    "bitstr = results[1]\n",
    "println(\"measured outcome: $bitstr\")\n",
    "println(\"probability of measuring the above outcome: \", FLOYao.bitstring_probability(reg, bitstr))\n",
    "\n",
    "temp_m = Matrix{BigFloat}(undef, dim, dim)\n",
    "temp_grad_m = Array{BigFloat}(undef, nparams, dim, dim)\n",
    "probabilities = Vector{BigFloat}(undef, nq)\n",
    "grad_probabilities = Matrix{BigFloat}(undef, nparams, nq)\n",
    "optimized_prob, optimized = log_grad_opt(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, probabilities, grad_probabilities)\n",
    "optimized;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m19.583 μs\u001b[22m\u001b[39m … \u001b[35m 34.250 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m19.709 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m19.882 μs\u001b[22m\u001b[39m ± \u001b[32m646.105 ns\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m0.00% ± 0.00%\n",
       "\n",
       "  \u001b[39m \u001b[39m▂\u001b[39m \u001b[39m▆\u001b[39m█\u001b[34m \u001b[39m\u001b[39m▇\u001b[39m \u001b[39m▅\u001b[39m▃\u001b[39m \u001b[39m▁\u001b[32m \u001b[39m\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m▂\u001b[39m▂\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\u001b[39m \u001b[39m▃\u001b[39m \u001b[39m▃\u001b[39m▂\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▂\n",
       "  \u001b[39m▅\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[34m▁\u001b[39m\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[32m▇\u001b[39m\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▆\u001b[39m▁\u001b[39m▅\u001b[39m▇\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▇\u001b[39m▇\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▆\u001b[39m▆\u001b[39m▁\u001b[39m▅\u001b[39m▅\u001b[39m▁\u001b[39m▆\u001b[39m▁\u001b[39m▆\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m█\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▇\u001b[39m▅\u001b[39m▁\u001b[39m▅\u001b[39m▄\u001b[39m \u001b[39m█\n",
       "  19.6 μs\u001b[90m       \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m      21.1 μs \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m16 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m1\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "\n",
    "function ff(x)\n",
    "    for _ in 1:10\n",
    "        sum(rand(10^4))\n",
    "    end\n",
    "    return sum(x)\n",
    "end\n",
    "\n",
    "function fff(x)\n",
    "    y = zeros(10^4,10)\n",
    "    for i in 1:10\n",
    "        y[:,i] = rand(10^4)\n",
    "        sum(y[:,i])\n",
    "    end\n",
    "    return sum(x), y\n",
    "end\n",
    "\n",
    "a = rand(10^5)\n",
    "\n",
    "@benchmark sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m136.250 μs\u001b[22m\u001b[39m … \u001b[35m  1.503 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m 0.00% …  0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m141.417 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m159.479 μs\u001b[22m\u001b[39m ± \u001b[32m124.586 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m10.07% ± 11.09%\n",
       "\n",
       "  \u001b[34m█\u001b[39m\u001b[39m▂\u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\n",
       "  \u001b[34m█\u001b[39m\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m▇\u001b[39m▆\u001b[39m▄\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▄\u001b[39m▇\u001b[39m█\u001b[39m \u001b[39m█\n",
       "  136 μs\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m       1.07 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m781.73 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m21\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@benchmark ff(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 10000 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m280.791 μs\u001b[22m\u001b[39m … \u001b[35m  4.650 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m 0.00% … 86.33%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m300.875 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m353.778 μs\u001b[22m\u001b[39m ± \u001b[32m221.630 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m13.82% ± 16.44%\n",
       "\n",
       "  \u001b[39m▆\u001b[34m█\u001b[39m\u001b[39m▄\u001b[39m▁\u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\n",
       "  \u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m▇\u001b[39m▅\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▅\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▁\u001b[39m▄\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▅\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m \u001b[39m█\n",
       "  281 μs\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m       1.29 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m2.29 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m43\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@benchmark fff(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mModule FlameGraphs with build ID fafbfcfd-60b1-2413-0000-0dcdd208d827 is missing from the cache.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis may mean FlameGraphs [08572546-2f56-4bcf-ba4e-bab62c3a3f89] does not support precompilation but is imported by a module that does.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ Base loading.jl:1793\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\"profile.pb.gz\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function profile_test(n)\n",
    "    for i = 1:n\n",
    "        A = randn(100,100,20)\n",
    "        m = maximum(A)\n",
    "        Am = mapslices(sum, A; dims=2)\n",
    "        B = A[:,:,5]\n",
    "        Bsort = mapslices(sort, B; dims=1)\n",
    "        b = rand(100)\n",
    "        C = B.*b\n",
    "    end\n",
    "end\n",
    "\n",
    "using Profile\n",
    "using PProf\n",
    "\n",
    "# Collect a profile\n",
    "Profile.clear()\n",
    "@profile profile_test(10)\n",
    "\n",
    "# Export pprof profile and open interactive profiling web interface.\n",
    "pprof()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2][3, 4][1 3; 2 4;;; 5 7; 6 8]"
     ]
    },
    {
     "data": {
      "text/plain": [
       "8-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6\n",
       " 7\n",
       " 8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = [1 2; 3 4]\n",
    "m = reshape(1:8, 2, 2, 2)\n",
    "print(m[:,1,1])\n",
    "print(m[:,2,1])\n",
    "print(m)\n",
    "m[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is thread 1 doing iteration 37500000\n",
      "This is thread 1 doing iteration 75000000\n",
      "This is thread 1 doing iteration 112500000\n",
      "This is thread 1 doing iteration 150000000\n",
      "This is thread 1 doing iteration 187500000\n",
      "This is thread 1 doing iteration 225000000\n",
      "This is thread 1 doing iteration 262500000\n",
      "This is thread 1 doing iteration 300000000\n",
      "time elapsed: 30.819150924682617\n"
     ]
    }
   ],
   "source": [
    "t = time()\n",
    "n = 3*10^8\n",
    "for i in 1:n\n",
    "    if i % (n ÷ 8) == 0\n",
    "        println(\"This is thread \", threadid(), \" doing iteration \", i)\n",
    "    end\n",
    "end\n",
    "diff = time() - t\n",
    "println(\"time elapsed: $diff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of threads: 4\n",
      "This is thread 1 doing iteration 37500000\n",
      "This is thread 2 doing iteration 187500000\n",
      "This is thread 3 doing iteration 112500000\n",
      "This is thread 4 doing iteration 262500000\n",
      "This is thread 1 doing iteration 75000000\n",
      "This is thread 3 doing iteration 150000000\n",
      "This is thread 2 doing iteration 225000000\n",
      "This is thread 4 doing iteration 300000000\n",
      "time elapsed: 6.341549873352051\n"
     ]
    }
   ],
   "source": [
    "using Base.Threads\n",
    "\n",
    "println(\"Number of threads: \", nthreads())\n",
    "\n",
    "t = time()\n",
    "@threads for i in 1:n\n",
    "    if i % (n ÷ 8) == 0\n",
    "        println(\"This is thread \", threadid(), \" doing iteration \", i)\n",
    "    end\n",
    "end\n",
    "diff = time() - t\n",
    "println(\"time elapsed: $diff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Base.Threads\n",
    "using BenchmarkTools\n",
    "\n",
    "function regular_sum(A)\n",
    "    sum = 0.0\n",
    "    for i in 1:length(A)\n",
    "        sum += A[i]\n",
    "    end\n",
    "    return sum\n",
    "end\n",
    "\n",
    "function parallel_sum(A)\n",
    "    n = length(A)\n",
    "    partial_sums = zeros(Float64, nthreads())\n",
    "    \n",
    "    @threads for i in 1:n\n",
    "        tid = threadid()\n",
    "        partial_sums[tid] += A[i]\n",
    "    end\n",
    "    \n",
    "    return sum(partial_sums)\n",
    "end\n",
    "\n",
    "A = rand(10^9)\n",
    "# @benchmark regular_sum(A)\n",
    "@benchmark parallel_sum(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 9 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m307.800 ms\u001b[22m\u001b[39m … \u001b[35m   1.447 s\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m645.727 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m665.546 ms\u001b[22m\u001b[39m ± \u001b[32m361.933 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m0.00% ± 0.00%\n",
       "\n",
       "  \u001b[39m█\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[34m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m▃\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[34m▇\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[32m▁\u001b[39m\u001b[39m▁\u001b[39m▁\u001b[39m█\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▇\u001b[39m \u001b[39m▁\n",
       "  308 ms\u001b[90m           Histogram: frequency by time\u001b[39m          1.45 s \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m16 bytes\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m1\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@benchmark regular_sum(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 4475 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m863.417 μs\u001b[22m\u001b[39m … \u001b[35m 27.409 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m931.459 μs               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m  1.100 ms\u001b[22m\u001b[39m ± \u001b[32m700.282 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m0.00% ± 0.00%\n",
       "\n",
       "  \u001b[39m▇\u001b[39m█\u001b[34m▅\u001b[39m\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[32m▃\u001b[39m\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\n",
       "  \u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▇\u001b[39m▆\u001b[39m▅\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▃\u001b[39m▅\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▅\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▁\u001b[39m▁\u001b[39m▅\u001b[39m▁\u001b[39m▁\u001b[39m▃\u001b[39m▄\u001b[39m \u001b[39m█\n",
       "  863 μs\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m       3.24 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m15.88 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m2\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Base.Threads\n",
    "using BenchmarkTools\n",
    "using Distributions\n",
    "\n",
    "function transform_matrix!(M, n)\n",
    "    row_n = M[n, :]\n",
    "    col_n = M[:, n]\n",
    "    \n",
    "    for i in 1:size(M, 1)\n",
    "        for j in 1:size(M, 2)\n",
    "            M[i, j] += row_n[j] + col_n[i]\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "function parallel_transform_matrix!(M, n)\n",
    "    row_n = M[n, :]\n",
    "    col_n = M[:, n]\n",
    "    \n",
    "    @threads for i in 1:size(M, 1)\n",
    "        for j in 1:size(M, 2)\n",
    "            M[i, j] += row_n[j] + col_n[i]\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "dim = 1000\n",
    "A = rand(Uniform(0,1), dim, dim)\n",
    "n = dim ÷ 2\n",
    "@benchmark transform_matrix!(A, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 2900 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m977.209 μs\u001b[22m\u001b[39m … \u001b[35m46.790 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 94.75%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m  1.255 ms              \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m  1.708 ms\u001b[22m\u001b[39m ± \u001b[32m 1.647 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m0.90% ±  1.76%\n",
       "\n",
       "  \u001b[39m█\u001b[39m▇\u001b[39m▅\u001b[34m▅\u001b[39m\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[32m▄\u001b[39m\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m \u001b[39m▁\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\n",
       "  \u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[32m█\u001b[39m\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m▇\u001b[39m▇\u001b[39m█\u001b[39m▇\u001b[39m▆\u001b[39m▇\u001b[39m▆\u001b[39m▅\u001b[39m▇\u001b[39m▇\u001b[39m▇\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[39m▇\u001b[39m▇\u001b[39m▅\u001b[39m▇\u001b[39m▅\u001b[39m▆\u001b[39m▆\u001b[39m▆\u001b[39m▅\u001b[39m▅\u001b[39m▅\u001b[39m▆\u001b[39m▃\u001b[39m▆\u001b[39m▄\u001b[39m▅\u001b[39m▆\u001b[39m▅\u001b[39m▁\u001b[39m▃\u001b[39m▅\u001b[39m▃\u001b[39m▅\u001b[39m▅\u001b[39m▃\u001b[39m▃\u001b[39m \u001b[39m█\n",
       "  977 μs\u001b[90m        \u001b[39m\u001b[90mHistogram: \u001b[39m\u001b[90m\u001b[1mlog(\u001b[22m\u001b[39m\u001b[90mfrequency\u001b[39m\u001b[90m\u001b[1m)\u001b[22m\u001b[39m\u001b[90m by time\u001b[39m      6.97 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m16.47 KiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m9\u001b[39m."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@benchmark parallel_transform_matrix!(A, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1001 ₍₂₎\n",
      "iteration 1, 0.74194878215525361664361980729154311120510101318359375\n",
      "iteration 2, 0.632569880954036933840001211137860082089900970458984375\n",
      "iteration 3, 0.9351023893884866655668020030134357511997222900390625\n",
      "iteration 4, 1.00000000000000011102230246251565404236316680908203125\n",
      "0.438875768237433431072794760855837884662546541921789713092295479266449970316187\n"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "using Printf\n",
    "using LinearAlgebra\n",
    "\n",
    "function print_matrix(A)\n",
    "    for i in 1:size(A, 1)\n",
    "        for j in 1:size(A, 2)\n",
    "            @printf(\"%6.2f \", A[i, j])  # Prints each element with 4 decimal places, padded to 6 characters\n",
    "        end\n",
    "        println()  # Move to the next line after each row\n",
    "    end\n",
    "end\n",
    "\n",
    "nq = 4\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function update_covariance_matrix!(M, i, pi, ni)\n",
    "    n = size(M,1)\n",
    "    for p in 2i+1:n \n",
    "        for q in p+1:n\n",
    "            M[p,q] += (-1)^ni * M[2i-1,q] * M[2i,p] / (2pi)\n",
    "            M[p,q] -= (-1)^ni * M[2i-1,p] * M[2i,q] / (2pi)\n",
    "            print(\"$p $q\")\n",
    "        end\n",
    "    end\n",
    "    return M\n",
    "end \n",
    "\n",
    "function actual_update_covariance_matrix!(M, i, pi, ni)\n",
    "    n = size(M,1)\n",
    "    temp = copy(M)\n",
    "    for p in 1:n \n",
    "        for q in 1:n\n",
    "            M[p,q] += (-1)^ni * temp[2i-1,q] * temp[2i,p] / (2pi)\n",
    "            M[p,q] -= (-1)^ni * temp[2i-1,p] * temp[2i,q] / (2pi)\n",
    "        end\n",
    "    end\n",
    "    return M\n",
    "end \n",
    "\n",
    "function bitstring_probability(reg, bit_string)\n",
    "    p = one(BigFloat)\n",
    "    M = covariance_matrix(reg)\n",
    "    N = length(bit_string)\n",
    "    for i in 1:N\n",
    "        # print_matrix(M)\n",
    "        ni = bit_string[i]\n",
    "        pi = (1 + (-1)^ni * M[2i-1,2i]) / 2\n",
    "        println(\"iteration $i, $pi\")\n",
    "        pi ≈ 0 && return zero(T)\n",
    "        p *= pi\n",
    "        actual_update_covariance_matrix!(M, i, pi, ni)\n",
    "    end\n",
    "    return p > zero(BigFloat) ? p : zero(BigFloat) # floating point issues can cause very small probabilities to get negative.\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "r = FLOYao.zero_state(nq) |> g\n",
    "results = measure(r, nshots = iters)\n",
    "bitstr = results[1]\n",
    "println(bitstr)\n",
    "println(bitstring_probability(r, bitstr))\n",
    "# p = (1+(-1)^bitstr[1]*covariance_matrix(r)[1,2]) / 2\n",
    "# println(p)\n",
    "# M = covariance_matrix(r)\n",
    "# print_matrix(M)\n",
    "# println(M[3,4] + ((-1)^bitstr[1])*(M[1,4]*M[2,3]-M[1,3]*M[2,4])/(2*p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 1 sample with 1 evaluation.\n",
       " Single result which took \u001b[34m41.248 s\u001b[39m (14.57% GC) to evaluate,\n",
       " with a memory estimate of \u001b[33m21.78 GiB\u001b[39m, over \u001b[33m395081098\u001b[39m allocations."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using SparseArrays\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 30\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    #it's fine, this outputs an Add object now so i can pass it through expect'\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return c*kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return im*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK WELL...)\n",
    "\n",
    "function update!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    t_tot = 0\n",
    "    for i in 1:nq\n",
    "        t = time()\n",
    "        ni = b[i]\n",
    "        if i > 1\n",
    "            cur_m = copy(temp_m)\n",
    "            cur_grad_m = copy(temp_grad_m)\n",
    "            cur_prob = copy(probabilities[i-1])\n",
    "            cur_grad_prob = copy(grad_probabilities[i-1, :])\n",
    "            ni = b[i-1]\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= (-1)^ni * (cur_m[2*(i-1)-1,p] * cur_m[2*(i-1),q]) / (2*cur_prob)\n",
    "                    temp_m[p,q] += (-1)^ni * (cur_m[2*(i-1)-1,q] * cur_m[2*(i-1),p]) / (2*cur_prob)\n",
    "                    temp_m[q,p] = -temp_m[p,q]\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_m[p,p] = 0.0 #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            ni = b[i]\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[p,q] .-= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,p] * cur_m[2*i,q]) .+ (cur_prob * (cur_grad_m[2*i-1,p]*cur_m[2*i,q] .+ cur_m[2*i-1,p] * cur_grad_m[2*i,q]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[p,q] .+= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,q] * cur_m[2*i,p]) .+ (cur_prob * (cur_grad_m[2*i-1,q]*cur_m[2*i,p] .+ cur_m[2*i-1,q] * cur_grad_m[2*i,p]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        else\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q)\n",
    "                    temp_grad_m[p,q] = expect'(ham, reg => g)[2]\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        end\n",
    "        if probabilities[i] > 1\n",
    "            probabilities[i] = 1.0\n",
    "        elseif probabilities[i] < 0\n",
    "            probabilities[i] = 0.0\n",
    "        end\n",
    "        diff = time() - t\n",
    "        t_tot += diff\n",
    "        # println(\"iteration $i: $diff\")\n",
    "    end\n",
    "    # println(\"total time: $t_tot\")\n",
    "end\n",
    "\n",
    "function log_grad(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Returns ∇_θlog(p_theta(X)), evaluated at theta (parameters of circuit) and b (measurement result); reg is the initial register (e.g. FLOYao.zero_state(nq))\n",
    "    nq = nqubits(reg)\n",
    "    update!(reg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[i, :] / probabilities[i]\n",
    "    end\n",
    "    # println(probabilities)\n",
    "    # println(prod(probabilities), \" should match first number\")\n",
    "    # println(all(0 .<= probabilities .<= 1))\n",
    "    return s\n",
    "end\n",
    "\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "\n",
    "iters = 1\n",
    "r = FLOYao.zero_state(nq) |> g\n",
    "results = measure(r, nshots = iters)\n",
    "bitstr = results[1]\n",
    "# println(bitstr)\n",
    "# println(FLOYao.bitstring_probability(r, bitstr))\n",
    "\n",
    "temp_m = Matrix{BigFloat}(undef, dim, dim)\n",
    "temp_grad_m = Matrix{Vector{BigFloat}}(undef, dim, dim)\n",
    "cur_m = Matrix{BigFloat}(undef, dim, dim)\n",
    "cur_grad_m = Matrix{Vector{BigFloat}}(undef, dim, dim)\n",
    "probabilities = Vector{BigFloat}(undef, nq)\n",
    "grad_probabilities = Matrix{BigFloat}(undef, nq, nparams)\n",
    "@benchmark log_grad(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "X\n",
      "-1\n",
      "-1\n",
      "true\n",
      "2\n",
      "X\n",
      "2\n",
      "-1\n",
      "true\n",
      "true\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using FLOYao\n",
    "\n",
    "nq = 4\n",
    "p = [1 => X, 2 => X]\n",
    "k = kron(nq, p...)\n",
    "# print(typeof(k))\n",
    "# FLOYao.kron2majoranaindices(k)\n",
    "# these are the indices in the majorana hamiltonian corresponding to this\n",
    "# kronecker product. swap accumulates the overall sign\n",
    "locs = collect(Iterators.flatten(k.locs))\n",
    "perm = sortperm(locs)\n",
    "firstindex, secondindex, swap = -1, -1, true \n",
    "for q in perm\n",
    "    println(q)\n",
    "    op = k.blocks[q]\n",
    "    println(op)\n",
    "    println(firstindex)\n",
    "    println(secondindex)\n",
    "    if firstindex == -1\n",
    "        if op == X\n",
    "            firstindex = 2locs[q]\n",
    "        elseif op == Y\n",
    "            firstindex = 2locs[q] - 1\n",
    "        elseif op == Z\n",
    "            firstindex = 2locs[q]\n",
    "            secondindex = 2locs[q]-1\n",
    "        elseif op == I2\n",
    "        else\n",
    "            print(\"$(k.blocks) acting on $(k.locs) is not FLO\")\n",
    "        end\n",
    "    elseif secondindex == -1\n",
    "        if op == X\n",
    "            secondindex = 2locs[q] - 1\n",
    "            # @debug \"second operator is γ1 on site $(locs[q])\"\n",
    "        elseif op == Y\n",
    "            secondindex = 2locs[q]\n",
    "            swap = !swap\n",
    "            # @debug \"second operator is γ2 on site $(locs[q])\"\n",
    "        elseif op == Z\n",
    "            swap = !swap\n",
    "        elseif op == I2\n",
    "            # @debug \"nothing on site $(locs[q])\"\n",
    "        else\n",
    "            print(\"$(k.blocks) acting on $(k.locs) is not FLO\")\n",
    "        end\n",
    "    elseif op != I2\n",
    "        print(\"$(k.blocks) acting on $(k.locs) is not FLO\")\n",
    "    end\n",
    "    println(swap)\n",
    "end\n",
    "firstindex != -1 && secondindex != -1 || print(\"$(k.blocks) acting on $(k.locs) is not FLO\")\n",
    "# swap if we picked up a minus sign in total\n",
    "println(swap)\n",
    "swap ? (secondindex, firstindex) : (firstindex, secondindex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 1.0\n",
       " 1.0\n",
       " 1.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Zygote\n",
    "using LinearAlgebra\n",
    "\n",
    "function f(x)\n",
    "    return sum(x)\n",
    "end\n",
    "\n",
    "function h(theta, x)\n",
    "    ret = (sin(2*theta) * x - 1)^2\n",
    "    return ret\n",
    "end\n",
    "\n",
    "function repeath(theta, n, x)\n",
    "    if (n == 1)\n",
    "        return h(theta, x)\n",
    "    else\n",
    "        return repeath(theta, n - 1, h(theta, x))\n",
    "    end\n",
    "end\n",
    "\n",
    "t = [1,2,3]\n",
    "Zygote.gradient(x -> f(x), t)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DitStr{2, 5, Int64}[0, 1, 0, 1, 0]5"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([0.0, 1.0, 0.0, 1.0, 0.0],)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Zygote\n",
    "using Yao\n",
    "using LinearAlgebra\n",
    "\n",
    "b = bit\"01010\" #make this a bitstr object\n",
    "print(typeof(b))\n",
    "b = [b...]\n",
    "print(b)\n",
    "a = [1,2,3,4,5]\n",
    "print(length(a))\n",
    "\n",
    "function ff(x)\n",
    "    sum = 0\n",
    "    n = length(x)\n",
    "    for i in 1:n\n",
    "        sum += x[i] * b[i]\n",
    "    end\n",
    "    return sum\n",
    "end\n",
    "\n",
    "Zygote.gradient(x -> ff(x), a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92\n",
      "[1.5793757338085936, 6.249332543892758, 5.527986851173641, 4.2070395894464605, 2.4231212968342484, 4.119279077500202, 1.1181757056445791, 1.908639542962989, 5.4805588557388285, 3.9668594499604195, 1.2241803804567972, 0.6649423018263291, 0.15357507485946728, 4.5709674388302215, 6.04566326175118, 1.7011766876800039, 5.552643142108157, 2.8590401907955894, 0.2772101121435975, 2.737870422818485, 3.712274388143635, 3.1861917897603487, 1.0640520031606115, 2.4301692027398083, 3.6037358003906084, 3.1263346869301314, 1.9271501289235058, 3.3869115038652944, 5.898687025475788, 2.2228748547014283, 5.991686606532885, 2.2312875375217835, 3.966972271784039, 0.5097022769061827, 2.285211703263904, 3.679467979687638, 2.3897335392663344, 3.0459765529491496, 2.157525892347725, 1.0464386503602756, 1.1268040015096183, 0.9368647652503312, 5.826792008503808, 1.0467715648924814, 3.8666175408009322, 0.7202171140874074, 2.551504279830512, 1.1099769925937641, 2.062685819902267, 5.783279317899103, 3.3154092170280647, 0.8875346336514089, 2.6663783274697965, 0.4097850074800665, 4.402363309090779, 5.337987252210415, 2.8136485609904107, 1.2310160933358345, 0.5757980039393241, 0.1623635829403594, 4.761061800134117, 5.928615798673297, 0.037836503328300235, 2.51992630265934, 6.259698344872563, 1.6591141657450885, 0.5059785728104094, 4.083027641257159, 2.0254049541165475, 2.3826392397241407, 3.9604093136278107, 6.190054572307588, 3.585615793666355, 4.775221946845065, 3.03952162849649, 5.831375308406569, 2.809025507637093, 0.033750280283890224, 0.6515737329599759, 1.4489278492398439, 5.112820903340961, 2.5945635598806325, 3.4125438589868993, 2.5956094918549417, 0.506569819873183, 5.260851452577721, 4.7347935925935065, 1.3163909035906425, 2.456326884994461, 2.547079097410114, 3.8593113949185534, 4.13010797357585]\n",
      "0011001001101000 ₍₂₎0011001001101000 ₍₂₎BitStr{16, BigInt}0001011001001100"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "using Zygote \n",
    "using LinearAlgebra\n",
    "\n",
    "nq = 16\n",
    "N = nq\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "p = rand(nparameters(g)).*2π\n",
    "println(nparameters(g))\n",
    "println(p)\n",
    "dispatch!(g, p)\n",
    "\n",
    "function fe_grad_prob(theta, x, eps = 1e-2) #This is actually slower than the parameter shift method...\n",
    "    temp_params = theta\n",
    "    fe_grad = []\n",
    "    for i in 1:nparameters(g)\n",
    "        temp_params[i] += eps\n",
    "        plus = prob(temp_params, x)\n",
    "        temp_params[i] -= 2*eps\n",
    "        minus = prob(temp_params, x)\n",
    "        push!(fe_grad, (plus - minus) / (2*eps))\n",
    "        temp_params[i] += eps #Resetting temp_params[i] back to original value\n",
    "    end\n",
    "    fe_grad\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "function covariance_matrix(theta) #Should output a 2n*2n matrix, the covariance matrix of g_{theta}|0>\n",
    "    circuit = dispatch(g, theta)\n",
    "    reg = apply(FLOYao.zero_state(nq), circuit)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function update_covariance_matrix!(M, i, pi, ni)\n",
    "    n = size(M,1)\n",
    "    for p in 2i+1:n \n",
    "        for q in p+1:n\n",
    "            M[p,q] += (-1)^ni * M[2i-1,q] * M[2i,p] / (2pi)\n",
    "            M[p,q] -= (-1)^ni * M[2i-1,p] * M[2i,q] / (2pi)\n",
    "        end\n",
    "    end\n",
    "    return M\n",
    "end\n",
    "\n",
    "function update_covariance_matrix(M, i, pi, ni) #Won't change M, as indicated by no ! in the function name\n",
    "    n = size(M,1)\n",
    "    ret = M\n",
    "    for p in 2i+1:n \n",
    "        for q in p+1:n\n",
    "            ret[p,q] += (-1)^ni * M[2i-1,q] * M[2i,p] / (2pi)\n",
    "            ret[p,q] -= (-1)^ni * M[2i-1,p] * M[2i,q] / (2pi)\n",
    "        end\n",
    "    end\n",
    "    return ret\n",
    "end\n",
    "\n",
    "function initialize_covariance_matrices(theta, bit_string)\n",
    "    cov_matrices = Vector{Matrix{Float64}}(undef, N)\n",
    "    cov_matrices[1] = covariance_matrix(theta)\n",
    "    for i in 1:N\n",
    "        ni = bit_string[i]\n",
    "        if i < N\n",
    "            cov_matrices[i+1] = update_covariance_matrix(cov_matrices[i], i, pi, ni)\n",
    "        end\n",
    "    end\n",
    "    return cov_matrices\n",
    "end\n",
    "\n",
    "function bitstring_probabilityy(theta, bit_string)\n",
    "    p = 1\n",
    "    m = initialize_covariance_matrices(theta)\n",
    "    for i in 1:N\n",
    "        ni = bit_string[i]\n",
    "        pi = (1 + (-1)^ni * m[i][2i-1,2i]) / 2\n",
    "        # pi = 0.5\n",
    "        pi ≈ 0 && return 0\n",
    "        p *= pi\n",
    "    end\n",
    "    return p > 0 ? p : 0 # floating point issues can cause very small probabilities to get negative.\n",
    "end\n",
    "\n",
    "\n",
    "iters = 5\n",
    "results = measure(FLOYao.zero_state(nq) |> g, nshots = iters)\n",
    "print(results)\n",
    "# b = [results[1]...]\n",
    "b = results[1]\n",
    "print(b)\n",
    "print(b)\n",
    "print(typeof(b))\n",
    "for i in 1:nq\n",
    "    print(b[i])\n",
    "end\n",
    "# Zygote.gradient(theta -> bitstring_probabilityy(theta, b), p)\n",
    "# Zygote.gradient(theta -> covariance_matrix(theta)[1,1], p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MajoranaReg{Float64}(30) => [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using SparseArrays\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 30\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -2*im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return -2*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "print(majoranaindices2kron(nq, 1, 6) |> typeof) #KronBlock\n",
    "print(-1*majoranaindices2kron(nq, 1, 6) |> typeof) #Scale\n",
    "ham = -1*majoranaindices2kron(nq, 1, 6) + 0*majoranaindices2kron(nq, 1, 6) \n",
    "ham = majoranaindices2kron(nq, 1, 6)\n",
    "ham = majorana_commutator(nq, 1, 6)\n",
    "# FLOYao.kron2majoranaindices(ham)\n",
    "# ham |> typeof\n",
    "expect'(ham, FLOYao.zero_state(nq) => g)\n",
    "# -1*majoranaindices2kron(nq, 1, 6) |> typeof"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.0e-323 5.0e-323 8.4e-323; 4.4e-323 5.4e-323 9.0e-323]"
     ]
    },
    {
     "data": {
      "text/plain": [
       "14-element Vector{Float64}:\n",
       " 2.76952659e-314\n",
       " 2.250113993e-314\n",
       " 2.2671679297e-314\n",
       " 2.2481020787e-314\n",
       " 2.2501141196e-314\n",
       " 2.2571463654e-314\n",
       " 2.257146413e-314\n",
       " 2.2571464365e-314\n",
       " 2.2501142144e-314\n",
       " 2.250114246e-314\n",
       " 2.2501142777e-314\n",
       " 2.257146318e-314\n",
       " 7.292909059161388e-304\n",
       " 5.0e-324"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a 3x3 matrix\n",
    "# M = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]\n",
    "M = Matrix{Float64}(undef, 2, 3)\n",
    "print(M)\n",
    "nq = 14\n",
    "global v = Vector{Float64}(undef, nq)\n",
    "v\n",
    "# Access the first row as a vector\n",
    "# first_row = M[1, :]\n",
    "# first_row |> typeof\n",
    "# # Print the first row vector\n",
    "# # println(\"First row: \", first_row)\n",
    "\n",
    "# v = [10.0, 11.0, 12.0]\n",
    "# M[1, :] = v\n",
    "\n",
    "\n",
    "# Check the type of the first row\n",
    "# println(\"Type of first row: \", typeof(first_row))  # Should output Vector{Float64}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hihiihiihhihiihiihhihiihiih"
     ]
    },
    {
     "data": {
      "text/plain": [
       "14-element Vector{Float64}:\n",
       " -8.35559280402534\n",
       " -3.316848201157868\n",
       "  2.812712869831361\n",
       " -1.323378163339525\n",
       " -0.2876764103917058\n",
       "  0.11482241488174083\n",
       "  4.134649996766404\n",
       "  1.2635469373258819\n",
       " -0.7802783664457694\n",
       " -2.2817885507700586\n",
       "  6.455946030403732\n",
       "  0.0\n",
       "  0.0\n",
       "  0.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "using SparseArrays\n",
    "using Yao\n",
    "using BenchmarkTools\n",
    "\n",
    "nq = 3\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "⊗ = kron\n",
    "\n",
    "function covariance_matrix(reg::MajoranaReg)\n",
    "    nq = nqubits(reg)\n",
    "    G = I(nq) ⊗ [0 1; -1 0]\n",
    "    return reg.state * G * reg.state'\n",
    "end\n",
    "\n",
    "function majoranaindices2kron(nq, i, j) #Returns γ_iγ_j, ASSUME i<j (ok i actually have no clue what's going on due to conflicts in definition of γ_i (FLOYao docs vs Jozsa Miyake paper vs Bill's paper))\n",
    "    p = []\n",
    "    c = (i % 2 == j % 2) ? 1 : -1 #deal with this c later..., once i figure out how to scale kronblocks so that they stay as kronblock objects...\n",
    "    a = min(i, j)\n",
    "    b = max(i, j)\n",
    "    first = (a+1) ÷ 2 \n",
    "    last = (b+1) ÷ 2 \n",
    "    if first == last #This means i=j-1 and j is even\n",
    "        c = -2*im\n",
    "        push!(p, first => Z)\n",
    "    else\n",
    "        if i % 2 == 0\n",
    "            push!(p, first => X)\n",
    "            c *= -im\n",
    "        else\n",
    "            push!(p, first => Y)\n",
    "            c *= im\n",
    "        end\n",
    "        for k in first+1:last-1\n",
    "            push!(p, k => Z)\n",
    "            c *= -1\n",
    "        end\n",
    "        if j % 2 == 0\n",
    "            push!(p, last => Y)\n",
    "        else\n",
    "            push!(p, last => X)\n",
    "        end\n",
    "    end\n",
    "    return kron(nq, p...)\n",
    "end\n",
    "\n",
    "function majorana_commutator(nq, i, j)\n",
    "    return -2*majoranaindices2kron(nq, i, j) + 0*kron(nq, 1 => Z)\n",
    "end\n",
    "\n",
    "nparams = nparameters(g)\n",
    "dim = 2*nq\n",
    "stored = 0 #Latest iteration number that has been stored\n",
    "#Preallocate the length of the vector\n",
    "sampled = Dict{BitStr, Vector}() #Keeps track of which x has been sampled before, so it doesn't recompute everything  (NOT REALLY SURE IF THIS WILL WORK)\n",
    "\n",
    "function update!(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Evolves all matrices and probabilities and gradients by nq steps, in-place\n",
    "    nq = nqubits(reg)\n",
    "    nparams = nparameters(g)\n",
    "    dim = 2*nq\n",
    "    for i in 1:nq\n",
    "        # i = stored + 1\n",
    "        ni = b[i]\n",
    "        if stored > 0\n",
    "            cur_m = temp_m\n",
    "            cur_grad_m = temp_grad_m\n",
    "            cur_prob = probabilities[i]\n",
    "            cur_grad_prob = grad_probabilities[i, :]\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_m[p,q] -= (-1)^ni * (cur_m[2*i-1,p] * cur_m[2*i,q]) / (2*cur_prob)\n",
    "                    temp_m[p,q] += (-1)^ni * (cur_m[2*i-1,q] * cur_m[2*i,p]) / (2*cur_prob)\n",
    "                    temp_m[q,p] = -temp_m[p,q]\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_m[p,p] = 0.0 #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    temp_grad_m[p,q] .-= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,p] * cur_m[2*i,q]) .+ (cur_prob * (cur_grad_m[2*i-1,p]*cur_m[2*i,q] .+ cur_m[2*i-1,p] * cur_grad_m[2*i,q]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[p,q] .+= (-1)^ni * ((cur_grad_prob * cur_m[2*i-1,q] * cur_m[2*i,p]) .+ (cur_prob * (cur_grad_m[2*i-1,q]*cur_m[2*i,p] .+ cur_m[2*i-1,q] * cur_grad_m[2*i,p]))) / (2*cur_prob^2)\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        else\n",
    "            print(\"hihiihiih\")\n",
    "            dispatch!(g, theta)\n",
    "            z = reg |> g\n",
    "            temp_m = covariance_matrix(z)\n",
    "            probabilities[i] = (1+(-1)^ni * temp_m[2*i-1, 2*i]) / 2\n",
    "            for p in 1:dim\n",
    "                for q in p+1:dim\n",
    "                    ham = majorana_commutator(nq, p, q) + 0*kron(nq, 1 => Z) #Need to do the commutator, not just γ_iγ_j... (whatever, fix this later)\n",
    "                    #Adding the 0*kron(nq, 1 => Z) just turns it into something that i can pass into expect'\n",
    "                    temp_grad_m[p,q] = expect'(ham, reg => g)[2]\n",
    "                    temp_grad_m[q,p] = -temp_grad_m[p,q] #this is correct but the way i'm defining temp[j,k] is not correct...\n",
    "                end\n",
    "            end\n",
    "            for p in 1:dim\n",
    "                temp_grad_m[p,p] = zeros(nparams) #i think this is correct but i don't really need to use it?? actually i don't know anymore, because shouldn't the main diagonal of a covariance matrix not be 0s????? maybe change it to ones for testing\n",
    "            end\n",
    "            grad_probabilities[i, :] = (-1)^ni * temp_grad_m[2*i-1, 2*i] / 2\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "function log_grad(reg::MajoranaReg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities) #Returns ∇_θlog(p_theta(X)), evaluated at theta (parameters of circuit) and b (measurement result); reg is the initial register (e.g. FLOYao.zero_state(nq))\n",
    "    nq = nqubits(reg)\n",
    "    update!(reg, theta, b, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "    s = zeros(length(theta))\n",
    "    for i in 1:nq\n",
    "        s += grad_probabilities[i, :] / probabilities[i]\n",
    "    end\n",
    "    return s\n",
    "end\n",
    "\n",
    "iters = 1\n",
    "p = rand(nparameters(g)).*2π\n",
    "dispatch!(g, p)\n",
    "results = measure(FLOYao.zero_state(nq) |> g, nshots = iters)\n",
    "bitstr = results[1]\n",
    "\n",
    "# FLOYao.bitstring_probability(FLOYao.zero_state(nq) |> g, bitstr)\n",
    "temp_m = Matrix{Float64}(undef, dim, dim)\n",
    "temp_grad_m = Matrix{Vector{Float64}}(undef, dim, dim)\n",
    "cur_m = Matrix{Float64}(undef, dim, dim)\n",
    "cur_grad_m = Matrix{Vector{Float64}}(undef, dim, dim)\n",
    "probabilities = Vector{Float64}(undef, nq)\n",
    "grad_probabilities = Matrix{Float64}(undef, nq, nparams)\n",
    "log_grad(FLOYao.zero_state(nq), p, bitstr, temp_m, temp_grad_m, cur_m, cur_grad_m, probabilities, grad_probabilities)\n",
    "\n",
    "# function sample_grad(vecs, theta, n, i, j)\n",
    "#     for i in 1:length(vecs)\n",
    "#         cur_key = vecs[i]\n",
    "#         println(\"iteration $i\")\n",
    "#         if haskey(dict, cur_key)\n",
    "#             println(dict[cur_key])\n",
    "#         else\n",
    "#             r = grad(theta, n, i, j)\n",
    "#             dict[cur_key] = r\n",
    "#             println(r)\n",
    "#         end\n",
    "#     end\n",
    "# end\n",
    "\n",
    "# iters = 5\n",
    "# results = measure(FLOYao.zero_state(nq) |> g, nshots = iters)\n",
    "\n",
    "# reg = FLOYao.zero_state(nq)\n",
    "# r = reg |> circuit\n",
    "# grad_covariance_matrix(reg, parameters(circuit))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "Mutating arrays is not supported -- called copyto!(SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, ...)\nThis error occurs when you ask Zygote to differentiate operations that change\nthe elements of arrays in place (e.g. setting values with x .= ...)\n\nPossible fixes:\n- avoid mutating operations (preferred)\n- or read the documentation and solutions for this error\n  https://fluxml.ai/Zygote.jl/latest/limitations\n",
     "output_type": "error",
     "traceback": [
      "Mutating arrays is not supported -- called copyto!(SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, ...)\n",
      "This error occurs when you ask Zygote to differentiate operations that change\n",
      "the elements of arrays in place (e.g. setting values with x .= ...)\n",
      "\n",
      "Possible fixes:\n",
      "- avoid mutating operations (preferred)\n",
      "- or read the documentation and solutions for this error\n",
      "  https://fluxml.ai/Zygote.jl/latest/limitations\n",
      "\n",
      "\n",
      "Stacktrace:\n",
      "  [1] error(s::String)\n",
      "    @ Base ./error.jl:35\n",
      "  [2] _throw_mutation_error(f::Function, args::SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true})\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/lib/array.jl:70\n",
      "  [3] (::Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}})(#unused#::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/lib/array.jl:85\n",
      "  [4] (::Zygote.var\"#2637#back#545\"{Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/ZygoteRules/M4xmc/src/adjoint.jl:72\n",
      "  [5] Pullback\n",
      "    @ ./broadcast.jl:884 [inlined]\n",
      "  [6] Pullback\n",
      "    @ ./broadcast.jl:881 [inlined]\n",
      "  [7] Pullback\n",
      "    @ ./broadcast.jl:877 [inlined]\n",
      "  [8] Pullback\n",
      "    @ ~/.julia/packages/FLOYao/EsxyP/src/instruct.jl:58 [inlined]\n",
      "  [9] (::Zygote.Pullback{Tuple{typeof(instruct!), MajoranaReg{Float64}, Val{:Rz}, Tuple{Int64}, Float64}, Tuple{Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{1, 1, Zygote.Context{false}, Int64}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.var\"#back#246\"{Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 2, Zygote.Context{false}, Float64}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.dotview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing, Nothing, Nothing}}, Zygote.Pullback{Tuple{typeof(Base.maybeview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}, Tuple{Nothing, Nothing}}, Zygote.ZBack{ChainRules.var\"#view_pullback#676\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.dotview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing, Nothing, Nothing}}, Zygote.Pullback{Tuple{typeof(Base.maybeview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}, Tuple{Nothing, Nothing}}, Zygote.ZBack{ChainRules.var\"#view_pullback#676\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Vector{Float64}}, Tuple{Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), Base.Broadcast.DefaultArrayStyle{1}, SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:args, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:f, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, typeof(identity)}}, Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.var\"#2637#back#545\"{Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing, Nothing}}}}, Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#back#245\"{Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}}, Zygote.var\"#3750#back#1181\"{Zygote.var\"#1175#1179\"{Tuple{Vector{Float64}, Vector{Float64}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#-_pullback#408\"{Int64, Bool, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 2, Zygote.Context{false}, Int64}}, Zygote.ZBack{ChainRules.var\"#getindex_pullback#666\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.ZBack{ChainRules.var\"#getindex_pullback#666\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}, Zygote.ZBack{ChainRules.var\"#-_pullback#408\"{Int64, Bool, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#sincos_pullback#389\"{Float64, Float64, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Vector{Float64}}, Tuple{Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), Base.Broadcast.DefaultArrayStyle{1}, SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:args, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:f, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, typeof(identity)}}, Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.var\"#2637#back#545\"{Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing, Nothing}}}}, Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.var\"#3766#back#1189\"{Zygote.var\"#1185#1188\"{Vector{Float64}, Vector{Float64}}}}})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [10] Pullback\n",
      "    @ ~/.julia/packages/FLOYao/EsxyP/src/apply_composite.jl:37 [inlined]\n",
      " [11] (::Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, PutBlock{2, 1, RotationGate{2, Float64, ZGate}}}, Tuple{Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:content, Zygote.Context{false}, PutBlock{2, 1, RotationGate{2, Float64, ZGate}}, RotationGate{2, Float64, ZGate}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:theta, Zygote.Context{false}, RotationGate{2, Float64, ZGate}, Float64}}, Zygote.Pullback{Tuple{typeof(instruct!), MajoranaReg{Float64}, Val{:Rz}, Tuple{Int64}, Float64}, Tuple{Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{1, 1, Zygote.Context{false}, Int64}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.var\"#back#246\"{Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 2, Zygote.Context{false}, Float64}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.dotview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing, Nothing, Nothing}}, Zygote.Pullback{Tuple{typeof(Base.maybeview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}, Tuple{Nothing, Nothing}}, Zygote.ZBack{ChainRules.var\"#view_pullback#676\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.dotview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing, Nothing, Nothing}}, Zygote.Pullback{Tuple{typeof(Base.maybeview), Matrix{Float64}, Int64, Colon}, Tuple{Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}, Tuple{Nothing, Nothing}}, Zygote.ZBack{ChainRules.var\"#view_pullback#676\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Vector{Float64}}, Tuple{Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), Base.Broadcast.DefaultArrayStyle{1}, SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:args, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:f, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, typeof(identity)}}, Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.var\"#2637#back#545\"{Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing, Nothing}}}}, Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#back#245\"{Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}}, Zygote.var\"#3750#back#1181\"{Zygote.var\"#1175#1179\"{Tuple{Vector{Float64}, Vector{Float64}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#-_pullback#408\"{Int64, Bool, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 2, Zygote.Context{false}, Int64}}, Zygote.ZBack{ChainRules.var\"#getindex_pullback#666\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#3814#back#1211\"{Zygote.ZBack{ChainRules.var\"#times_pullback#567\"{Float64, Vector{Float64}, ChainRulesCore.ProjectTo{AbstractArray, NamedTuple{(:element, :axes), Tuple{ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, Tuple{Base.OneTo{Int64}}}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}, Zygote.ZBack{ChainRules.var\"#getindex_pullback#666\"{Matrix{Float64}, Tuple{Int64, Colon}, Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2033#back#213\"{Zygote.var\"#back#211\"{2, 1, Zygote.Context{false}, Float64}}, Zygote.ZBack{ChainRules.var\"#-_pullback#408\"{Int64, Bool, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.ZBack{ChainRules.var\"#sincos_pullback#389\"{Float64, Float64, ChainRulesCore.ProjectTo{Float64, NamedTuple{(), Tuple{}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Vector{Float64}}, Tuple{Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2173#back#293\"{Zygote.var\"#291#292\"{Tuple{Tuple{Nothing}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing}}}}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize!), Base.Broadcast.DefaultArrayStyle{1}, SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, Tuple{Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:args, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:f, Zygote.Context{false}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, typeof(identity)}}, Zygote.ZBack{ChainRules.var\"#uninstantiate#788\"}, Zygote.var\"#2637#back#545\"{Zygote.var\"#543#544\"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(getproperty), Module, Symbol}, Tuple{Zygote.Pullback{Tuple{typeof(getglobal), Module, Symbol}, Tuple{typeof(getglobal)}}}}, Zygote.Pullback{Tuple{typeof(Core.Typeof), typeof(identity)}, Any}, Zygote.Pullback{Tuple{Type{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}}, typeof(identity), Tuple{Vector{Float64}}, Tuple{Base.OneTo{Int64}}}, Tuple{Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Vector{Float64}}}, Tuple{Vector{Float64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.Pullback{Tuple{typeof(convert), Type{Tuple{Base.OneTo{Int64}}}, Tuple{Base.OneTo{Int64}}}, Tuple{}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2214#back#313\"{Zygote.Jnew{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Tuple{Base.OneTo{Int64}}, typeof(identity), Tuple{Vector{Float64}}}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{typeof(identity)}, typeof(identity)}, Tuple{}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.var\"#combine_styles_pullback#1166\"{Tuple{Nothing, Nothing, Nothing}}}}, Zygote.var\"#2017#back#204\"{typeof(identity)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.var\"#3766#back#1189\"{Zygote.var\"#1185#1188\"{Vector{Float64}, Vector{Float64}}}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:locs, Zygote.Context{false}, PutBlock{2, 1, RotationGate{2, Float64, ZGate}}, Tuple{Int64}}}, Zygote.var\"#1926#back#161\"{Zygote.var\"#157#160\"}}})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [12] Pullback\n",
      "    @ ~/.julia/packages/YaoBlocks/DuDXk/src/composite/chain.jl:136 [inlined]\n",
      " [13] (::Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, ChainBlock{2}}, Any})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [14] Pullback\n",
      "    @ ~/.julia/packages/YaoBlocks/DuDXk/src/abstract_block.jl:32 [inlined]\n",
      " [15] (::Zygote.Pullback{Tuple{typeof(apply!), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, ChainBlock{2}}, Any}, Zygote.Pullback{Tuple{typeof(YaoBlocks._check_size), MajoranaReg{Float64}, ChainBlock{2}}, Any}}})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [16] Pullback\n",
      "    @ ~/.julia/packages/YaoBlocks/DuDXk/src/abstract_block.jl:424 [inlined]\n",
      " [17] (::Zygote.Pullback{Tuple{typeof(apply), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(apply!), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, ChainBlock{2}}, Any}, Zygote.Pullback{Tuple{typeof(YaoBlocks._check_size), MajoranaReg{Float64}, ChainBlock{2}}, Any}}}, Zygote.Pullback{Tuple{typeof(copy), MajoranaReg{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg}, Matrix{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg{Float64}}, Matrix{Float64}}, Tuple{Zygote.var\"#2214#back#313\"{Zygote.Jnew{MajoranaReg{Float64}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{Matrix{Float64}}, Matrix{Float64}}, Any}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}, Zygote.var\"#2482#back#476\"{Zygote.var\"#472#475\"}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}}}}})(Δ::Nothing)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [18] Pullback\n",
      "    @ ~/Desktop/Desktop - Peter’s MacBook Air/Harvard/2.5/PRISE/Project/MatchgateGAN/juliatest.ipynb:73 [inlined]\n",
      " [19] (::Zygote.Pullback{Tuple{typeof(cov_mat), Vector{Float64}}, Tuple{Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, Int64}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, Int64}}, Zygote.ZBack{YaoBlocks.AD.var\"#51#52\"{Vector{Float64}}}, Zygote.ZBack{YaoBlocks.AD.var\"#47#48\"{ChainBlock{2}, ArrayReg{2, ComplexF64, Matrix{ComplexF64}}}}, Zygote.Pullback{Tuple{typeof(FLOYao.zero_state), Int64}, Tuple{Zygote.Pullback{Tuple{typeof(FLOYao.zero_state), Type{Float64}, Int64}, Tuple{Zygote.ZBack{ChainRules.var\"#Array_pullback#434\"{ChainRulesCore.ProjectTo{ChainRulesCore.NoTangent, NamedTuple{(), Tuple{}}}}}, Zygote.Pullback{Tuple{UniformScaling{Bool}, Int64}, Tuple{Zygote.ZBack{typeof(ChainRules._Diagonal_pullback)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:λ, Zygote.Context{false}, UniformScaling{Bool}, Bool}}}}, Zygote.Pullback{Tuple{Type{MajoranaReg}, Matrix{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg{Float64}}, Matrix{Float64}}, Tuple{Zygote.var\"#2214#back#313\"{Zygote.Jnew{MajoranaReg{Float64}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{Matrix{Float64}}, Matrix{Float64}}, Any}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, UniformScaling{Bool}}}}}}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, ChainBlock{2}}}, Zygote.Pullback{Tuple{typeof(apply), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(apply!), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, ChainBlock{2}}, Any}, Zygote.Pullback{Tuple{typeof(YaoBlocks._check_size), MajoranaReg{Float64}, ChainBlock{2}}, Any}}}, Zygote.Pullback{Tuple{typeof(copy), MajoranaReg{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg}, Matrix{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg{Float64}}, Matrix{Float64}}, Tuple{Zygote.var\"#2214#back#313\"{Zygote.Jnew{MajoranaReg{Float64}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{Matrix{Float64}}, Matrix{Float64}}, Any}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}, Zygote.var\"#2482#back#476\"{Zygote.var\"#472#475\"}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}}}}}}})(Δ::Int64)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface2.jl:0\n",
      " [20] (::Zygote.var\"#75#76\"{Zygote.Pullback{Tuple{typeof(cov_mat), Vector{Float64}}, Tuple{Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, Int64}}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, Int64}}, Zygote.ZBack{YaoBlocks.AD.var\"#51#52\"{Vector{Float64}}}, Zygote.ZBack{YaoBlocks.AD.var\"#47#48\"{ChainBlock{2}, ArrayReg{2, ComplexF64, Matrix{ComplexF64}}}}, Zygote.Pullback{Tuple{typeof(FLOYao.zero_state), Int64}, Tuple{Zygote.Pullback{Tuple{typeof(FLOYao.zero_state), Type{Float64}, Int64}, Tuple{Zygote.ZBack{ChainRules.var\"#Array_pullback#434\"{ChainRulesCore.ProjectTo{ChainRulesCore.NoTangent, NamedTuple{(), Tuple{}}}}}, Zygote.Pullback{Tuple{UniformScaling{Bool}, Int64}, Tuple{Zygote.ZBack{typeof(ChainRules._Diagonal_pullback)}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:λ, Zygote.Context{false}, UniformScaling{Bool}, Bool}}}}, Zygote.Pullback{Tuple{Type{MajoranaReg}, Matrix{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg{Float64}}, Matrix{Float64}}, Tuple{Zygote.var\"#2214#back#313\"{Zygote.Jnew{MajoranaReg{Float64}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{Matrix{Float64}}, Matrix{Float64}}, Any}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}, Zygote.ZBack{ChainRules.var\"#times_pullback2#419\"{Int64, Int64}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, UniformScaling{Bool}}}}}}}, Zygote.var\"#1990#back#194\"{Zygote.var\"#190#193\"{Zygote.Context{false}, GlobalRef, ChainBlock{2}}}, Zygote.Pullback{Tuple{typeof(apply), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(apply!), MajoranaReg{Float64}, ChainBlock{2}}, Tuple{Zygote.Pullback{Tuple{typeof(YaoAPI.unsafe_apply!), MajoranaReg{Float64}, ChainBlock{2}}, Any}, Zygote.Pullback{Tuple{typeof(YaoBlocks._check_size), MajoranaReg{Float64}, ChainBlock{2}}, Any}}}, Zygote.Pullback{Tuple{typeof(copy), MajoranaReg{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg}, Matrix{Float64}}, Tuple{Zygote.Pullback{Tuple{Type{MajoranaReg{Float64}}, Matrix{Float64}}, Tuple{Zygote.var\"#2214#back#313\"{Zygote.Jnew{MajoranaReg{Float64}, Nothing, false}}, Zygote.Pullback{Tuple{typeof(convert), Type{Matrix{Float64}}, Matrix{Float64}}, Any}, Zygote.ZBack{Returns{Tuple{ChainRulesCore.NoTangent, ChainRulesCore.NoTangent, ChainRulesCore.NoTangent}}}}}}}, Zygote.var\"#2482#back#476\"{Zygote.var\"#472#475\"}, Zygote.var\"#2184#back#303\"{Zygote.var\"#back#302\"{:state, Zygote.Context{false}, MajoranaReg{Float64}, Matrix{Float64}}}}}}}}}})(Δ::Int64)\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface.jl:91\n",
      " [21] gradient(::Function, ::Vector{Float64}, ::Vararg{Vector{Float64}})\n",
      "    @ Zygote ~/.julia/packages/Zygote/nsBv0/src/compiler/interface.jl:148\n",
      " [22] top-level scope\n",
      "    @ ~/Desktop/Desktop - Peter’s MacBook Air/Harvard/2.5/PRISE/Project/MatchgateGAN/juliatest.ipynb:81"
     ]
    }
   ],
   "source": [
    "#timing test for FLOYao functions of expect'\n",
    "\n",
    "using Yao, FLOYao\n",
    "using Zygote \n",
    "\n",
    "nq = 2\n",
    "layers = 2\n",
    "g = chain(nq)\n",
    "for _ in 1:layers\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:nq-1\n",
    "        push!(g, rot(kron(nq, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:nq\n",
    "        push!(g, put(nq, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "p = rand(nparameters(g)).*2π\n",
    "\n",
    "function L(p_gen)\n",
    "    circuit = dispatch(g, p_gen)\n",
    "    r = Yao.zero_state(nq)\n",
    "    ex = expect(h, r => circuit)\n",
    "    ex |> real\n",
    "end\n",
    "\n",
    "# L(p) |> println\n",
    "# Zygote.gradient(L, p) |> println\n",
    "# dispatch!(g, p);\n",
    "\n",
    "# reg = Yao.zero_state(nq)\n",
    "# expect(h, reg => g) |> println\n",
    "# state_grad, params_grad = expect'(h, reg => g)\n",
    "# println(params_grad)\n",
    "\n",
    "function prob(theta, x)\n",
    "    circuit = dispatch(g, theta)\n",
    "    r = apply(FLOYao.zero_state(nq), circuit)\n",
    "    return FLOYao.bitstring_probability(r, x)\n",
    "end\n",
    "\n",
    "function grad_prob(theta, x)\n",
    "    Zygote.gradient(theta -> prob(theta, x), theta)[1]\n",
    "end\n",
    "\n",
    "TIME COMPARISION WITH CURRENT METHOD OF OBTAINING GRADIENTS AND ALSO ACCURACY TEST\n",
    "function fe_grad_prob(theta, x, eps = 1e-2) #This is actually slower than the parameter shift method...\n",
    "    temp_params = theta\n",
    "    fe_grad = []\n",
    "    for i in 1:nparameters(g)\n",
    "        temp_params[i] += eps\n",
    "        plus = prob(temp_params, x)\n",
    "        temp_params[i] -= 2*eps\n",
    "        minus = prob(temp_params, x)\n",
    "        push!(fe_grad, (plus - minus) / (2*eps))\n",
    "        temp_params[i] += eps #Resetting temp_params[i] back to original value\n",
    "    end\n",
    "    fe_grad\n",
    "end\n",
    "\n",
    "function cov_mat(theta)\n",
    "   circuit = dispatch(g, theta)\n",
    "   reg = apply(Yao.zero_state(nq), circuit)\n",
    "   reg = apply(FLOYao.zero_state(nq), circuit) #This doesn't work... somehow, \n",
    "   return 2\n",
    "#    G = I(nq) ⊗ [0 1; -1 0]\n",
    "#    dens = state(reg)\n",
    "#    dens * G * dens'\n",
    "end\n",
    "\n",
    "dispatch!(g, p)\n",
    "println(Zygote.gradient(cov_mat, p))\n",
    "# reg = FLOYao.zero_state(nq) |> g\n",
    "# Zygote.gradient(covariance_matrix(reg)[1,1])\n",
    "# result = measure(reg) |> first\n",
    "# println(typeof(state(reg)))\n",
    "# iters = 1\n",
    "# results = measure(reg, nshots = iters)\n",
    "# xx = results[1]\n",
    "# println(xx)\n",
    "\n",
    "# grad_prob(p, xx) |> println\n",
    "# fe_grad_prob(p, xx) |> println\n",
    "# for i in 1:iters\n",
    "#     r = results[i] #r needs to be a DitStr object\n",
    "#     FLOYao.bitstring_probability(reg, r) |> println\n",
    "# end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5125865044503471\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([-0.06400978977659509, -0.17675820021029692, -0.3062414877261301], [0.06400978977659509, 0.17675820021029698, -0.3062414877261301])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#From https://github.com/QuantumBFS/Yao.jl/issues/365\n",
    "\n",
    "using Yao\n",
    "using Zygote\n",
    "n_qubits = 3\n",
    "hterm = put(n_qubits, 1=>Z)\n",
    "hterm *= put(n_qubits, 2=>X)\n",
    "hterm *= put(n_qubits, 3=>Y)\n",
    "hterm += put(n_qubits, 1=>X)\n",
    "\n",
    "circ_left = chain(put(n_qubits, 1=>X), \n",
    "                    put(n_qubits, 1=>Rx(0.1)), \n",
    "                    put(n_qubits, 2=>Ry(0.1)), \n",
    "                    put(n_qubits, 1=>Rz(0.1)))\n",
    "\n",
    "circ_right = chain(put(n_qubits, 1=>Rx(0.1)), \n",
    "                    put(n_qubits, 2=>Ry(0.1)), \n",
    "                    put(n_qubits, 1=>Rz(0.1)))\n",
    "\n",
    "function loss(pl, pr)\n",
    "    cl = dispatch(circ_left, pl)\n",
    "    cr = dispatch(circ_right, pr)\n",
    "    regl = apply(zero_state(n_qubits), cl)\n",
    "    regr = apply(apply(zero_state(n_qubits), cr), hterm)\n",
    "    expectation = regl' * regr\n",
    "    return real(expectation)\n",
    "end\n",
    "\n",
    "a = randn(3)\n",
    "b = randn(3)\n",
    "loss(a, b) |> println\n",
    "Zygote.gradient(loss, a, b) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.5747915499772245\n",
      "Any[-0.3053330783518649, 0.13827656999623295, 0.2379368303783624, -0.6456718719999549]\n",
      "1.3272183507264153\n",
      "BitStr{2, BigInt}[10 ₍₂₎, 01 ₍₂₎, 10 ₍₂₎, 10 ₍₂₎, 10 ₍₂₎, 01 ₍₂₎, 10 ₍₂₎, 10 ₍₂₎, 10 ₍₂₎, 10 ₍₂₎]\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.2149780630056934940868942891263455154690288112540968309196444342625692547343874\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.2149780630056934940868942891263455154690288112540968309196444342625692547343874\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n",
      "0.7850219369943061412024066258927221965719859154649675617124977920324030433718576\n"
     ]
    }
   ],
   "source": [
    "using Yao, FLOYao\n",
    "using LinearAlgebra\n",
    "\n",
    "N = 2\n",
    "layers = 5\n",
    "g = chain(N)\n",
    "for _ in 1:layers\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:N\n",
    "        push!(g, put(N, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "dispatch!(g, rand(nparameters(g)).*2π)\n",
    "reg = FLOYao.rand_state(N) |> g\n",
    "m = state(reg)\n",
    "println(tr(m))\n",
    "ell = size(m)[1]\n",
    "probability = []\n",
    "for i in 1:ell\n",
    "    push!(probability, m[i, i])\n",
    "end\n",
    "println(probability)\n",
    "println(sum(abs.(probability)))\n",
    "# result = measure(reg) |> first\n",
    "iters = 10\n",
    "results = measure(reg, nshots = iters)\n",
    "println(results)\n",
    "\n",
    "for i in 1:iters\n",
    "    r = results[i] #r needs to be a DitStr object\n",
    "    FLOYao.bitstring_probability(reg, r) |> println\n",
    "end\n",
    "\n",
    "#GOAL: To find grad \n",
    "\n",
    "#pseudocode, only part i need to work on is the grad log thing\n",
    "# M = samplemean_size\n",
    "# iters = M\n",
    "# z = FLOYao.zero_state(N)\n",
    "# reg = z |> g\n",
    "# x = measure(reg, nshots = iters)\n",
    "# sum = 0\n",
    "# for i in 1:iters\n",
    "#     sum += log(D(x[i])) * grad(log(FLOYao.bitstring_probability(x[i])))\n",
    "# end\n",
    "# println(sum / M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DitStr{2, 1, Int64}[1 ₍₂₎]\n",
      "DitStr{2, 1, Int64}[0 ₍₂₎]\n",
      "DitStr{2, 1, Int64}[0 ₍₂₎]\n",
      "DitStr{2, 1, Int64}[0 ₍₂₎]\n",
      "DitStr{2, 1, Int64}[0 ₍₂₎]\n"
     ]
    }
   ],
   "source": [
    "using Yao, YaoPlots\n",
    "\n",
    "c = chain(1, put(1 => H))\n",
    "reg = zero_state(1)\n",
    "new_state = reg |> c\n",
    "for _ in 1:5\n",
    "    new_state |> measure |> println\n",
    "end\n",
    "# plot(c)\n",
    "\n",
    "# WTF I'M BADDDDD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DitStr{2, 16, BigInt}[1001001101010101 ₍₂₎]\n",
      "DitStr{2, 16, BigInt}[0110000100000001 ₍₂₎]\n",
      "DitStr{2, 16, BigInt}[1010111010000101 ₍₂₎]\n",
      "DitStr{2, 16, BigInt}[0110000000100001 ₍₂₎]\n",
      "DitStr{2, 16, BigInt}[1100010101011100 ₍₂₎]\n"
     ]
    }
   ],
   "source": [
    "using FLOYao, Yao\n",
    "\n",
    "N = 16\n",
    "\n",
    "ratio = 0 #if ratio = 0 then pprior() is all 0s\n",
    "function pprior() #For each square, probability ratio that it's white, where ratio ~ N(mean(data), std(data)) /  N; maybe we can vary pprior later?\n",
    "    a = rand(N) .< ratio\n",
    "    return FLOYao.product_state(Int.(a)) #Returns MajoranaReg; Prepares it to be sent through the generator \n",
    "end\n",
    "\n",
    "layers = 5\n",
    "g = chain(N)\n",
    "for _ in 1:layers\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => X), 0.)) #Implemented using qiskit's definition (https://qiskit.org/documentation/stubs/qiskit.circuit.library.RXXGate.html)\n",
    "    end\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => Y), 0.))\n",
    "    end\n",
    "    # for i in 1:N-1\n",
    "    #     push!(g, rot(kron(N, i => Y, i+1 => Y), 0.))\n",
    "    # end\n",
    "    # Not needed YY = XX and IZ and ZI\n",
    "    for i in 1:N\n",
    "        push!(g, put(N, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "nparams = nparameters(g)\n",
    "dispatch!(g, rand(nparams).*2π);\n",
    "\n",
    "z = pprior()\n",
    "reg = z |> g\n",
    "results = []\n",
    "for _ in 1:5\n",
    "    x = reg |> measure\n",
    "    println(x)\n",
    "    push!(results, x)\n",
    "end\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Vector{Float32}:\n",
       " 0.5046749"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Flux\n",
    "using Random\n",
    "\n",
    "N = 100\n",
    "f = Chain(Dense(N, 10, relu), Dense(10, 1, sigmoid))\n",
    "rng = MersenneTwister(1234)\n",
    "f(rand!(rng, ones(N))*3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "MethodError",
     "evalue": "MethodError: no method matching statevec(::MajoranaReg{Float64})\n\nClosest candidates are:\n  statevec(!Matched::ArrayRegOrAdjointArrayReg)\n   @ YaoArrayRegister ~/.julia/packages/YaoArrayRegister/qGeWF/src/register.jl:390\n",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching statevec(::MajoranaReg{Float64})\n",
      "\n",
      "Closest candidates are:\n",
      "  statevec(!Matched::ArrayRegOrAdjointArrayReg)\n",
      "   @ YaoArrayRegister ~/.julia/packages/YaoArrayRegister/qGeWF/src/register.jl:390\n",
      "\n",
      "\n",
      "Stacktrace:\n",
      " [1] |>(x::MajoranaReg{Float64}, f::typeof(statevec))\n",
      "   @ Base ./operators.jl:907\n",
      " [2] top-level scope\n",
      "   @ ~/Desktop/Desktop - Peter’s MacBook Air/Harvard/2.5/PRISE/Project/MatchgateGAN/juliatest.ipynb:16"
     ]
    }
   ],
   "source": [
    "using FLOYao, Yao\n",
    "\n",
    "nq = 2\n",
    "circuit = chain(nq)\n",
    "push!(circuit, put(nq, 1=>Rz(0.5)))\n",
    "\n",
    "regs = []\n",
    "nbatch = 3\n",
    "for _ in 1:nbatch\n",
    "    push!(regs, FLOYao.rand_state(nq))\n",
    "end\n",
    "\n",
    "new_states = regs .|> circuit\n",
    "\n",
    "for i in 1:nbatch\n",
    "    new_states[i] |> state |> println\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Params([Float32[0.20867641 -0.09953784 -0.2744833 -0.060649093; -0.07846074 -0.28188977 0.51880085 0.16879; 0.022156563 0.5367327 -0.32628304 0.023158919; 0.46422225 -0.29927474 0.51862746 -0.46004108; 0.57037085 0.29454353 0.5618482 -0.26967162; 0.55754495 0.438143 0.45003965 0.3186188; 0.46268275 -0.23369958 -0.44315523 0.5249952; -0.40607437 -0.060406543 0.025855698 0.14175853; -0.051993042 -0.36091137 -0.5173313 0.4533024; 0.17403223 0.109289035 -0.31764245 -0.055448454], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.12800086 0.061296966 -0.29575455 -0.50621027 -0.41743946 0.43206602 -0.4413093 0.57333267 0.23807795 0.715324], Float32[0.0]])\n"
     ]
    }
   ],
   "source": [
    "using Flux\n",
    "\n",
    "N = 4\n",
    "\n",
    "f = Chain(Dense(N, 10, relu), Dense(10, 1, sigmoid))\n",
    "println(Flux.params(f))\n",
    "#Flux.params(f) .= randn.(Flux.params(f))\n",
    "#println(\"randomized params\"Flux.params(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
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     "output_type": "display_data"
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   ],
   "source": [
    "using Random\n",
    "using Plots\n",
    "\n",
    "n = 5\n",
    "nbatch = 25\n",
    "\n",
    "function bars_and_stripes(nbatch = 10)\n",
    "    data = []\n",
    "    for i in 1:nbatch\n",
    "        S = Int64[]\n",
    "        while length(S) == 0 #Ensures length(S) is not 0 so we get truly uniform distribution over the whole bars and stripes dataset\n",
    "            randsubseq!(S, collect(1:n), 0.5)\n",
    "        end\n",
    "        if 1 in S\n",
    "            b = repeat(Bool[1], n)\n",
    "        else\n",
    "            b = repeat(Bool[0], n)\n",
    "        end\n",
    "        for i in 2:n\n",
    "            temp = repeat(Bool[0], n)\n",
    "            if i in S\n",
    "                temp = repeat(Bool[1], n)\n",
    "            end\n",
    "            b = hcat(b, temp)\n",
    "        end\n",
    "        flip = rand() < 0.5\n",
    "        if length(S) == n\n",
    "            ret = flip ? b : .!b\n",
    "        else\n",
    "            ret = flip ? b : rotl90(b)\n",
    "        end\n",
    "        push!(data, ret)\n",
    "    end\n",
    "    return data\n",
    "end\n",
    "\n",
    "plot([heatmap(x, color=:grays, colorbar = false, ticks = false) for x in bars_and_stripes(nbatch)]...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bool[0 0 0; 0 0 0; 0 0 0; 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "using Combinatorics\n",
    "using Plots\n",
    "\n",
    "#Query\n",
    "#Pick a random subset of {1,...,n} (could be empty or the entire set), then flip a coin (corresponds to rows or columns)\n",
    "#parameters: nbatch, n\n",
    "\n",
    "n = 4\n",
    "\n",
    "#modification: sample s uniformly at random from all possible subsets, run make_data, and also with half probability, do rotl90\n",
    "function make_data(s)\n",
    "    if 1 in s\n",
    "        b = Bool[1 1 1]\n",
    "    else\n",
    "        b = Bool[0 0 0]\n",
    "    end\n",
    "    for i in 2:n\n",
    "        if i in s\n",
    "            b = vcat(b, Bool[1 1 1])\n",
    "        else\n",
    "            b = vcat(b, Bool[0 0 0])\n",
    "        end\n",
    "    end\n",
    "    return b\n",
    "end\n",
    "\n",
    "my_set = Set(1:n)\n",
    "\n",
    "# Generate all subsets\n",
    "all_subsets = powerset(collect(my_set))\n",
    "\n",
    "data = []\n",
    "\n",
    "for subset in all_subsets\n",
    "    push!(data, make_data(subset))\n",
    "end\n",
    "\n",
    "for i in 2:(2^n - 1)\n",
    "    push!(data, data[i] |> rotl90)\n",
    "end\n",
    "\n",
    "plot([heatmap(x, color=:grays, colorbar = false, ticks = false) for x in data]...)\n",
    "\n",
    "# Iterate over all subsets\n",
    "# for subset in all_subsets\n",
    "#     println(Set(subset))\n",
    "# end\n",
    "\n",
    "println(data[1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bool[0 0 1; 0 0 1; 0 0 1]"
     ]
    },
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Plots\n",
    "\n",
    "data_train = []\n",
    "\n",
    "push!(data_train,Bool[0 0 0;0 0 0; 0 0 0])\n",
    "push!(data_train,Bool[0 0 0;0 0 0; 1 1 1])\n",
    "push!(data_train,Bool[0 0 0;1 1 1; 0 0 0])\n",
    "push!(data_train,Bool[1 1 1;0 0 0; 0 0 0])\n",
    "push!(data_train,Bool[1 1 1;1 1 1; 0 0 0])\n",
    "push!(data_train,Bool[1 1 1;0 0 0; 1 1 1])\n",
    "push!(data_train,Bool[0 0 0;1 1 1; 1 1 1])\n",
    "push!(data_train,Bool[1 1 1;1 1 1; 1 1 1])\n",
    "\n",
    "print(data_train[2] |> rotl90)\n",
    "\n",
    "for i in 2:7\n",
    "    push!(data_train, data_train[i] |> rotl90)\n",
    "end\n",
    "\n",
    "# for d in data_train\n",
    "#     print(d)\n",
    "# end\n",
    "# for d in data_train\n",
    "#     push!(data_train, rotl90(d))\n",
    "# end\n",
    "\n",
    "plot([heatmap(x, color=:grays, colorbar = false, ticks = false) for x in data_train]...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "ename": "ArgumentError",
     "evalue": "ArgumentError: number of rows of each array must match (got (5, 5, 1, 5, 1, 1, 1, 5, 5, 5))",
     "output_type": "error",
     "traceback": [
      "ArgumentError: number of rows of each array must match (got (5, 5, 1, 5, 1, 1, 1, 5, 5, 5))\n",
      "\n",
      "Stacktrace:\n",
      " [1] _typed_hcat(#unused#::Type{Int64}, A::Tuple{Vector{Int64}, Vector{Int64}, Matrix{Int64}, Vector{Int64}, Matrix{Int64}, Matrix{Int64}, Matrix{Int64}, Vector{Int64}, Vector{Int64}, Vector{Int64}})\n",
      "   @ Base ./abstractarray.jl:1652\n",
      " [2] typed_hcat(::Type{Int64}, ::Vector{Int64}, ::Vector{Int64}, ::Matrix{Int64}, ::Vararg{AbstractVecOrMat})\n",
      "   @ Base ./abstractarray.jl:1639\n",
      " [3] hcat(::Vector{Int64}, ::Vector{Int64}, ::Matrix{Int64}, ::Vararg{VecOrMat{Int64}})\n",
      "   @ Base ./array.jl:1956\n",
      " [4] generate_bars_and_stripes(n_samples::Int64, image_size::Int64)\n",
      "   @ Main ~/Desktop/Harvard/2.5/PRISE/Project/MatchgateGAN/juliatest.ipynb:25\n",
      " [5] top-level scope\n",
      "   @ ~/Desktop/Harvard/2.5/PRISE/Project/MatchgateGAN/juliatest.ipynb:43"
     ]
    }
   ],
   "source": [
    "using Random\n",
    "using Plots\n",
    "\n",
    "function generate_bars_and_stripes(n_samples, image_size)\n",
    "    dataset = []\n",
    "    labels = []\n",
    "\n",
    "    for i in 1:n_samples\n",
    "        # Randomly choose whether to generate a bar or a stripe\n",
    "        is_bar = rand([true, false])\n",
    "\n",
    "        # Generate the image\n",
    "        if is_bar\n",
    "            image = hcat(fill(1, image_size)...)\n",
    "            label = 1  # 1 represents a bar\n",
    "        else\n",
    "            image = vcat(fill(1, image_size)...)\n",
    "            label = 0  # 0 represents a stripe\n",
    "        end\n",
    "\n",
    "        push!(dataset, image)\n",
    "        push!(labels, label)\n",
    "    end\n",
    "\n",
    "    return hcat(dataset...), labels\n",
    "end\n",
    "\n",
    "function plot_bars_and_stripes(data, labels, image_size)\n",
    "    n_samples = length(labels)\n",
    "    plot_grid = reshape(data, image_size, image_size, n_samples)\n",
    "\n",
    "    plot_array = []\n",
    "    for i in 1:n_samples\n",
    "        push!(plot_array, heatmap(1:image_size, 1:image_size, plot_grid[:, :, i], c=:grays, color=:black, axis=false))\n",
    "    end\n",
    "\n",
    "    plot(plot_array..., layout=(1, n_samples), legend=false)\n",
    "end\n",
    "\n",
    "# Example usage\n",
    "n_samples = 10\n",
    "image_size = 5\n",
    "data, labels = generate_bars_and_stripes(n_samples, image_size)\n",
    "plot_bars_and_stripes(data, labels, image_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "144"
     ]
    }
   ],
   "source": [
    "using Flux\n",
    "\n",
    "function create_cnn()\n",
    "    return Chain(\n",
    "        Conv((3, 3), 1=>16, relu, bias = false), #Want to train 16 kernels, params = each entry in the kernel + the bias\n",
    "        # MaxPool((2, 2)),\n",
    "        # Conv((3, 3), 16=>32, relu),\n",
    "        # MaxPool((2, 2)),\n",
    "        # Flux.flatten,\n",
    "        # Dense(50, 20, relu),\n",
    "        # Dense(20, 10)\n",
    "    )\n",
    "end\n",
    "\n",
    "function nparams(model)\n",
    "    sum(length, Flux.params(model))\n",
    "end\n",
    "\n",
    "n = create_cnn()\n",
    "Flux.params(n)\n",
    "print(nparams(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BatchedArrayReg{2, ComplexF64, Transpose...}\n",
       "    active qubits: 4/4\n",
       "    nlevel: 2\n",
       "    nbatch: 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Yao\n",
    "using FLOYao\n",
    "\n",
    "nbatch = 10\n",
    "yao_reg = zero_state(4; nbatch)\n",
    "floyao_reg = FLOYao.zero_state(4; nbatch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "5"
     ]
    }
   ],
   "source": [
    "function asdf(; a = 2, b = 3)\n",
    "    a + b\n",
    "end\n",
    "\n",
    "result = asdf(b = 5)\n",
    "println(result)  # This will correctly print 7\n",
    "\n",
    "if 2<3 & 3<4\n",
    "    print(5)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9776682445628029, 0.0, 0.0, 0.02233175543719699]\n",
      "[0.9776682445628031, 0.0, 0.0, 0.02233175543719693]\n"
     ]
    }
   ],
   "source": [
    "using Yao\n",
    "using FLOYao\n",
    "using Statistics\n",
    "\n",
    "N = 2\n",
    "\n",
    "g = chain(N)\n",
    "push!(g, rot(kron(N, 1 => X, 2 => X), 0.)) #Rxx on two qubits\n",
    "dispatch!(g, [0.3])\n",
    "\n",
    "t = zero_state(N)\n",
    "t |> g |> probs |> println\n",
    "\n",
    "dispatch!(g, [0.3 + 2π])\n",
    "\n",
    "t = zero_state(N)\n",
    "t |> g |> probs |> println"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true gradient: 0.42957693580613227\n",
      "original loss: 0.7596"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "original true loss: 0.7558586645462962\n",
      "plus: 0.7586\n",
      "plus true loss: 0.7558629603028613\n",
      "true finitediff: 0.4295756565020347\n",
      "-0.0010000000000000009\n",
      "4.295756565020348e-6\n",
      "[-100.00000000000009]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.4304]\n"
     ]
    }
   ],
   "source": [
    "using Yao\n",
    "using FLOYao\n",
    "using Statistics\n",
    "\n",
    "N = 2\n",
    "\n",
    "g = chain(N)\n",
    "push!(g, rot(kron(N, 1 => X, 2 => X), 0.)) #Rxx on two qubits\n",
    "dispatch!(g, rand(nparameters(g)).*2π)\n",
    "theta = first(parameters(g))\n",
    "println(\"true gradient: \", sin(theta)/2)\n",
    "\n",
    "function loss(theta = theta)\n",
    "    sin(theta/2)^2\n",
    "end\n",
    "\n",
    "ratio = 0\n",
    "function pprior() #For each square, probability ratio that it's white, where ratio ~ N(mean(data), std(data)) /  N; maybe we can vary pprior later?\n",
    "    a = rand(N) .< ratio\n",
    "    return FLOYao.product_state(Int.(a)) #Returns MajoranaReg; Prepares it to be sent through the generator \n",
    "end\n",
    "\n",
    "function postprocess(g_output::Vector) #turns the output of reg |> g |> measure into an Int vector\n",
    "    result = []\n",
    "    for i in 1:N \n",
    "        push!(result, g_output[1][end - i + 1])\n",
    "    end\n",
    "    Int.(result)\n",
    "end\n",
    "\n",
    "samplemean_batch = 5000\n",
    "function run_g(nbatch = samplemean_batch)\n",
    "    samples = []\n",
    "    for i in 1:nbatch\n",
    "        z = pprior() #MajoranaReg object\n",
    "        result = z |> g |> measure |> postprocess\n",
    "        if i == 1\n",
    "            samples = result\n",
    "        else\n",
    "            samples = hcat(samples, result) #is this operation slow; on another note there has to be a better way to write this function right\n",
    "        end\n",
    "    end\n",
    "    samples\n",
    "end\n",
    "#outputs an N * #samples matrix\n",
    "\n",
    "function run_d_fake(samples)\n",
    "    # if size(samples)[1] != N || typeof(samples) != Matrix{Int64} #Require samples to be an N x #samples matrix\n",
    "    #     println(\"Improper formatting of samples\")\n",
    "    #     return\n",
    "    # end\n",
    "    # samples |> d\n",
    "    mean(samples, dims = 1)\n",
    "end\n",
    "\n",
    "function gLoss(nbatch = samplemean_batch)\n",
    "    #-mean(log.(run_d_fake(run_g(nbatch))))\n",
    "    mean(run_d_fake(run_g(nbatch)))\n",
    "end\n",
    "\n",
    "eps = 1e-5\n",
    "function finitediff_grad(g = g, eps = eps) #Computes forward finite differences\n",
    "    original = gLoss()\n",
    "    println(\"original loss: $original\")\n",
    "    a = loss(theta)\n",
    "    println(\"original true loss: $a\")\n",
    "    temp_params = parameters(g)\n",
    "    grad = zeros(nparameters(g))\n",
    "    temp = 0\n",
    "    for i in 1:nparameters(g)\n",
    "        plus = 0\n",
    "        temp = parameters(g)[i]\n",
    "        temp_params[i] = temp + eps\n",
    "        dispatch!(g, temp_params)\n",
    "        plus = gLoss()\n",
    "        println(\"plus: $plus\")\n",
    "        b = loss(theta + eps)\n",
    "        println(\"plus true loss: $b\")\n",
    "        grad[i] = (plus - original) / eps #(L(θ+ε_i) - L(θ))/ε; L is computed by sample means\n",
    "        println(\"true finitediff: \", (b-a) / eps)\n",
    "        println(plus - original)\n",
    "        println(b - a)\n",
    "        temp_params[i] = temp\n",
    "        dispatch!(g, temp_params)\n",
    "    end\n",
    "    grad\n",
    "end\n",
    "\n",
    "function parametershift_grad()\n",
    "    temp_params = parameters(g)\n",
    "    grad = zeros(nparameters(g))\n",
    "    for i in 1:nparameters(g)\n",
    "        plus = 0\n",
    "        minus = 0\n",
    "        temp = parameters(g)[i]\n",
    "        temp_params[i] = temp + π/2\n",
    "        dispatch!(g, temp_params)\n",
    "        plus = gLoss()\n",
    "        temp_params[i] = temp - π/2\n",
    "        dispatch!(g, temp_params)\n",
    "        minus = gLoss()\n",
    "        grad[i] = (plus - minus) / 2\n",
    "        temp_params[i] = temp\n",
    "        dispatch!(g, temp_params)\n",
    "    end\n",
    "    grad\n",
    "end\n",
    "\n",
    "finitediff_grad() |> println\n",
    "parametershift_grad() |> println\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = chain(N)\n",
    "push!(g, rot(kron(N, 1 => X, 2 => X), 0.)) #Rxx on two qubits\n",
    "dispatch!(g, rand(nparameters(g)).*2π)\n",
    "\n",
    "batch = 100\n",
    "function gLoss(nbatch = batch)\n",
    "    \n",
    "end\n",
    "\n",
    "function parametershift_grad()\n",
    "    temp_params = parameters(g)\n",
    "    grad = zeros(nparameters(g))\n",
    "    for i in 1:nparameters(g)\n",
    "        plus = 0\n",
    "        minus = 0\n",
    "        temp = parameters(g)[i]\n",
    "        temp_params[i] = temp + 0.5 #CHECK HOW SCALING WORKS FOR PARAMETERS\n",
    "        dispatch!(g, temp_params)\n",
    "        plus = gLoss()\n",
    "        temp_params[i] = temp - 0.5\n",
    "        dispatch!(g, temp_params)\n",
    "        minus = gLoss()\n",
    "        grad[i] = (minus - plus) / 2\n",
    "        temp_params[i] = temp\n",
    "        dispatch!(g, temp_params)\n",
    "    end\n",
    "    grad\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train = 4\n",
    "digit = 6\n",
    "\n",
    "train_set = MNIST(:train)\n",
    "train_labels = MNIST(split=:train).targets\n",
    "\n",
    "data_train = []\n",
    "c = 1\n",
    "for _ in 1:train\n",
    "    while train_labels[c] != digit\n",
    "        c += 1\n",
    "    end\n",
    "    push!(data_train, rotl90(train_set[c][1]) .> 0.5)\n",
    "    c += 1\n",
    "end\n",
    "\n",
    "plot([heatmap(x, color=:grays, colorbar = false, ticks = false) for x in data_train]...) #Is there any way to make this look nicer? oh well it's not a big deal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "RU5ErkJggg==\n",
       "\" transform=\"translate(47, 47)\"/>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using MLDatasets\n",
    "using Plots\n",
    "using Pipe\n",
    "\n",
    "train_set = MNIST(:train)\n",
    "\n",
    "x = train_set[1][1] .> 0.5\n",
    "#plot(heatmap(rotl90(x), color=:grays, colorbar = false, ticks = false))\n",
    "\n",
    "@pipe x |> vec |> reshape(_,28,28) |> plot(heatmap(rotl90(_), color=:grays, colorbar = false, ticks = false))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5454626686557851, 0.7574492625513849, 0.8288533351588325, 0.8121839130737354, 0.12552915101072648, 0.9449062360449023, 0.5463687791664117, 0.09229772257843483, 0.5568924549066308, 0.5606486321948967, 0.010461406276843888, 0.9396887583769711, 0.5033459341696521, 0.1588589384576673, 0.20351001955108505, 0.023185381445060105, 0.020737005973914036, 0.7693453064289135, 0.4291949836119133, 0.038512856382333926, 0.4138697495045821, 0.3528613744291771, 0.0886504059715808, 0.7546837896669328, 0.9065112630180457, 0.014435950938044062, 0.31341134606466803, 0.8191564311438772, 0.014977154750417832, 0.19440099431543445, 0.022222811440033463, 0.2803969484485763, 0.1863378011903839, 0.9780947319509354, 0.9770000768581694, 0.9695813150441435, 0.22121343888594558, 0.5430396689439804, 0.8361670777653141, 0.4457170689144183, 0.29415865993639234, 0.6995218848765529, 0.773505573960813, 0.8338676902023647, 0.6136888339641369, 0.42417479772483313, 0.44765139314548197, 0.23702216203722126, 0.8979280257836546, 0.5602480440219287, 0.7573779590931555, 0.9090742768287515, 0.8606376912411616, 0.7262289293053301, 0.3937299845563429, 0.44005642525581656, 0.5319547529472646, 0.6542371555708973, 0.3884457334009249, 0.9482723408165142, 0.2403737028438262, 0.5663037358714048, 0.7206795813519381, 0.03390801795774068, 0.3514962773885498, 0.8473268019364545, 0.053754013366613784, 0.30084869222103205, 0.20592040132756184, 0.38543041804431266, 0.3914328318414949, 0.6296730207037385, 0.4903808474595429, 0.6396942685844448, 0.7269079773209252, 0.7213379452564345, 0.8862922144207886, 0.7441939885507873, 0.849579617583642, 0.6250897349988238, 0.48314671076382587, 0.6153077311921927, 0.9225528917914065, 0.19888851810291563, 0.32321774326861064, 0.7028002888989304, 0.02768911811534014, 0.5953924964992539, 0.06014905147896321, 0.548381687326715, 0.07030412265168728, 0.33405318899478664, 0.7964849561113981, 0.6742690203665617, 0.7973883259378004, 0.930888953834794, 0.28717945261814626, 0.2798159407891324, 0.8891496186683855, 0.41809988588990143, 0.981666815706195, 0.9613899059788584, 0.41378314765567825, 0.942632752294508, 0.4966501528949542, 0.09723656649317536, 0.7615421828671134, 0.1903115607158138, 0.3866461439664155, 0.9935923350689152, 0.5744232931035761, 0.3992191089327253, 0.6873376927040766, 0.3339904939704532, 0.10888085834720096, 0.6171214286146958, 0.6373901273638236, 0.3663931837651436, 0.08007761578784023, 0.5561306942747316, 0.3797764525342131, 0.21652936898201314, 0.10060204348593504, 0.6888042884915329, 0.18184384864519032, 0.41520051042534245, 0.27639832091679617, 0.2874800379210549, 0.5448755088870026, 0.9296529219479072, 0.8115402738881511, 0.14083918556317732, 0.24629791880124208, 0.3264164206029614, 0.9545832613501553, 0.34569695355414964, 0.7225425713718997, 0.8567982831353423, 0.8360335640279568, 0.7625871244087875, 0.809544357538341, 0.20704834140761263, 0.8122977182817037, 0.89429402471085, 0.37409216543365753, 0.937143658828154, 0.8435866874878712, 0.5016347475894488, 0.7203040779051336, 0.8398667714658543, 0.35480035436439494, 0.10522284063184495, 0.2674980671838326, 0.18051862119208506, 0.09851563791585605, 0.776988672749135, 0.842682119177488, 0.5095548727468128, 0.43531028496200375, 0.9804581576651497, 0.26180210338730403, 0.5108610064913492, 0.12802739300811028, 0.26048913206412216, 0.47925531047801184, 0.0615381736158328, 0.058409437110250706, 0.3112580852900676, 0.5407936867897314, 0.8398209562673692, 0.1809432327111773, 0.3141303082121243, 0.38653690412906194, 0.47140235407761233, 0.9859121939546915, 0.6498745826395818, 0.7177038107924223, 0.8113588289929323, 0.9173864141504489, 0.6244282737985856, 0.9780269965774994, 0.08655639435581075, 0.970811550101768, 0.9597361223387076, 0.9743699316807422, 0.061685847650022274, 0.1558395751946945, 0.3396809036788606, 0.8227398159792941, 0.14897617460128454, 0.7056305141647072, 0.7515425747948269, 0.5146522843709697, 0.6062709074623442, 0.2633049556672685, 0.1737176862031422, 0.8008722608905997, 0.9826662443474544, 0.769869391597624, 0.10183927052832298, 0.6562962617601443, 0.8067329328564792, 0.3753173664286281, 0.3570653441788715, 0.05738025484479736, 0.4277498408212026, 0.3066363921560049, 0.36306027528724716, 0.322375314981875, 0.8342519996669411, 0.9851135173291669, 0.21937971029915437, 0.7093016978576271, 0.4234728329978813, 0.7633140996939424, 0.9655955348910965, 0.3396591978387008, 0.8712848083821441, 0.5389271588868905, 0.5007658226448296, 0.41678776280335206, 0.8171631799819219, 0.3459440055008378, 0.0009138199045322093, 0.27848172359754353, 0.3166608905804127, 0.8429423502283416, 0.35704047864954436, 0.33361695234691024, 0.5564342780242109, 0.036299362034717064, 0.6312811089803845, 0.4676088719790038, 0.9540083053484033, 0.6034918402783753, 0.43414060715085445, 0.3579940462938286, 0.3589705562842217, 0.8338759118763048, 0.2752965411870433, 0.11885219653404833, 0.8878701187234893, 0.8702576261771535, 0.7542962101986084, 0.28945212666920717]\n"
     ]
    },
    {
     "ename": "UndefVarError",
     "evalue": "UndefVarError: `gradient` not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: `gradient` not defined\n",
      "\n",
      "Stacktrace:\n",
      " [1] top-level scope\n",
      "   @ ~/Desktop/Harvard/2.5/PRISE/Project/Matchgate/FLOYao/juliatest.ipynb:17"
     ]
    }
   ],
   "source": [
    "using Yao\n",
    "\n",
    "N = 25\n",
    "layers = 5\n",
    "g = chain(N) #Making the generator, which is a matchgate ansatz\n",
    "for _ in 1:layers\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => X), 0.))\n",
    "    end\n",
    "    for i in 1:N\n",
    "        push!(g, put(N, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "dispatch!(g, :random)\n",
    "println(parameters(g))\n",
    "println(gradient(g))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "UndefVarError",
     "evalue": "UndefVarError: `autodiff` not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: `autodiff` not defined\n",
      "\n",
      "Stacktrace:\n",
      " [1] getproperty(x::Module, f::Symbol)\n",
      "   @ Base ./Base.jl:31\n",
      " [2] top-level scope\n",
      "   @ ~/Desktop/Harvard/2.5/PRISE/Project/Matchgate/FLOYao/juliatest.ipynb:3"
     ]
    }
   ],
   "source": [
    "using Yao\n",
    "circuit = chain(4, repeat(4, H, 1:4), put(4, 3=>Rz(0.5)), control(2, 1=>X), put(4, 4=>Ry(0.2)))\n",
    "circuit = circuit |> Yao.autodiff(:BP) #???????"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial Parameters:\n",
      "Float32[0.2586 0.2564478 -0.14705507 -0.6034778 -0.006969022 -0.55017704 -0.6041567 -0.5692597 0.5514455 0.40842122; 0.37690863 0.123033695 0.05006682 0.4423845 -0.63022286 0.43721518 -0.5289191 -0.38148215 0.47268787 -0.30389434; 0.18071061 0.6046077 0.25994346 0.4808553 -0.47517708 0.51701206 0.19030918 0.07959194 -0.48305234 0.037443433; 0.45869675 -0.21159495 -0.19798404 0.5784383 -0.0682152 -0.3134224 0.07947719 0.60297364 -0.3178038 0.28330582; 0.450709 -0.44164377 -0.38924357 0.023509612 -0.22734238 0.25996125 -0.3176807 -0.3897135 0.3003256 0.34115252]\n",
      "Float32[0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "Float32[-0.46451345 -0.7161916 0.30781022 -0.5166258 -0.29030392; -0.772016 0.45951253 -0.09930434 0.38461727 -0.91004753]\n",
      "Float32[0.0, 0.0]\n"
     ]
    },
    {
     "ename": "ErrorException",
     "evalue": "cannot assign a value to imported variable Flux.params from module Main",
     "output_type": "error",
     "traceback": [
      "cannot assign a value to imported variable Flux.params from module Main\n",
      "\n",
      "Stacktrace:\n",
      " [1] top-level scope\n",
      "   @ ~/Desktop/Harvard/2.5/PRISE/Project/Matchgate/FLOYao/juliatest.ipynb:12"
     ]
    }
   ],
   "source": [
    "using Flux\n",
    "\n",
    "# Define a simple neural network\n",
    "model = Chain(Dense(10, 5, relu), Dense(5, 2))\n",
    "\n",
    "# Display the initial parameters\n",
    "println(\"Initial Parameters:\")\n",
    "for p in params(model)\n",
    "    println(p)\n",
    "end\n",
    "const initial = params\n",
    "params = params(model)\n",
    "println(\"initial: \", initial)\n",
    "\n",
    "# Suppose you have new parameter values as vectors (of the correct dimensions)\n",
    "new_params_layer1 = randn(5, 10)\n",
    "new_params_layer2 = randn(5)\n",
    "new_params_layer3 = randn(2, 5)\n",
    "new_params_layer4 = randn(2)\n",
    "\n",
    "# Set the new parameters\n",
    "println(\"length \", length(params(model)))\n",
    "params_layer1, params_layer2, params_layer3, params_layer4 = params(model)\n",
    "println(size(params_layer1))\n",
    "println(size(params_layer2))\n",
    "println(size(params_layer3))\n",
    "println(size(params_layer4))\n",
    "params_layer1 .= new_params_layer1  # Use broadcasting assignment .=\n",
    "params_layer2 .= new_params_layer2\n",
    "params_layer3 .= new_params_layer3\n",
    "params_layer4 .= new_params_layer4\n",
    "println(\"initial: \", initial)\n",
    "\n",
    "# Display the updated parameters\n",
    "println(\"\\nUpdated Parameters:\")\n",
    "for p in Flux.params(model)\n",
    "    println(p)\n",
    "end\n",
    "\n",
    "new_params_layer1, new_params_layer2, new_params_layer3, new_params_layer4 = initial\n",
    "println(\"asdf \", new_params_layer1)\n",
    "params_layer1, params_layer2, params_layer3, params_layer4 = params(model)\n",
    "params_layer1 .= new_params_layer1  # Use broadcasting assignment .=\n",
    "params_layer2 .= new_params_layer2\n",
    "params_layer3 .= new_params_layer3\n",
    "params_layer4 .= new_params_layer4\n",
    "\n",
    "println(\"\\nInitial Parameters:\")\n",
    "for p in Flux.params(model)\n",
    "    println(p)\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13\n",
      "asdf Params([Float32[-0.82332647 -0.59481263 -0.40093803 0.38192046; -0.9954989 0.3614949 0.47065997 0.6134633], Float32[0.0, 0.0], Float32[0.017256774 -0.73138165], Float32[0.0]])\n",
      "[10.0 30.0; 20.0 40.0]\n",
      "Params([Float32[-0.82332647 -0.59481263 -0.40093803 0.38192046; -0.9954989 0.3614949 0.47065997 0.6134633], Float32[0.0, 0.0], Float32[0.017256774 -0.73138165], Float32[0.0]])\n",
      "Params(["
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Float32[-0.82332647 -0.59481263 -0.40093803 0.38192046; -0.9954989 0.3614949 0.47065997 0.6134633], Float32[0.0, 0.0], Float32[0.017256774 -0.73138165], Float32[0.0]])\n"
     ]
    }
   ],
   "source": [
    "using Flux\n",
    "using LinearAlgebra\n",
    "using Random\n",
    "\n",
    "Random.seed!(2)\n",
    "\n",
    "function n(a::Vector)\n",
    "    return a[1]\n",
    "end\n",
    "\n",
    "model = Chain(\n",
    "    Dense(4, 2, relu),\n",
    "    Dense(2, 1),\n",
    "    softmax\n",
    ")\n",
    "\n",
    "println(sum(length, Flux.params(model)))\n",
    "\n",
    "data = [([1,2,3,4], 2), ([2,3,4,5], 3), ([3,4,5,6], 3)]\n",
    "x = [1,2,3,4]\n",
    "y = 2\n",
    "loss3(m, x, y) = norm(m(x) .- y)     # the model is the first argument\n",
    "\n",
    "opt_state = Flux.setup(Adam(), model)\n",
    "\n",
    "initial = Flux.params(model)\n",
    "println(\"asdf \", initial)\n",
    "# for p in Flux.params(model)\n",
    "#     p .= (ones(size(p)) .* 0.08)\n",
    "# end\n",
    "\n",
    "# epochs = 10\n",
    "# for i in 1:epochs\n",
    "#     Flux.train!(loss3, model, data, opt_state) \n",
    "#     s = 0\n",
    "#     for d in data\n",
    "#         s += loss3(model, d[1], d[2])\n",
    "#     end\n",
    "#     println(\"iteration $i: loss is $s\")\n",
    "# end\n",
    "\n",
    "A = zeros(2,2)\n",
    "setindex!(A, [10,20], [1,2])\n",
    "A[[3, 4]] = [30, 40]\n",
    "println(A)\n",
    "\n",
    "println(Flux.params(model))\n",
    "\n",
    "Flux.train!(loss3, model, data, opt_state)\n",
    "#nparams = sum(length, Flux.params(model))\n",
    "\n",
    "# for i in 1:nparams\n",
    "#     #Flux.params(model)[i] = initial[i]\n",
    "#     setindex!(Flux.params(model), initial[i],)\n",
    "# end\n",
    "\n",
    "println(Flux.params(model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Float32[0.5029387, 0.4970613]\n",
      "Float32[0.52733314, 0.47266683]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "10×2 Matrix{Float64}:\n",
       " 0.0262499  0.979999\n",
       " 0.332267   0.141428\n",
       " 0.75646    0.554159\n",
       " 0.154411   0.393257\n",
       " 0.461534   0.627533\n",
       " 0.818963   0.352821\n",
       " 0.912385   0.921515\n",
       " 0.948366   0.962068\n",
       " 0.104596   0.253137\n",
       " 0.736038   0.346649"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Flux\n",
    "\n",
    "# model = Chain(\n",
    "#     Dense(4, 2, relu),\n",
    "#     Dense(2, 1),\n",
    "#     softmax\n",
    "# )\n",
    "\n",
    "# println(Flux.params(model))\n",
    "# x = rand(Float32, 4)\n",
    "# println(x)\n",
    "# model(x)\n",
    "\n",
    "model2 = Chain(\n",
    "  Dense(10 => 5, σ),\n",
    "  Dense(5 => 2),\n",
    "  softmax)\n",
    "\n",
    "x = rand(10)\n",
    "y = rand(10)\n",
    "model2(x) |> println\n",
    "model2(y) |> println\n",
    "hcat(x,y)\n",
    "#model2(hcat(x,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux\n",
    "\n",
    "N = 196\n",
    "\n",
    "function NeuralNetwork(num_dim = N, random = true)\n",
    "    net = Chain(Dense(num_dim, 25, relu), Dense(25, 1, x -> σ.(x)))\n",
    "    if !random\n",
    "        for p in Flux.params(net)\n",
    "            p .= ones(size(p)) .* 0.08\n",
    "        end\n",
    "    end\n",
    "    return x -> first(net(x))\n",
    "end\n",
    "\n",
    "\n",
    "d = NeuralNetwork()\n",
    "d(ones(196))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function dLoss(data::Vector) #the first half of data is D's output on real, the second half is D's output on fake\n",
    "    len = length(data)÷2\n",
    "    real = data[1:len]\n",
    "    fake = data[len+1:end]\n",
    "    (sum(log.(real)) + sum(log.(1 .- fake))) / len\n",
    "end\n",
    "\n",
    "print(dLoss([0.5,0.5,0.5,0.5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using FLOYao\n",
    "\n",
    "a = FLOYao.zero_state(4)\n",
    "\n",
    "typeof(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "\n",
    "# Sample data (matrices)\n",
    "data_matrices = [rand(3, 3) for _ in 1:4]  # Create an array of 4 random 3x3 matrices\n",
    "\n",
    "# Create an array of heatmap plots\n",
    "heatmaps = [heatmap(data_matrix, title=\"Heatmap $i\", color=:grays, c=:auto) for (i, data_matrix) in enumerate(data_matrices)]\n",
    "\n",
    "# Combine the heatmaps into a single plot\n",
    "plot(heatmaps..., layout=(2, 2))  # Arrange heatmaps in a 2x2 grid\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux\n",
    "\n",
    "# # Create a sample input tensor (4x4) with random values\n",
    "# input_tensor = rand(4, 4)\n",
    "\n",
    "# # Perform average pooling with a pooling size of 2x2 and a stride of 2\n",
    "# pooled_tensor = Flux.MeanPool(input_tensor, (2, 2), (2, 2))\n",
    "\n",
    "# println(\"Original tensor:\")\n",
    "# println(input_tensor)\n",
    "# println(\"Pooled tensor:\")\n",
    "# println(pooled_tensor)\n",
    "\n",
    "\n",
    "xs = rand(Float32, 100, 100, 3, 50);\n",
    "\n",
    "m = Chain(Conv((5,5), 3 => 7), MeanPool((5,5), pad=SamePad()))\n",
    "Chain(\n",
    "  Conv((5, 5), 3 => 7),                 # 532 parameters\n",
    "  MeanPool((5, 5), pad=2),\n",
    ")\n",
    "\n",
    "m[1](xs) |> size\n",
    "#(96, 96, 7, 50)\n",
    "\n",
    "m(xs) |> size\n",
    "#(20, 20, 7, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux\n",
    "\n",
    "function NeuralNetwork()\n",
    "    return Chain(\n",
    "            Dense(2, 25,relu),\n",
    "            Dense(25,1,x->σ.(x))\n",
    "            )\n",
    "end\n",
    "\n",
    "m = NeuralNetwork()\n",
    "\n",
    "#Flux.params(m)\n",
    "\n",
    "print(m([1,2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_size = 5\n",
    "N = image_size * image_size\n",
    "\n",
    "ratio = 1/2\n",
    "function pprior() #For each square, probability 1/ratio that it's white, where ratio ~ N(mean(data), std(data)); maybe we can vary pprior later?\n",
    "    return rand(N) .< ratio\n",
    "end\n",
    "\n",
    "x = Int.(pprior())\n",
    "x |> println\n",
    "\n",
    "#heatmap(rotl90(reshape(x, image_size, image_size)) .> 0.5, color=:grays, colorbar = false, ticks = false)\n",
    "\n",
    "using FLOYao\n",
    "using Yao\n",
    "\n",
    "state1 = FLOYao.product_state([0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0])\n",
    "eeeee = FLOYao.product_state(x) \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Yao\n",
    "using FLOYao\n",
    "\n",
    "n = 4\n",
    "t = FLOYao.rand_state(n)\n",
    "print(typeof(t))\n",
    "\n",
    "t |> probs |> println\n",
    "\n",
    "v = state(t)\n",
    "sum =  0\n",
    "for x in v\n",
    "    sum += abs2(x)\n",
    "end\n",
    "println(sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.4186772651923395, 0.9443010326818442, 0.9604670690207017, 0.5014306245878104, 0.014814455133769333, 0.6637267892324535, 0.8004070214160125, 0.9933734646203043, 0.49515398288064283, 0.6727919478530155, 0.9453560786450677, 0.710193597552303, 0.07214187955821183, 0.8230923362961615, 0.08832122393214437, 0.40454056488880863, 0.7390263600292579, 0.5797557119669229, 0.30810036517773787, 0.6289055969175638, 0.5962374481127165, 0.6674566970526364, 0.3979664999995305, 0.2099511355743473, 0.4881279629787322, 0.721705513844638, 0.5959050022663406, 0.5104686890941542, 0.0906731497983767, 0.4016255460353315, 0.19651094999005136, 0.7133541848227378, 0.2259995313122779, 0.785819033906092, 0.35806641608012, 0.19741465119134816, 0.8937175847359243, 0.6891482434572337, 0.11512139314014469, 0.06888338178360953, 0.7300923035673231, 0.07082591622038015, 0.29573783538328047, 0.26422556923924934, 0.3990292986480022, 0.23689209314395354, 0.6309343564611205, 0.5260734735640302, 0.2257064801596993, 0.484390236773382, 0.45502859215382985, 0.647098094391134, 0.038417648150330774, 0.5153836945373883, 0.6774330588123008, 0.36636331651374154, 0.4284363550938708, 0.5746681768664929, 0.7431118350246343, 0.2585295419756932, 0.42046889191871084, 0.48452979291955545, 0.7059674568401322, 0.23633428795402744, 0.7690905463547443, 0.3800342421481584, 0.6796784934802005, 0.5758483477093199, 0.5717840297593535, 0.2593760629220462, 0.8179663683408765, 0.466589740922586, 0.021706374873816325, 0.5781605022795673, 0.5063370142422039, 0.144778750910723, 0.3369240203275293, 0.6701697645155233, 0.7061434714124456, 0.38763969006986254, 0.12250881120507495, 0.9584000966824896, 0.06189313161785459, 0.9333082173164469, 0.4936521132124284, 0.08074274153057814, 0.9618338541947671, 0.14280742362807153, 0.9024689337731638, 0.09483990638910245, 0.5839641097905169, 0.955465442247295, 0.35124897477776995, 0.3610972248759853, 0.8615137789815688, 0.18384794172707153, 0.8943263303022136, 0.8956882977970335, 0.888642027418079, 0.576549153304661, 0.12655942470841441, 0.6825383558635549, 0.3766650671289804, 0.751291755208542, 0.419983938249861, 0.3632877030037267, 0.33988164151248146, 0.9299547091247325, 0.9008177238510006, 0.8514855419614971, 0.06991084715701057, 0.8700022022857136, 0.8383770809176931, 0.9496657157270281, 0.08214979842609782, 0.6430006778564455, 0.2980667212857111, 0.8374217185094861, 0.7894626595593348, 0.35639189892013134, 0.7631857092759126, 0.6881084574343496, 0.7825834439939624, 0.20198598871459306, 0.030584825179223007, 0.39286625152489063, 0.05696737770206062, 0.26295439218687655, 0.462594495186484, 0.24266485220098077, 0.44742528097434164, 0.5586456456610214, 0.8092707955410317, 0.0478060478499166, 0.7909578778352939, 0.18157647589307546, 0.08465941194479476, 0.4878238018036327, 0.8531923960377689, 0.877700022651779, 0.7898076550458848, 0.1639336749104866, 0.8756448290579778, 0.6192612138138579, 0.6835061464678569, 0.880772569915499, 0.5821860067523762, 0.3380417968772881, 0.6520746847100869, 0.2835510572748634, 0.6326145794894733, 0.9951621530134717, 0.2531668092199333, 0.1053657088732114, 0.8462668223642574]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vector{"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Float64}"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.4186772651923394, 1.9443010326818442, 1.9604670690207016, 1.5014306245878104, 1.0148144551337692, 1.6637267892324537, 1.8004070214160124, 1.9933734646203043, 1.4951539828806428, 1.6727919478530155, 1.9453560786450677, 1.710193597552303, 1.0721418795582118, 1.8230923362961615, 1.0883212239321445, 1.4045405648888085, 1.739026360029258, 1.5797557119669228, 1.3081003651777379, 1.6289055969175639, 1.5962374481127166, 1.6674566970526365, 1.3979664999995305, 1.2099511355743473, 1.4881279629787323, 1.721705513844638, 1.5959050022663406, 1.510468689094154, 1.0906731497983766, 1.4016255460353315, 1.1965109499900515, 1.7133541848227378, 1.225999531312278, 1.785819033906092, 1.3580664160801201, 1.1974146511913482, 1.8937175847359242, 1.6891482434572338, 1.1151213931401447, 1.0688833817836096, 1.7300923035673232, 1.0708259162203801, 1.2957378353832805, 1.2642255692392492, 1.3990292986480022, 1.2368920931439535, 1.6309343564611205, 1.5260734735640302, 1.2257064801596993, 1.484390236773382, 1.45502859215383, 1.647098094391134, 1.0384176481503307, 1.5153836945373884, 1.6774330588123008, 1.3663633165137417, 1.4284363550938708, 1.574668176866493, 1.7431118350246342, 1.2585295419756932, 1.420468891918711, 1.4845297929195556, 1.7059674568401322, 1.2363342879540276, 1.7690905463547444, 1.3800342421481584, 1.6796784934802005, 1.57584834770932, 1.5717840297593535, 1.2593760629220463, 1.8179663683408767, 1.4665897409225859, 1.0217063748738164, 1.5781605022795673, 1.506337014242204, 1.144778750910723, 1.3369240203275292, 1.6701697645155233, 1.7061434714124455, 1.3876396900698627, 1.122508811205075, 1.9584000966824897, 1.0618931316178546, 1.9333082173164469, 1.4936521132124283, 1.0807427415305781, 1.961833854194767, 1.1428074236280716, 1.902468933773164, 1.0948399063891023, 1.583964109790517, 1.955465442247295, 1.35124897477777, 1.3610972248759854, 1.8615137789815688, 1.1838479417270715, 1.8943263303022135, 1.8956882977970335, 1.8886420274180789, 1.576549153304661, 1.1265594247084145, 1.682538355863555, 1.3766650671289804, 1.751291755208542, 1.4199839382498611, 1.3632877030037267, 1.3398816415124815, 1.9299547091247327, 1.9008177238510005, 1.851485541961497, 1.0699108471570105, 1.8700022022857135, 1.8383770809176931, 1.949665715727028, 1.082149798426098, 1.6430006778564454, 1.298066721285711, 1.837421718509486, 1.7894626595593348, 1.3563918989201313, 1.7631857092759127, 1.6881084574343497, 1.7825834439939623, 1.201985988714593, 1.030584825179223, 1.3928662515248906, 1.0569673777020605, 1.2629543921868764, 1.462594495186484, 1.2426648522009809, 1.4474252809743415, 1.5586456456610214, 1.8092707955410317, 1.0478060478499165, 1.790957877835294, 1.1815764758930754, 1.0846594119447948, 1.4878238018036327, 1.8531923960377688, 1.877700022651779, 1.7898076550458848, 1.1639336749104867, 1.8756448290579777, 1.619261213813858, 1.683506146467857, 1.8807725699154991, 1.582186006752376, 1.3380417968772882, 1.652074684710087, 1.2835510572748634, 1.6326145794894733, 1.9951621530134718, 1.2531668092199333, 1.1053657088732114, 1.8462668223642575]\n",
      "true\n"
     ]
    }
   ],
   "source": [
    "using Yao\n",
    "\n",
    "N = 16\n",
    "layers = 5\n",
    "g = chain(N) #Making the generator, which is a matchgate ansatz\n",
    "for _ in 1:layers\n",
    "    for i in 1:N-1\n",
    "        push!(g, rot(kron(N, i => X, i+1 => X), 0.))\n",
    "    end\n",
    "    for i in 1:N\n",
    "        push!(g, put(N, i => Rz(0.)))\n",
    "    end\n",
    "end\n",
    "\n",
    "dispatch!(g, :random)\n",
    "arr = parameters(g)\n",
    "println(parameters(g))\n",
    "print(typeof(ones(155)))\n",
    "dispatch!(+, g, ones(155))\n",
    "println(parameters(g))\n",
    "println(parameters(g) == (arr .+ 1))"
   ]
  }
 ],
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