debug.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true gradient: -0.4984640760288773\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "parametershift_grad (generic function with 2 methods)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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(theta = parameters(g)) #Shift parameters in-place\n",
    "    l = nparameters(g)\n",
    "    temp_params = theta\n",
    "    temp_params[1] += π/2\n",
    "    grad = zeros(l)\n",
    "    for i in 1:l\n",
    "        plus = 0\n",
    "        minus = 0\n",
    "        dispatch!(g, temp_params)\n",
    "        plus = gLoss() #This is the problem\n",
    "        temp_params[i] -= π\n",
    "        dispatch!(g, temp_params)\n",
    "        minus = gLoss()\n",
    "        grad[i] = (plus - minus) / 2\n",
    "        if i < l\n",
    "            temp_params[i] += π/2\n",
    "            temp_params[i+1] += π/2\n",
    "        end\n",
    "    end\n",
    "    temp_params[l] += π/2\n",
    "    dispatch!(g, temp_params)\n",
    "    grad\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Plots \n",
    "\n",
    "p = []\n",
    "\n",
    "for _ in 1:100\n",
    "    push!(p, first(parametershift_grad()))\n",
    "end\n",
    "\n",
    "histogram(p, bins=20, xlabel=\"parametershift_grad\", ylabel=\"Frequency\")"
   ]
  }
 ],
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