QIP_Rydberg_Bloqade_LinearChain_GS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6821d96d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# declaration\n",
    "\n",
    "using Graphs\n",
    "using Bloqade\n",
    "using Random\n",
    "using GenericTensorNetworks\n",
    "using Optim\n",
    "using KrylovKit\n",
    "using SparseArrays\n",
    "\n",
    "using PythonCall\n",
    "\n",
    "plt = pyimport(\"matplotlib.pyplot\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "511ec77b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <use xlink:href=\"#glyph1-1\" x=\"44.671875\" y=\"65.59375\"/>\n",
       "  <use xlink:href=\"#glyph1-3\" x=\"53.570313\" y=\"65.59375\"/>\n",
       "  <use xlink:href=\"#glyph1-4\" x=\"63.34375\" y=\"65.59375\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "5-element AtomList{1, Float64}:\n",
       " (0.0,)\n",
       " (5.72,)\n",
       " (11.44,)\n",
       " (17.16,)\n",
       " (22.88,)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nsites = 5\n",
    "atoms = generate_sites(ChainLattice(), nsites, scale = 5.72)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9c494c4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ω = 2π * 4 # Rabi\n",
    "Δ_step = 30 # Detuning increment\n",
    "Δ = LinRange(-2π * 10, 2π * 10, Δ_step); # Detuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d85100ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "density_g = zeros(Δ_step, nsites)\n",
    "\n",
    "for ii in 1:Δ_step\n",
    "    h_ii = rydberg_h(atoms; Δ=Δ[ii], Ω) # create the Rydberg Hamiltonian\n",
    "    h_m = mat(h_ii) # convert the Hamiltonian into a matrix\n",
    "    vals, vecs, info = KrylovKit.eigsolve(h_m,  1, :SR) # find the ground state eigenvalue and eigenvector\n",
    "    g_state = ArrayReg(vecs[1]) # creates the initial state with all atoms in ``| 0 \\rangle`` state\n",
    "\n",
    "    for jj in 1:nsites\n",
    "        density_g[ii, jj] = rydberg_density(g_state, jj) # measure the density of Rydberg excitations on each site\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "77f7f15c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (10, 4))\n",
    "ax.bar(1:nsites, density_g[1, :])\n",
    "ax.set_xticks(1:nsites)\n",
    "ax.set_xlabel(\"Sites\")\n",
    "ax.set_ylabel(\"Rydberg density\")\n",
    "ax.set_title(\"Density Profile: 1D Chain, Δ = -2π * 10 MHz\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c7242a02",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (10, 4))\n",
    "ax.bar(1:nsites, density_g[30, :])\n",
    "ax.set_xticks(1:nsites)\n",
    "ax.set_xlabel(\"Sites\")\n",
    "ax.set_ylabel(\"Rydberg density\")\n",
    "ax.set_title(\"Density Profile: 1D Chain, Δ = 2π * 10 MHz\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "60612f25",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "order_para = map(1: Δ_step) do ii\n",
    "    sum(density_g[ii, 1:2:nsites]) - sum(density_g[ii, 2:2:nsites])\n",
    "end\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (10,4))\n",
    "ax.plot(Δ/2π, order_para)\n",
    "ax.set_xlabel(\"Δ/2π (MHz) \")\n",
    "ax.set_ylabel(\"Order parameter\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a0638b35",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Preparing ordered state\n",
    "\n",
    "total_time = 3.0;\n",
    "Ω_max = 2π * 4;\n",
    "Ω = piecewise_linear(clocks = [0.0, 0.1, 2.1, 2.2, total_time], values = [0.0, Ω_max, Ω_max, 0, 0]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "55dfe36a",
   "metadata": {},
   "outputs": [],
   "source": [
    "U1 = -2π * 10;\n",
    "U2 = 2π * 10;\n",
    "Δ = piecewise_linear(clocks = [0.0, 0.6, 2.1, total_time], values = [U1, U1, U2, U2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c100a2cc",
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 2400x800 with 2 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(ncols = 2, figsize = (12, 4))\n",
    "Bloqade.plot!(ax1, Ω)\n",
    "ax1.set_ylabel(\"Ω/2π (MHz)\")\n",
    "Bloqade.plot!(ax2, Δ)\n",
    "ax2.set_ylabel(\"Δ/2π (MHz)\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cce761b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\sum \\frac{2π \\cdot 0.863\\times 10^{6.0}}{|r_i-r_j|^6} n_i n_j+1\\cdotΩ(t) ⋅ \\sum σ^x_i-Δ(t) ⋅ \\sum n_i$"
      ],
      "text/plain": [
       "\u001b[36mnqubits: 5\u001b[39m\n",
       "\u001b[31m\u001b[1m+\u001b[22m\u001b[39m\n",
       "├─ \u001b[33m\u001b[1m[+] \u001b[22m\u001b[39m∑ 2π ⋅ 8.627e6.0/|r_i-r_j|^6 n_i n_j\n",
       "├─ \u001b[33m\u001b[1m[+] \u001b[22m\u001b[39mΩ(t) ⋅ ∑ σ^x_i\n",
       "└─ \u001b[33m\u001b[1m[-] \u001b[22m\u001b[39mΔ(t) ⋅ ∑ n_i\n"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nsites = 5\n",
    "atoms = generate_sites(ChainLattice(), nsites, scale = 5.72)\n",
    "\n",
    "h01 = rydberg_h(atoms; Δ, Ω)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1262ec81",
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = zero_state(5);\n",
    "prob = SchrodingerProblem(reg, total_time, h01);\n",
    "integrator = init(prob, Vern8());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5e91f7ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "densities = []\n",
    "for _ in TimeChoiceIterator(integrator, 0.0:1e-3:total_time)\n",
    "    push!(densities, rydberg_density(reg))\n",
    "end\n",
    "D = hcat(densities...);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8f8ead41",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 2000x800 with 2 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (10,4))\n",
    "shw = ax.imshow(real(D), interpolation=\"nearest\", aspect=\"auto\", extent=[0,total_time,0.5,nsites+0.5])\n",
    "ax.set_xlabel(\"time (μs)\")\n",
    "ax.set_ylabel(\"site\")\n",
    "ax.set_xticks(0:0.2:total_time)\n",
    "ax.set_yticks(1:nsites)\n",
    "bar = fig.colorbar(shw)\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ff537438",
   "metadata": {},
   "outputs": [
    {
     "data": {
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