demo_unitary_decomposition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.stats import unitary_group\n",
    "from qiskit import Aer, execute, QuantumCircuit\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "\n",
    "backend = Aer.get_backend(\"qasm_simulator\")\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "from utils_decompose import multiplexor, demultiplexor, unitary_diag, cos_sin_decomposition\n",
    "from utils_decompose import zyz_decomposition, ucry_decomposition_optimize, ucrz_decomposition, global_phase_gate\n",
    "from utils import universal_ud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n",
      "Reconstruct matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = np.random.RandomState(77)\n",
    "\n",
    "N = 2\n",
    "M = unitary_group.rvs(2**N,random_state=r)\n",
    "print(\"Original matrix:\\n\",np.round(M,3))\n",
    "\n",
    "U, CS, V = cos_sin_decomposition(M,N)\n",
    "\n",
    "U1,D1,V1 = demultiplexor(U,N)\n",
    "U2,D2,V2 = demultiplexor(V,N)\n",
    "\n",
    "rcst_U = multiplexor(U1,D1,V1,N)\n",
    "uni_D1 = unitary_diag(D1,N)\n",
    "\n",
    "rcst_V = multiplexor(U2,D2,V2,N)\n",
    "uni_D2 = unitary_diag(D2,N)\n",
    "\n",
    "print(\"Reconstruct matrix:\\n\", np.round(rcst_U@CS@rcst_V,3))\n",
    "\n",
    "qc = QuantumCircuit(N)\n",
    "\n",
    "qc.unitary(Operator(M),range(N))\n",
    "qc.measure_all()\n",
    "\n",
    "result = execute(qc, backend=backend,shots=4096).result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1350.65x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "phase = 0\n",
    "\n",
    "\n",
    "##################################################\n",
    "##### Optimized MxorRy \n",
    "\n",
    "mxory_optimize = np.eye(len(V))\n",
    "for i in range(len(V)//4): mxory_optimize[(len(V)//2+2*i+1)][(len(V)//2+2*i+1)] = -1\n",
    "V = mxory_optimize@V\n",
    "\n",
    "U1,D1,V1 = demultiplexor(U,N)\n",
    "U2,D2,V2 = demultiplexor(V,N)\n",
    "\n",
    "##################################################\n",
    "\n",
    "phase = zyz_decomposition(qc,V2,0,phase)\n",
    "ucrz_decomposition(qc,N,D2,[0,1])\n",
    "phase = zyz_decomposition(qc,U2,0,phase)\n",
    "\n",
    "ucry_decomposition_optimize(qc,N,CS,[0,1])\n",
    "\n",
    "phase = zyz_decomposition(qc,V1,0,phase)\n",
    "ucrz_decomposition(qc,N,D1,[0,1])\n",
    "phase = zyz_decomposition(qc,U1,0,phase)\n",
    "\n",
    "qc.barrier()\n",
    "global_phase_gate(qc,phase,0)\n",
    "\n",
    "qc.draw(output=\"mpl\",fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n",
      "Circuit matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Original matrix:\\n\",np.round(M,3))\n",
    "print(\"Circuit matrix:\\n\",np.round(np.matrix(Operator(qc)),3))\n",
    "qc.measure_all()\n",
    "\n",
    "result = execute(qc, backend=backend,shots=4096).result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cartan Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n",
      "Circuit matrix:\n",
      " [[ 0.069-0.393j  0.258-0.271j -0.82 +0.141j  0.041+0.077j]\n",
      " [ 0.143-0.033j -0.647-0.277j -0.147-0.151j -0.661-0.049j]\n",
      " [ 0.48 -0.654j -0.049+0.287j  0.237+0.189j -0.001-0.407j]\n",
      " [-0.321-0.243j -0.529-0.003j -0.131-0.392j  0.594-0.185j]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 869.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "phase = 0\n",
    "phase = universal_ud(qc,M,[0,1],phase)\n",
    "\n",
    "qc.barrier()\n",
    "global_phase_gate(qc,phase,0)\n",
    "\n",
    "print(\"Original matrix:\\n\",np.round(M,3))\n",
    "print(\"Circuit matrix:\\n\",np.round(np.matrix(Operator(qc)),3))\n",
    "\n",
    "qc.draw(output=\"mpl\",fold=-1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "567066c23fe75d4951ebba463616a12e21f3ac884aba845053c257fc26c45e45"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}