4_quantum/qc_tensor_mapping.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Yao, TensorOperations"
   ]
  },
  {
   "attachments": {
    "origin.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contracting a Tensor network\n",
    "<img src=\"attachment:origin.png\" width=\"400\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2372274789611332e6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dims = [1, 3, 3, 3, 2, 4, 2]\n",
    "A, B, C, D, E, F, G = map(nd->randn(fill(20, nd)...), dims)\n",
    "\n",
    "@tensor begin\n",
    "    Y1[b, c] := A[a] * B[a,b,c]         # N^3\n",
    "    Y2[c,d,e] := Y1[b,c] * C[b,d,e]        # N^4\n",
    "    Y3[d,e,f,g] := Y2[c,d,e] * D[c,f,g]       # N^5\n",
    "    Y4[d,g,h,i] := Y3[d,e,f,g] * F[e,f,h,i]       # N^6\n",
    "    Y5[g,i] := Y4[d,g,h,i] * E[d,h]       # N^4\n",
    "    Y5[g,i] * G[g,i]        # N^2\n",
    "end"
   ]
  },
  {
   "attachments": {
    "_qft.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mapping a QFT circuit to a probability graph\n",
    "\n",
    "<img src=\"attachment:_qft.png\" width=\"800\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "CRk(i::Int, j::Int, k::Int) = control([i, ], j=>shift(2π/(1<<k)))\n",
    "CRot(n::Int, i::Int) = chain(n, i==j ? kron(i=>H) : CRk(j, i, j-i+1) for j = i:n)\n",
    "QFTCircuit(n::Int) = chain(n, CRot(n, i) for i = 1:n)\n",
    "\n",
    "qft = QFTCircuit(5);"
   ]
  },
  {
   "attachments": {
    "_qftslice.png": {
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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. labeling legs in a quantum circuit\n",
    "* If a gate is diagonal, or a control gate, do not change the label, e.g. CPHASE gate in this example,\n",
    "* otherwise a asign a new label (like `H` gate in this example)\n",
    "\n",
    "![_qftslice.png](attachment:_qftslice.png)\n",
    "\n",
    "### 2. these labels are nodes in a probability graph\n",
    "\n",
    "<img src=\"images/qfttn.png\" width=\"300\"/>\n",
    "\n",
    "We can define a elimination order for this graph, or map it to a tensor network (by introducing $\\delta$ notations) and contract it using `TensorOperations.jl`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "TR(k::Int) = [1 1; 1 exp(2im*π/(1<<k))]\n",
    "function D(dim::Int)\n",
    "    ts = zeros(fill(2,dim)...)\n",
    "    ts[1] = 1\n",
    "    ts[end] = 1\n",
    "    ts\n",
    "end\n",
    "TH = mat(H);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "TR2 = TR(2)\n",
    "TR3 = TR(3)\n",
    "TR4 = TR(4)\n",
    "TR5 = TR(5)\n",
    "δ3 = D(3);\n",
    "δ4 = D(4);\n",
    "δ5 = D(5);\n",
    "δ6 = D(6);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "using TensorOperations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2×2×2×2 Array{Complex{Float64},5}:\n",
       "[:, :, 1, 1, 1] =\n",
       "  -0.176071-0.0726608im  -0.260603-0.0888657im\n",
       " -0.0301986+0.185368im   -0.238037-0.107873im \n",
       "\n",
       "[:, :, 2, 1, 1] =\n",
       " 0.172762-0.00389244im    0.146348+0.0836913im\n",
       " 0.165943+0.103285im    -0.0640828-0.0503977im\n",
       "\n",
       "[:, :, 1, 2, 1] =\n",
       "  0.0697918+0.000757422im  0.0429287+0.154713im \n",
       " -0.0250555+0.149688im      0.183045-0.0463401im\n",
       "\n",
       "[:, :, 2, 2, 1] =\n",
       " 0.00032432+0.109026im   -0.129909+0.0417873im\n",
       "  0.0682505-0.0110009im  -0.148282+0.0232732im\n",
       "\n",
       "[:, :, 1, 1, 2] =\n",
       " -0.101134-0.00979302im  0.0624712-0.161836im\n",
       "  0.169794-0.159708im     0.191211+0.134413im\n",
       "\n",
       "[:, :, 2, 1, 2] =\n",
       " -0.0253867+0.00635099im  -0.248987+0.111993im\n",
       " -0.0553132-0.0536716im    0.043826+0.20316im \n",
       "\n",
       "[:, :, 1, 2, 2] =\n",
       "  0.059548-0.126707im  -0.114875-0.103951im\n",
       " -0.091108+0.127783im  -0.270757-0.156469im\n",
       "\n",
       "[:, :, 2, 2, 2] =\n",
       "  -0.145703-0.0514439im  0.0620345-0.0384791im\n",
       " -0.0664184-0.0668034im   0.100633+0.214655im "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = rand_state(5);\n",
    "res = copy(reg) |> qft\n",
    "ψ = dropdims(reg |> hypercubic, dims=6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2×2×2×2 Array{Complex{Float64},5}:\n",
       "[:, :, 1, 1, 1] =\n",
       "    -0.115437+0.0601132im  0.0571661+0.22924im  \n",
       " -0.000301617-0.0877855im  0.0285023+0.0650688im\n",
       "\n",
       "[:, :, 2, 1, 1] =\n",
       " 0.00379363+0.0582227im    0.159786-0.186479im\n",
       "  0.0267162-0.00502365im  -0.237809-0.12276im \n",
       "\n",
       "[:, :, 1, 2, 1] =\n",
       "   -0.109134+0.0229597im  0.204501+0.0460059im\n",
       " -0.00671519+0.0221776im  0.134229-0.235786im \n",
       "\n",
       "[:, :, 2, 2, 1] =\n",
       "  -0.206345-0.0747273im  0.00624298-0.0369912im\n",
       " 0.00739291-0.128292im    0.0719049-0.1962im   \n",
       "\n",
       "[:, :, 1, 1, 2] =\n",
       " 0.0366493+0.106254im  -0.127927+0.0144893im\n",
       " -0.168109-0.135717im  0.0436267+0.035253im \n",
       "\n",
       "[:, :, 2, 1, 2] =\n",
       " -0.435699+0.0349771im  0.0801935+0.244325im \n",
       " 0.0718952-0.0268589im  0.0268003-0.0620978im\n",
       "\n",
       "[:, :, 1, 2, 2] =\n",
       " -0.0128536-0.154923im    0.0262584+0.110406im\n",
       " -0.0567237-0.00909317im  -0.207715+0.198225im\n",
       "\n",
       "[:, :, 2, 2, 2] =\n",
       " -0.157867-0.171715im    0.0072535+0.0166267im\n",
       "  -0.10733-0.0262286im  -0.0389537-0.0146979im"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@tensoropt begin\n",
    "    out[f,g,h,i,j] :=\n",
    "    ψ[a,b,c,d,e] * \n",
    "    TH[a,f1] * TR2[f2,b1] * TR3[f3,c1] * TR4[f4,d1] * TR5[f5,e1] *\n",
    "    TH[b2,g1] * TR2[g2,c2] * TR3[g3,d2] * TR4[g4,e2] *\n",
    "    TH[c3,h1] * TR2[h2,d3] * TR3[h3,e3] *\n",
    "    TH[d4,i1] * TR2[i2,e4] *\n",
    "    TH[e5,j] *\n",
    "    δ3[b2,b1,b] *\n",
    "    δ4[c3,c2,c1,c] *\n",
    "    δ5[d4,d3,d2,d1,d] *\n",
    "    δ6[e5,e4,e3,e2,e1,e] *\n",
    "    δ3[i2,i1,i] *\n",
    "    δ4[h3,h2,h1,h] *\n",
    "    δ5[g4,g3,g2,g1,g] *\n",
    "    δ6[f5,f4,f3,f2,f1,f]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "statevec(res) ≈ vec(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Call for Treewidth algorithm in Julia!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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