Week1_Rydberg/Calculations/task4_calculations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "55b5d50c",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Bloqade\n",
    "using PythonCall\n",
    "using KrylovKit\n",
    "using SparseArrays\n",
    "using Yao, YaoPlots\n",
    "using Graphs\n",
    "using Random\n",
    "using GenericTensorNetworks\n",
    "using Optim\n",
    "using PythonCall\n",
    "plt = pyimport(\"matplotlib.pyplot\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c886bb99",
   "metadata": {},
   "source": [
    "First, we specify the array of possible tower locations. Our example calculation will consider a 4x4 array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "88ba3d00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specify 4x4 array\n",
    "atoms = generate_sites(SquareLattice(), 4, 4; scale = 4.5);\n",
    "Bloqade.plot(atoms, blockade_radius = 7.5);\n",
    "\n",
    "# specify adiabatic protocol\n",
    "T_max = 0.6\n",
    "Ω_max = 2π * 4\n",
    "Ω = piecewise_linear(clocks = [0.0, 0.1, 0.5, T_max], values = [0.0, Ω_max, Ω_max, 0])\n",
    "Δ_start = -2π * 13\n",
    "Δ_end = 2π * 11\n",
    "Δ = piecewise_linear(clocks = [0.0, 0.1, 0.5, T_max], values = [Δ_start, Δ_start, Δ_end, Δ_end])\n",
    "\n",
    "# specify Hamiltonian and dynamics\n",
    "hamiltonian = rydberg_h(atoms; Ω = Ω, Δ = Δ)\n",
    "reg = zero_state(nqubits(hamiltonian))\n",
    "prob = SchrodingerProblem(reg, T_max, hamiltonian)\n",
    "emulate!(prob)\n",
    "\n",
    "bitstring_hist(prob.reg; nlargest = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "883ed3dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# determine MIS size classically\n",
    "graph = BloqadeMIS.unit_disk_graph(atoms, 7.5)\n",
    "mis_size_and_counting = GenericTensorNetworks.solve(IndependentSet(graph), CountingMax())[]\n",
    "mis_size_and_counting[1]\n",
    "mis_size = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fa7d8b64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in order to get a set of bitstring solutions that we can manipulate, we make a large number of measurements,\n",
    "# determine the unique set of measurements, and eliminate the bitstrings that do not have MIS length of 4\n",
    "solutions = String[]\n",
    "\n",
    "for i in 1:100\n",
    "    m = Integer(measure(reg)[1])\n",
    "    str = \"\"\n",
    "    for i in 1:16\n",
    "        str = str * string(m[i])\n",
    "    end\n",
    "    append!(solutions, [str])\n",
    "end\n",
    "\n",
    "# get unique solutions\n",
    "unique!(solutions);\n",
    "\n",
    "solutions_fixed = String[]\n",
    "for i in 1:length(solutions)\n",
    "    sum = 0\n",
    "    for j in 1:16\n",
    "        sum = sum + parse(Int, solutions[i][j])\n",
    "    end\n",
    "    if sum==4\n",
    "        append!(solutions_fixed, [solutions[i]])\n",
    "    end\n",
    "end\n",
    "\n",
    "number_of_solutions = length(solutions_fixed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "07c389cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bitstring        Rating\n",
      "1001000000001001 1.5793766670083484\n",
      "1010000000001010 2.0685979486952313\n",
      "0001010000001001 1.619442778453172\n",
      "0000010100001001 1.5929585440116867\n",
      "1001000010000001 1.2956550003137908\n",
      "1000001000001001 1.769332713399164\n",
      "1010000000000101 1.929256872144633\n",
      "1001000000001010 1.5257297961842728\n",
      "0001010000011000 1.6627330914036365\n",
      "1000000100001001 1.5528924325668636\n",
      "1001000000000101 1.3863887196336746\n",
      "0010100000001001 2.029389018020144\n",
      "1000000110000001 1.269170765872306\n",
      "1010000000001001 2.1222448195193073\n",
      "1000001000001010 1.7156858425750885\n",
      "1001000001000001 1.6216214939761544\n",
      "0101000000011000 1.2971027486162772\n",
      "1001000010000010 1.2420081294897152\n",
      "1001000000011000 1.6226669799588131\n",
      "0101000000000101 1.0608244882911384\n",
      "0101000000001001 1.2538124356658127\n",
      "0001100000001001 1.4865208655091857\n",
      "0001100000011000 1.5298111784596502\n"
     ]
    }
   ],
   "source": [
    "# randomly generate metric associated with each of the 16 sites\n",
    "metrics = zeros(0)\n",
    "for i in 1:16\n",
    "    append!(metrics, rand())\n",
    "end\n",
    "\n",
    "# for each bitstring solution, multiply each bit by the corresonding metric\n",
    "println(\"Bitstring        Rating\")\n",
    "for i in 1:length(solutions_fixed)\n",
    "    print(solutions_fixed[i], \" \")\n",
    "    \n",
    "    sum = 0\n",
    "    for j in 1:16\n",
    "        sum = sum + parse(Int, solutions_fixed[i][j])*metrics[j]\n",
    "    end\n",
    "    println(sum, \"\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fd2c5f8",
   "metadata": {},
   "source": [
    "We see that out of the solutions that do not have neighboring excitations, 1010000000001001 has the highest overall rating. This corresponds to cell towers positioned at sites 1, 3, 13, and 16. Next, we simulate a power-outage at a random site."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3d012f1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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0.41935483870967744cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.5806451612903226cx, 0.41935483870967744cy), (0.41935483870967744cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.5806451612903226cx, 0.41935483870967744cy), (0.5806451612903226cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.5806451612903226cx, 0.41935483870967744cy), (0.7419354838709679cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.7419354838709679cx, 0.41935483870967744cy), (0.5806451612903226cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.7419354838709679cx, 0.41935483870967744cy), (0.7419354838709679cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.2580645161290323cx, 0.25806451612903225cy), (0.41935483870967744cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.41935483870967744cx, 0.25806451612903225cy), (0.5806451612903226cx, 0.25806451612903225cy)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.5806451612903226cx, 0.25806451612903225cy), (0.7419354838709679cx, 0.25806451612903225cy)])], Symbol(\"\"))]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.7419354838709679cx, 0.25806451612903225cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(1.0,1.0,1.0,1.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.5806451612903226cx, 0.25806451612903225cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(1.0,1.0,1.0,1.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.41935483870967744cx, 0.25806451612903225cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), 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List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.7419354838709679cx, 0.41935483870967744cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(1.0,1.0,1.0,1.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.5806451612903226cx, 0.41935483870967744cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(1.0,1.0,1.0,1.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, 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Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}}(Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}[Compose.CirclePrimitive{Tuple{Measures.Measure, Measures.Measure}, Measures.Measure}((0.2580645161290323cx, 0.41935483870967744cy), 4.645161290322582mm)], Symbol(\"\"))]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.LineWidthPrimitive}(Compose.LineWidthPrimitive[Compose.LineWidthPrimitive(0.9290322580645163mm)]), Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(1.0,1.0,1.0,1.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.CirclePrimitive{Tuple{Measures.Measure, 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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(7)\n",
    "atoms = generate_sites(SquareLattice(), 4, 4; scale = 4.5) |> random_dropout(0.0625);\n",
    "Bloqade.plot(atoms, blockade_radius = 7.5)\n",
    "# code was run until randomly dropped site corresponded to one of the initial tower locations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f89e034d",
   "metadata": {},
   "source": [
    "Site 3 (according to the original labelling) has been removed from our array. We rerun our algorithm to determine the MIS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0da25460",
   "metadata": {},
   "outputs": [],
   "source": [
    "# specify adiabatic protocol\n",
    "T_max = 0.6\n",
    "Ω_max = 2π * 4\n",
    "Ω = piecewise_linear(clocks = [0.0, 0.1, 0.5, T_max], values = [0.0, Ω_max, Ω_max, 0])\n",
    "Δ_start = -2π * 13\n",
    "Δ_end = 2π * 11\n",
    "Δ = piecewise_linear(clocks = [0.0, 0.1, 0.5, T_max], values = [Δ_start, Δ_start, Δ_end, Δ_end])\n",
    "\n",
    "# specify Hamiltonian and dynamics\n",
    "hamiltonian = rydberg_h(atoms; Ω = Ω, Δ = Δ)\n",
    "reg = zero_state(nqubits(hamiltonian))\n",
    "prob = SchrodingerProblem(reg, T_max, hamiltonian)\n",
    "emulate!(prob)\n",
    "\n",
    "# determine MIS size classically\n",
    "graph = BloqadeMIS.unit_disk_graph(atoms, 7.5)\n",
    "mis_size_and_counting = GenericTensorNetworks.solve(IndependentSet(graph), CountingMax())[]\n",
    "mis_size_and_counting[1]\n",
    "mis_size = 4\n",
    "\n",
    "# in order to get a set of bitstring solutions that we can manipulate, we make a large number of measurements,\n",
    "# determine the unique set of measurements, and eliminate the bitstrings that do not have MIS length of 4\n",
    "solutions = String[]\n",
    "\n",
    "for i in 1:100\n",
    "    m = Integer(measure(reg)[1])\n",
    "    str = \"\"\n",
    "    for i in 1:15\n",
    "        str = str * string(m[i])\n",
    "    end\n",
    "    append!(solutions, [str])\n",
    "end\n",
    "\n",
    "# get unique solutions\n",
    "unique!(solutions);\n",
    "\n",
    "solutions_fixed = String[]\n",
    "for i in 1:length(solutions)\n",
    "    sum = 0\n",
    "    for j in 1:15\n",
    "        sum = sum + parse(Int, solutions[i][j])\n",
    "    end\n",
    "    if sum==4\n",
    "        append!(solutions_fixed, [solutions[i]])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41035d22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bitstring        Metric\n",
      "101000010100000 0.30166967414897516\n",
      "101000000001001 1.0846040936329597\n",
      "101000000001010 0.9652539393884894\n",
      "101000010000001 0.686189123790324\n",
      "101000010000010 0.5668389695458536\n",
      "001100000001001 1.2986596072214058\n",
      "100001000001001 1.2147138673459328\n",
      "011000000001001 1.913642422713388\n",
      "101000000011000 1.2462594991197984\n",
      "011000010000001 1.5152274528707521\n",
      "000101000001001 1.4287693809343789\n",
      "101000000000101 1.5246675618655097\n",
      "001100000011000 1.4603150127082445\n",
      "011000000000101 2.353705890945938\n",
      "001010000000101 1.9964571546425094\n",
      "100001000001010 1.0953637131014622\n",
      "000100100001001 2.0576323979675\n",
      "001010000001001 1.5563936864099595\n"
     ]
    }
   ],
   "source": [
    "# randomly generate metric associated with each of the 15 sites\n",
    "metrics = zeros(0)\n",
    "for i in 1:15\n",
    "    append!(metrics, rand())\n",
    "end\n",
    "\n",
    "# for each bitstring solution, multiply each bit by the corresonding metric\n",
    "println(\"Bitstring        Metric\")\n",
    "for i in 1:length(solutions_fixed)\n",
    "    print(solutions_fixed[i], \" \")\n",
    "    \n",
    "    sum = 0\n",
    "    for j in 1:15\n",
    "        sum = sum + parse(Int, solutions_fixed[i][j])*metrics[j]\n",
    "    end\n",
    "    println(sum, \"\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45479732",
   "metadata": {},
   "source": [
    "We see that out of the solutions that do not have neighboring excitations 000100100001001 has the highest overall rating. This corresponds to cell towers positioned at sites 4, 7, 12, and 15. Since site 3 was removed from our original array, these sites correpond to 5,8,13,16 on the original lattice. Combining the two solutions, we have determined that cell towers should be positioned at sites 1, 5, 8, 13, 16. \n",
    "\n",
    "Our solution has neighboring cell towers. Introducing redundancy into our network may result in direct neighbors. Of course, our basic calculations only simulated a single random power-outage. A more complete calculation would consider a larger array and numerous power-outage simulations- perhaps involving more than one site that goes down. That aside, our example illustrates a potential application that could be used in an industrial setting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3b8a94a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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