linlin_2x2_symmetric.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import linalg\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "\n",
    "from utils_decompose import global_phase_gate, ucry_decomposition_2x2_symmetric, ucry_decomposition_optimize\n",
    "from utils_block_encode import is_unitary, transfer_matrix\n",
    "from utils import universal_be\n",
    "from utils_linlin import linlin_2x2_symmetric_optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[-0.36391889 -0.07510659]\n",
      " [-0.07510659 -0.36391889]]\n",
      "-> untary: False\n",
      "Enlarge:\n",
      " [[-0.364 -0.075 -0.364  0.075 -0.343 -0.494 -0.343  0.494]\n",
      " [-0.075 -0.364  0.075 -0.364 -0.494 -0.343  0.494 -0.343]\n",
      " [-0.364  0.075 -0.364 -0.075 -0.343  0.494 -0.343 -0.494]\n",
      " [ 0.075 -0.364 -0.075 -0.364  0.494 -0.343 -0.494 -0.343]\n",
      " [ 0.343  0.494  0.343 -0.494 -0.364 -0.075 -0.364  0.075]\n",
      " [ 0.494  0.343 -0.494  0.343 -0.075 -0.364  0.075 -0.364]\n",
      " [ 0.343 -0.494  0.343  0.494 -0.364  0.075 -0.364 -0.075]\n",
      " [-0.494  0.343  0.494  0.343  0.075 -0.364 -0.075 -0.364]]\n",
      "-> untary: True\n"
     ]
    }
   ],
   "source": [
    "a,b = np.random.rand()*2-1,np.random.rand()*2-1\n",
    "\n",
    "M = 0.5*np.matrix([[a,b],[b,a]])\n",
    "print(\"Matrix:\\n\",M)\n",
    "print(\"-> untary:\", is_unitary(M))\n",
    "\n",
    "enlarge_a = 0.5*np.matrix([[a,b,a,-b],\n",
    "                           [b,a,-b,a],\n",
    "                           [a,-b,a,b],\n",
    "                           [-b,a,b,a]])\n",
    "\n",
    "c,d = np.sqrt(1-a**2),np.sqrt(1-b**2)\n",
    "enlarge_b = 0.5*np.matrix([[c,d,c,-d],\n",
    "                           [d,c,-d,c],\n",
    "                           [c,-d,c,d],\n",
    "                           [-d,c,d,c]])\n",
    "\n",
    "enlarge_M = np.eye(8)\n",
    "enlarge_M[:4,:4] = enlarge_a\n",
    "enlarge_M[:4,4:] = -enlarge_b\n",
    "enlarge_M[4:,:4] = enlarge_b\n",
    "enlarge_M[4:,4:] = enlarge_a\n",
    "\n",
    "print(\"Enlarge:\\n\",np.round(enlarge_M,3))\n",
    "print(\"-> untary:\", is_unitary(enlarge_M))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)}\\\\0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)}\\\\0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)}\\\\- 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} \\right)}\\\\0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)}\\\\0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)}\\\\0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)}\\\\- 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\sin{\\left(\\frac{a}{2} \\right)} & - 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} + \\frac{b}{2} \\right)} & 0.5 \\cos{\\left(\\frac{a}{2} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[0.5*cos(a/2), 0.5*cos(a/2 + b/2), 0.5*cos(a/2), -0.5*cos(a/2 + b/2), -0.5*sin(a/2), -0.5*sin(a/2 + b/2), -0.5*sin(a/2), 0.5*sin(a/2 + b/2)], [0.5*cos(a/2 + b/2), 0.5*cos(a/2), -0.5*cos(a/2 + b/2), 0.5*cos(a/2), -0.5*sin(a/2 + b/2), -0.5*sin(a/2), 0.5*sin(a/2 + b/2), -0.5*sin(a/2)], [0.5*cos(a/2), -0.5*cos(a/2 + b/2), 0.5*cos(a/2), 0.5*cos(a/2 + b/2), -0.5*sin(a/2), 0.5*sin(a/2 + b/2), -0.5*sin(a/2), -0.5*sin(a/2 + b/2)], [-0.5*cos(a/2 + b/2), 0.5*cos(a/2), 0.5*cos(a/2 + b/2), 0.5*cos(a/2), 0.5*sin(a/2 + b/2), -0.5*sin(a/2), -0.5*sin(a/2 + b/2), -0.5*sin(a/2)], [0.5*sin(a/2), 0.5*sin(a/2 + b/2), 0.5*sin(a/2), -0.5*sin(a/2 + b/2), 0.5*cos(a/2), 0.5*cos(a/2 + b/2), 0.5*cos(a/2), -0.5*cos(a/2 + b/2)], [0.5*sin(a/2 + b/2), 0.5*sin(a/2), -0.5*sin(a/2 + b/2), 0.5*sin(a/2), 0.5*cos(a/2 + b/2), 0.5*cos(a/2), -0.5*cos(a/2 + b/2), 0.5*cos(a/2)], [0.5*sin(a/2), -0.5*sin(a/2 + b/2), 0.5*sin(a/2), 0.5*sin(a/2 + b/2), 0.5*cos(a/2), -0.5*cos(a/2 + b/2), 0.5*cos(a/2), 0.5*cos(a/2 + b/2)], [-0.5*sin(a/2 + b/2), 0.5*sin(a/2), 0.5*sin(a/2 + b/2), 0.5*sin(a/2), -0.5*cos(a/2 + b/2), 0.5*cos(a/2), 0.5*cos(a/2 + b/2), 0.5*cos(a/2)]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "\n",
    "aa,bb = sp.symbols('a'),sp.symbols('b')\n",
    "ii = np.eye(2)\n",
    "c1 = np.matrix([[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]])\n",
    "c2 = np.matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])\n",
    "h = np.matrix([[1,1],[1,-1]])/np.sqrt(2)\n",
    "\n",
    "def sym_ry(x): return np.matrix([[sp.cos(x/2),-sp.sin(x/2)],[sp.sin(x/2),sp.cos(x/2)]])\n",
    "\n",
    "# difusser\n",
    "T1 = np.kron(np.kron(ii,h),ii)\n",
    "# oracle_c\n",
    "T2 = np.kron(ii,c2)\n",
    "# oracle_a\n",
    "T3 = np.kron(np.kron(sym_ry(bb/2),ii),ii)\n",
    "T4 = np.kron(c1,ii)\n",
    "T5 = np.kron(np.kron(sym_ry(-bb/2),ii),ii)\n",
    "T6 = np.kron(np.kron(sym_ry(aa),ii),ii)\n",
    "\n",
    "TT = T1@T6@T4@T5@T4@T3@T2@T1\n",
    "\n",
    "sp.simplify(TT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = 2*np.arccos(a)\n",
    "t2 = 2*np.arccos(b) - t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[-0.364 -0.075]\n",
      " [-0.075 -0.364]]\n",
      "-> untary: False\n",
      "Circuit matrix (upper left block):\n",
      " [[-0.364+0.j -0.075+0.j -0.364+0.j  0.075+0.j]\n",
      " [-0.075+0.j -0.364+0.j  0.075+0.j -0.364+0.j]\n",
      " [-0.364+0.j  0.075+0.j -0.364+0.j -0.075+0.j]\n",
      " [ 0.075+0.j -0.364+0.j -0.075+0.j -0.364+0.j]]\n",
      "-> untary: True\n",
      "Successfully encode matrix using Block Encoding: True\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 447.797x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(3)\n",
    "\n",
    "qc.h(1)\n",
    "# qc.cx(1,0)\n",
    "\n",
    "# cry\n",
    "qc.ry(t2/2,2)\n",
    "qc.cx(1,2)\n",
    "qc.ry(-t2/2,2)\n",
    "qc.cx(1,2)\n",
    "\n",
    "qc.ry(t1,2)\n",
    "\n",
    "qc.cx(1,0)\n",
    "qc.h(1)\n",
    "\n",
    "print(\"Matrix:\\n\",np.round(M,3)[:2,:2])\n",
    "print(\"-> untary:\", is_unitary(M))\n",
    "\n",
    "print(\"Circuit matrix (upper left block):\\n\",np.round(np.matrix(Operator(qc)),3)[:4,:4])\n",
    "print(\"-> untary:\", is_unitary(Operator(qc)))\n",
    "\n",
    "print(\"Successfully encode matrix using Block Encoding:\",np.allclose(M[:2,:2], np.matrix(Operator(qc))[:2,:2]))\n",
    "qc.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[-0.364 -0.075]\n",
      " [-0.075 -0.364]]\n",
      "-> untary: False\n",
      "Circuit matrix (upper left block):\n",
      " [[-0.364+0.j -0.075+0.j -0.029-0.j  0.928-0.j]\n",
      " [-0.075+0.j -0.364+0.j  0.928-0.j -0.029-0.j]\n",
      " [-0.928+0.j  0.029+0.j -0.075+0.j -0.364+0.j]\n",
      " [ 0.029+0.j -0.928+0.j -0.364+0.j -0.075+0.j]]\n",
      "-> untary: True\n",
      "Successfully encode matrix using Block Encoding: True\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 447.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "phase = 0\n",
    "phase = universal_be(qc,M,range(2),phase)\n",
    "\n",
    "global_phase_gate(qc,phase,0)\n",
    "\n",
    "print(\"Matrix:\\n\",np.round(M,3)[:2,:2])\n",
    "print(\"-> untary:\", is_unitary(M))\n",
    "\n",
    "print(\"Circuit matrix (upper left block):\\n\",np.round(np.matrix(Operator(qc)),3))\n",
    "print(\"-> untary:\", is_unitary(Operator(qc)))\n",
    "\n",
    "print(\"Successfully encode matrix using Block Encoding:\",np.allclose(M[:2,:2], np.matrix(Operator(qc))[:2,:2]))\n",
    "qc.draw(output=\"mpl\",fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[-0.364 -0.075]\n",
      " [-0.075 -0.364]]\n",
      "-> untary: False\n",
      "Circuit matrix (upper left block):\n",
      " [[-0.364+0.j -0.075+0.j  0.029+0.j -0.928+0.j]\n",
      " [-0.075+0.j -0.364+0.j -0.928+0.j  0.029+0.j]\n",
      " [ 0.928+0.j -0.029+0.j -0.075+0.j -0.364+0.j]\n",
      " [-0.029+0.j  0.928+0.j -0.364+0.j -0.075+0.j]]\n",
      "-> untary: True\n",
      "Successfully encode matrix using Block Encoding: True\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAB7CAYAAAAWqE6tAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAANS0lEQVR4nO3df1RU553H8TczjPwQWcE5SsUYiyAqBRZJiJbmoElM0VqjNmaDkXMiu2IBk1Rjd7Mhxq1RSCxJapON7alJJTU0WYi/EtGN64+Jqb9CayQkGlh1RSJVQY1gUJlh9o+JowMioPPMvTN+X+fMOc5z7zz36+N8vPc+c2eun91utyOEUMKgdQFC+DIJmBAKScCEUEgCJoRCEjAhFJKACaGQBEwIhSRgQigkARNCIQmYEApJwIRQSAImhEISMCEUkoAJoZAETAiFJGBCKCQBE0IhCZgQCknAhFBIAiaEQhIwIRSSgAmhkARMCIUkYEIoJAETQiEJmBAK+WtdgN6tqYCvz2qz7cgwmHaXNtvWgi+OtQSsC1+fhcOntK7i9uCLYy2HiEIoJAETQiEJmBAKScCEUEgCJoRCEjAhFJKACaGQBEwIhSRgwsUlKzS1gNWmdSW+QdcBa2tro6ioiJiYGAIDA0lMTMRisRAbG0t2drbW5V1X2ZKx7Fu3pNvtenH4FPxhBzzzHixcA/9eCv+1Dxqbta6sc94w1rq+VCorK4u1a9eycOFCkpOT2bVrFxkZGZw+fZr58+drXZ7PqDgK7+xy/Nn+XVurDXbXwGfHYO4DMDBMs/K8mm73YCUlJRQXF7NhwwYWLFjAuHHjyM/PZ8yYMVitVpKTkwE4efIkDz74IMHBwSQmJrJ//36NK/cuZy9AyW5HsOztltmBllZ4aye0tV8oukW3ASssLCQ9PZ20tDSX9ujoaEwmE/Hx8QDk5OQwfPhwGhsbycvL4+GHH8ZmkxOI7tpVc+Pw2O3Q0AQ1f/dcTb5ElwGrq6ujqqqK6dOnd1hWW1tLXFwcAQEBNDU1sXHjRp5//nmCgoLIzs7GZrOxZ8+eLrfh5+fXrYfFsqPH9e9bv5QV2X1dHieqP+lxPxbLjm7XebOPt9ftxm6/8e7Jbrcz66mlymvxlrHuCV2eg9XV1QEQERHh0t7S0oLFYmHixIkA1NTU0K9fP8xms3Od+Ph4vvzyS1JTUz1XcDspD+WTMuU5l7ayJWO1KaYLfgZjN940dgwGo0fq6Sm9j7Uu92BXAlNdXe3SvmzZMurr6xk1ahQAFy5cIDQ01GWd0NBQmpu7nvqy2+3deqSljXXPX+ompKWN7XadN/t4OD2lyzr8/Ay8/tIzymvxlrHuCV3uwaKiokhISKCgoIDw8HAiIyMpKyujvLwcwDnB0bt3b5qamlxee/78eUJCQjxes7dKHQaf1HS+3A/oHQDxd3isJJ+iyz2YwWCgtLSUuLg4cnJymDVrFmazmby8PPz9/UlISAAgJiaGhoYGGhsbna+tqqpi5MiRWpXudb7XF9Id80W0P1D0A/z8YGYqGHX5TtE/P3tP93kayszM5MCBA1RWVjrbpk2bxuDBg3nxxRdZvXo1BQUF1NTUYDS655zhtS3afY19aH94YrxntrX3MGypgoZrjq6H9oefJEJUf8/U4ItjrctDxM5UVFQwevRol7YVK1Ywc+ZMwsLCiImJ4f3333dbuG4n9wyFlCiYV+J4/txkMPfRtiZf4DUBa25uprq6mtzcXJf2AQMGsGXLFo2q8i3XTiZKuNzDawIWEhIiHyALryOnrkIoJAETQiEJmBAKScCEUEgCJoRCEjAhFJKACaGQ13wOppVIDb8qr+W2teCLYy0B68LtdH8urfniWMshohAKScCEUEgCJoRCEjAhFJKACaGQBEwIhSRgQigkARNCIQmYEApJwIRQSAImhEISMCEUkoAJoZBcTd+Fr7ZBk0a/NtunP8Tep822teCLYy0B60LTKThXp3UVtwdfHGs5RBRCIQmYEArJIaLg7AWoPA51Z662/fYjGBgGg/tBwh0QaNKuPm8mAXOTp1eM5eCx3RiNJgwGIxFh32fG/fmkJXa8z7Re1J+DjQfgizpofw+rI6cdD4D3P4W7vw8TEh0349OSt42zBMyNHntgIY898Bw2m5X1u16nsGQG0ZFJRJqjtS7NRZsdtn4Bmz8HW1vX61+yOu6CeeA4PHoPxA1SX+ONeMs4g5yDKWE0+jPhntnY2qwcPvGZ1uW4aLPDe3sde67uhOtaTRdhpcVxsz490PM4XyEBU6DVepkPd60AYJB5mMbVuNpceWsBsQPv7oGDJ9xW0k3T8zhfIQFzo5KtS5mysC+Tng3ij//9HPOnryRqoON+0kvfyeAvVeuc6y5aNYX9/7vNo/X9X4PjNrE38pvHHI8bsePYC7ZcdltpPaL3cb6WrgPW1tZGUVERMTExBAYGkpiYiMViITY2luzsbK3L62DG/fmse+EcZf/RQMrwiXx2zT9s7kPLefujRXx7sYmdn6+hT3A4SdGevUxj7V87TmbcrHPfwv984abOekjv43wtXQcsKyuLF154gTlz5rBp0yYeeeQRMjIyOHLkCMnJyVqX16k+wWHMn76SfYfK2VW1HoCwkP5Mu3ce/7n+SUq2LiF7UpFHazreCMca3NvnnsNg1fCmo3oc5/Z0G7CSkhKKi4vZsGEDCxYsYNy4ceTn5zNmzBisVqszYIsWLWLkyJEYDAbKyso0rvqq0OBwfnbvfN7a/CxtbY7ZhB/f/ThfN9QwJfVJQoPDPVrP3465v88Ll+Crevf32xN6G+f2dBuwwsJC0tPTSUtLc2mPjo7GZDIRHx8PQExMDMuXLyclJUWLMm9o6r1PceZ8PVv++razbWC/aE2mk2sbFfV7put1VNPTOLeny8/B6urqqKqqYt68eR2W1dbWEhcXR0CA4xPPmTNnArB06VKP1tjeyzk7OrT1DgxlzWIdvAOBv3+jqN9zavrtjN7HuT3dBgwgIiLCpb2lpQWLxcLEiRNveRt+fn7dWq/o59tJHDr2lrd3MyyWHdydMc4tfeWubMYU2Nv5vKuZws6W/+Id1+frPthIVtqkW6zOwVvG2m7v/lSRLgNmNpsBqK6udgnTsmXLqK+vZ9SoUVqVdsv+9dFVmmzX2nrRJWDuYrt80e19uoNW49yeLgMWFRVFQkICBQUFhIeHExkZSVlZGeXl5QBumUHs7v9CFe9q9x2ltLSx2Fe4Z2J9+Udw9PTV5+33RFdc2XN1try93Kyf8eFy99ToK2N9LV1OchgMBkpLS4mLiyMnJ4dZs2ZhNpvJy8vD39+fhIQErUv0OncomkxT1a+v0OUeDGDYsGFs377dpS0zM5MRI0YQFBTkbGttbcVms9HW1kZraysXL14kICCg2+dYt4ukO+Hjr9zbZ5AJYr/n3j59jW4Ddj0VFRWMHj3apW327NkUFxcDsHPnTgCOHj3KkCFDPFJTwzcnWPjHSRw7+SUfLGnGaLw6pG+s/4XzItQj9QdYu/gsH1UUs3nfm1y2XuTBux5n8g9zPVLnEDMMCoO6s+7rM2Uo9PLgO+hg7V5+t2EeBoORYYPuImfyq85lf95WyKeHNnGptYWM+57lR/FTKd/7BzbtexOAqT96kvuSZniu2O/o8hDxepqbm6muru4wwbFq1SrsdrvLw1PhAscHncuytzJi8OgOy3If+g0v5+wgZ/Kr3DP8JwDclzSDV3I/Zvnc3Wzc83uP1ennB1PcePFLSCCMj3Nff90xoO+d/HrONl7N3cm55lMcrf/cuWx62gJeyf2Yop9v570dLwEwKmY8rz2xh1dzd1JmedmzxX7Ha/ZgISEh2GwaXpfTiV6mQHqZAm+4zidVa0mNnwaAv9Hx1WCr7TKD+49QXt+1ogdA2nCwHOp8ne5ObjyS4giZJ4WHXv3Yxmjwx2AwOp9fGddLrS0MifgBABHhQ667rid5zR7Mm1V8tZm7Y9Odz/+0ZTGPvxRDzCDPX085OQn+cfCt9TE12fEzAlo5cqKSby40cOeAkS7tv12Ty5xXEjpc3Pvh7t/xw7gpHqzwKgmYYnWnazCHRhLYK9jZljn+eYqfOczHlaWcv6DoGqZOGA2QmQr3j4SeTgMFmRyvTRuupLRuOf/tGV5fN5enp7/ZYdmT097grV8eomTr1at6DtbuZd+hcv5p3L95skwnrzlE9FZ/qVpL6g+mOp9ftl6il38AJmMvAkzBmPw9/yMXRgP8NAni74AP9sPhLn7s02iApMGO1/xD8I3XVclms/Lin2cye9KvXQ4X4eq49jIFERwQCkDDN1/z+w+eZvGsDRg1OkSUgN0iq62VZ1dO4Ej9AZ5Z+WOyJhSw9W+rmTvlNQD2HvyQXz2+3rn+u9sKOXB4B1bbZR4YlUlQQIhWpTPEDE+Md1ynWFkLx8/AqfNgbYMAEwzs6/hVqaQ7oY+Hz7eux1JZSvXxT1m50bE3+ucJhWz7rIS5U17jjfVPcfzUIay2y0wf+0sAVm9ZzNnmk/yq2HH+W/AvmwgwBXXavwp+9p5cWHUb0vLqgr6D4K5Htdm2FnxxrOUcTAiFJGBCKCTnYF3o0//23LYWfHGs5RxMCIXkEFEIhSRgQigkARNCIQmYEApJwIRQSAImhEISMCEUkoAJoZAETAiFJGBCKCQBE0IhCZgQCknAhFBIAiaEQhIwIRSSgAmhkARMCIUkYEIo9P94qwP1WtalMQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "qc.h(0)\n",
    "\n",
    "D_optimized = linlin_2x2_symmetric_optimize(M)\n",
    "ucry_decomposition_optimize(qc,2,np.real(D_optimized)@transfer_matrix(2),range(2))\n",
    "\n",
    "qc.h(0)\n",
    "\n",
    "print(\"Matrix:\\n\",np.round(M,3)[:2,:2])\n",
    "print(\"-> untary:\", is_unitary(M))\n",
    "\n",
    "print(\"Circuit matrix (upper left block):\\n\",np.round(np.matrix(Operator(qc)),3)[:4,:4])\n",
    "print(\"-> untary:\", is_unitary(Operator(qc)))\n",
    "\n",
    "print(\"Successfully encode matrix using Block Encoding:\",np.allclose(M[:2,:2], np.matrix(Operator(qc))[:2,:2]))\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
}