operator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8b24f5d3",
   "metadata": {},
   "source": [
    "# Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5482b331",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import SparsePauliOp, random_pauli, random_hermitian, random_clifford, random_unitary, pauli_basis, Pauli, PauliList, random_density_matrix\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20f66836",
   "metadata": {},
   "source": [
    "## Gate identity "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "6859c72c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## H = 1/sqrt(2) (X + Z)\n",
    "hdm = 1/np.sqrt(2)*(SparsePauliOp('Z') + SparsePauliOp('X'))\n",
    "## HZH = X\n",
    "(hdm @ SparsePauliOp('Z') @ hdm).simplify() == SparsePauliOp('X')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "d77e5812",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['Y'],\n",
       "              coeffs=[-1.+1.23259516e-32j])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Clifford gate maps one Pauli to another Pauli\n",
    "theta = np.pi/4\n",
    "s_gate = np.exp(1j*theta)*(np.cos(-theta)*SparsePauliOp('I') + 1j*np.sin(-theta)*SparsePauliOp('Z'))\n",
    "(s_gate.adjoint() @ SparsePauliOp('X') @ s_gate).simplify() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "362cb29b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['X', 'Y'],\n",
       "              coeffs=[ 0.70710678+2.55564914e-17j, -0.70710678+1.21941298e-17j])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## T gate transforms one Pauli to two Paulis\n",
    "# t_gate = np.array([[1, 0], [0, np.exp(1j*np.pi/4)]])\n",
    "theta = np.pi/8\n",
    "t_gate = np.exp(1j*theta)*(np.cos(-theta)*SparsePauliOp('I') + 1j*np.sin(-theta)*SparsePauliOp('Z'))\n",
    "# t_gate\n",
    "# t_gate == t_gate_p.to_matrix()\n",
    "(t_gate.adjoint() @ SparsePauliOp('X') @ t_gate).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "61778b02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## CNOT gate\n",
    "cnot = 0.5*(SparsePauliOp('I')+SparsePauliOp('Z')).tensor(SparsePauliOp('I')) + 0.5*(SparsePauliOp('I')-SparsePauliOp('Z')).tensor(SparsePauliOp('X'))\n",
    "cnot.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e35bd5dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator([[1.+0.j, 0.+0.j],\n",
      "          [0.+0.j, 0.+0.j]],\n",
      "         input_dims=(2,), output_dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "Statevector.from_label('0').to_operator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a6c7b32a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
      "          [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n",
      "          [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
      "          [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j]],\n",
      "         input_dims=(2, 2), output_dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector, SparsePauliOp\n",
    "Statevector.from_label('0').to_operator().tensor(SparsePauliOp('I'))+Statevector.from_label('1').to_operator().tensor(SparsePauliOp('X'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5f62482",
   "metadata": {},
   "source": [
    "### Rotation (real-time evolution) of a Pauli string\n",
    "\n",
    "https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/Hamiltonian_simulation.ipynb\n",
    "\n",
    "$$\n",
    "e^{-i XX t} = \\text{CNOT} (I\\otimes e^{-i X t}) \\text{CNOT}\n",
    "$$\n",
    "\n",
    "[1] J.D. Whitfield, J. Biamonte and A. Aspuru-Guzik, Molecular Physics, \"Simulation of electronic structure Hamiltonians using quantum computers\" (2011)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "dbb5e87a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.54030231+0.j         0.        +0.j         0.        +0.j\n",
      "  0.        +0.84147098j]\n",
      " [0.        +0.j         0.54030231+0.j         0.        +0.84147098j\n",
      "  0.        +0.j        ]\n",
      " [0.        +0.j         0.        +0.84147098j 0.54030231+0.j\n",
      "  0.        +0.j        ]\n",
      " [0.        +0.84147098j 0.        +0.j         0.        +0.j\n",
      "  0.54030231+0.j        ]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.54030231+0.j        , 0.        +0.j        ,\n",
       "        0.        +0.j        , 0.        +0.84147098j],\n",
       "       [0.        +0.j        , 0.54030231+0.j        ,\n",
       "        0.        +0.84147098j, 0.        +0.j        ],\n",
       "       [0.        +0.j        , 0.        +0.84147098j,\n",
       "        0.54030231+0.j        , 0.        +0.j        ],\n",
       "       [0.        +0.84147098j, 0.        +0.j        ,\n",
       "        0.        +0.j        , 0.54030231+0.j        ]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.linalg import expm\n",
    "t = 1\n",
    "print(expm(1j*t*SparsePauliOp('XX').to_matrix()))\n",
    "cnot.to_matrix() @ np.kron(expm(1j*t*SparsePauliOp('X').to_matrix()), SparsePauliOp('I').to_matrix()) @ cnot.to_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a299aec9",
   "metadata": {},
   "source": [
    "## Observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "64d12a4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.+0.j,  1.+0.j],\n",
       "       [-1.+0.j,  0.+0.j]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.multi_dot([SparsePauliOp('Z'), SparsePauliOp('X')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "af232ab6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['XZ'],\n",
       "              coeffs=[1.+0.j])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SparsePauliOp('IZ') @ SparsePauliOp('XI')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1a45019",
   "metadata": {},
   "source": [
    "### Pauli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "82e526be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PauliList(['III', 'IIX', 'IIY', 'IIZ', 'IXI', 'IYI', 'IZI', 'XII', 'YII',\n",
       "           'ZII', 'IXX', 'IXY', 'IXZ', 'IYX', 'IYY', 'IYZ', 'IZX', 'IZY',\n",
       "           'IZZ', 'XIX', 'XIY', 'XIZ', 'XXI', 'XYI', 'XZI', 'YIX', 'YIY',\n",
       "           'YIZ', 'YXI', 'YYI', 'YZI', 'ZIX', 'ZIY', 'ZIZ', 'ZXI', 'ZYI',\n",
       "           'ZZI', 'XXX', 'XXY', 'XXZ', 'XYX', 'XYY', 'XYZ', 'XZX', 'XZY',\n",
       "           'XZZ', 'YXX', 'YXY', 'YXZ', 'YYX', 'YYY', 'YYZ', 'YZX', 'YZY',\n",
       "           'YZZ', 'ZXX', 'ZXY', 'ZXZ', 'ZYX', 'ZYY', 'ZYZ', 'ZZX', 'ZZY',\n",
       "           'ZZZ'])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pauli_basis(3, weight=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ab1edc76",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.  ['II', 'ZI', '-iYY']\n",
      "2.  ['iXI']\n",
      "3.  ['iXI', 'iZZ']\n",
      "4.  ['YZ', '-iIX']\n"
     ]
    }
   ],
   "source": [
    "# 1. init from list[str]\n",
    "pauli_list = PauliList([\"II\", \"+ZI\", \"-iYY\"])\n",
    "print(\"1. \", pauli_list)\n",
    "pauli1 = Pauli(\"iXI\")\n",
    "pauli2 = Pauli(\"iZZ\")\n",
    "# 2. init from Pauli\n",
    "print(\"2. \", PauliList(pauli1))\n",
    "# 3. init from list[Pauli]\n",
    "print(\"3. \", PauliList([pauli1, pauli2]))\n",
    "# 4. init from np.ndarray\n",
    "z = np.array([[True, True], [False, False]])\n",
    "x = np.array([[False, True], [True, False]])\n",
    "phase = np.array([0, 1])\n",
    "pauli_list = PauliList.from_symplectic(z, x, phase)\n",
    "print(\"4. \", pauli_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c9e65e8",
   "metadata": {},
   "source": [
    "### random pauli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e88a7cc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pauli('ZYX')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_pauli(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64c69ef6",
   "metadata": {},
   "source": [
    "### random pauli with fixed weight"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5d3033f",
   "metadata": {},
   "source": [
    "### random Hermitian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "aad2e009",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator([[-0.55707039+0.j        ,  0.84206074+0.26216488j,\n",
      "           -0.43266326-0.16221111j,  0.05284663-0.61020708j],\n",
      "          [ 0.84206074-0.26216488j, -0.17670864+0.j        ,\n",
      "           -0.96305908+0.12418724j,  0.26573818-0.38604076j],\n",
      "          [-0.43266326+0.16221111j, -0.96305908-0.12418724j,\n",
      "            0.7518909 +0.j        , -0.82331876-0.15159718j],\n",
      "          [ 0.05284663+0.61020708j,  0.26573818+0.38604076j,\n",
      "           -0.82331876+0.15159718j, -3.26656753+0.j        ]],\n",
      "         input_dims=(2, 2), output_dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "random_hermitian(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40ed2fee",
   "metadata": {},
   "source": [
    "### Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eb78baf6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fe120002",
   "metadata": {},
   "source": [
    "### Spin: magnetization, correlation, OTOC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7e01d90f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['IIIZ', 'IIZI', 'IZII', 'ZIII'],\n",
       "              coeffs=[0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n  = 4\n",
    "magn_op = SparsePauliOp.from_sparse_list([('Z', [i], 1/n) for i in range(0, n)], n)\n",
    "corr_op = SparsePauliOp.from_sparse_list([('ZZ', [i,i+1], 1/(n-1)) for i in range(0, n-1)], n)\n",
    "magn_op"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9953ce8d",
   "metadata": {},
   "source": [
    "### Expectation value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10437725",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.024740064059499516+0j)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit.quantum_info import DensityMatrix\n",
    "\n",
    "n = 4\n",
    "dm = random_density_matrix(2**n)\n",
    "dm.expectation_value(SparsePauliOp('X'*n))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc805515",
   "metadata": {},
   "source": [
    "## Unitaries"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "811c4ebc",
   "metadata": {},
   "source": [
    "### Random unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c2c270c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator([[ 0.23134833+0.04369654j, -0.32008479+0.25942886j,\n",
      "            0.82028777-0.18289223j, -0.15268571-0.21254751j],\n",
      "          [-0.09206845-0.63233525j, -0.6159064 -0.37495105j,\n",
      "           -0.08357862-0.07129137j, -0.20810924+0.12794238j],\n",
      "          [-0.56136202+0.34079881j,  0.17333584-0.45960825j,\n",
      "            0.30110793-0.17322879j, -0.39228545+0.22996028j],\n",
      "          [-0.28081993-0.16159555j,  0.06509485-0.25454079j,\n",
      "            0.21719542-0.337287j  ,  0.79330534-0.18902107j]],\n",
      "         input_dims=(2, 2), output_dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "random_unitary(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b9c3404",
   "metadata": {},
   "source": [
    "### Random gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6f3ea6aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Clifford(array([[False,  True,  True, False,  True,  True,  True, False, False],\n",
       "       [ True, False,  True, False,  True,  True,  True, False,  True],\n",
       "       [False,  True,  True, False, False, False, False,  True, False],\n",
       "       [False, False, False, False,  True,  True,  True, False, False],\n",
       "       [False,  True,  True,  True, False,  True, False, False, False],\n",
       "       [False,  True,  True, False, False,  True,  True,  True,  True],\n",
       "       [ True, False,  True,  True, False, False, False, False, False],\n",
       "       [ True, False, False,  True, False, False,  True,  True, False]]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_clifford(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "387c5763",
   "metadata": {},
   "source": [
    "## Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c22860",
   "metadata": {},
   "source": [
    "### (Anti) commutator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c445f6d2",
   "metadata": {},
   "source": [
    "## Norms"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "915b263c",
   "metadata": {},
   "source": [
    "### Vector induced norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96dd2d8b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "op:  SparsePauliOp(['XIIZI', 'IYIIY'],\n",
      "              coeffs=[1.+0.j, 2.+0.j])\n",
      "Spectral norm:  3.0000000000000004\n",
      "Trace norm:  63.999999999999986\n",
      "Frobenius norm:  12.649110640673518\n"
     ]
    }
   ],
   "source": [
    "op = SparsePauliOp.from_list([(\"XIIZI\", 1), (\"IYIIY\", 2)])\n",
    "print('op: ', op)\n",
    "print('Spectral norm: ', norm(op, ord=2))\n",
    "print('Trace norm: ', norm(op, ord='nuc'))\n",
    "print('Frobenius norm: ', norm(op, ord='fro'))\n",
    "# print(norm(SparsePauliOp.from_list([(\"XYZI\", 1)]), ord='nuc'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f736ec33",
   "metadata": {},
   "source": [
    "### Schatten p norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1866ad8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.605551275463989"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = SparsePauliOp.from_list([('XX', 2), ('YX', 3)])\n",
    "np.linalg.norm(test.to_matrix(), ord='nuc')\n",
    "np.linalg.norm(test.to_matrix(), ord=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcba2d92",
   "metadata": {},
   "source": [
    "## Entenglement "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3ba6d208",
   "metadata": {},
   "outputs": [],
   "source": [
    "### purity\n",
    "### entropy\n",
    "### negativity\n",
    "### concurrence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16d8bc21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.253540852652231"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 4\n",
    "ket = random_statevector(4).data\n",
    "# ket = Statevector.from_label('+').data\n",
    "dm = random_density_matrix(2**n).data\n",
    "entropy(ket, base=2)\n",
    "entropy(dm, base=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "476f64d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Entropy distribution')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mb8Z8gLAOASUoKEiPPvqoof7WW29p1apVLvf5+OOP9d577+V4e0REhNPvOb0gm+0Z5w6zsO7yEwIDVuWv9egNu92ujz76SPXr11dcXJzpfTp37qw33njDZ2MCecEK6zEzM1N333230wmwK1SooE8//dTl8YGCwp9r0uwojUvPd1WoUCG9/PLL2r9/vz7++GMNGTJEXbp0Uc+ePfWf//xHU6dO1V9//aVx48YpJCTE0Oupp54yvfAaYFVWeI+UpG+//VbXX3+9pk6dqszMTJfHvdS5c+f02muvqXHjxl5dXA25j7AOAWf48OGqWLGiUy0rK0tdu3bVZ599JrvdnuO2hw8f1rBhw/R///d/Vxzj8hfanHqGhYW5OGtzZn293VsPyEv+WI+e2rhxo5o3b64RI0bkeAWwHj16aN68eaZ/nABW5+/1+Mwzz+inn366+HtQUJBmzJhhemJvIBD4a01e6YvfokWLKj4+Xs8888wV13N4eLief/55TZo0yXBbdna2nnnmmSvOC7Aaf79HfvbZZ+rbt6/plWRLlCihgQMH6sMPP9SCBQu0dOlSzZo1S08++aThSs4X/Pnnn2rdurXpBWVgDVxgAgEnIiJCs2fPVvv27Z12NT537pzuvfdevfbaa7r99tvVpEkTlSlTRg6HQwcPHtTKlSs1f/58wweYqlWrGq7oU7RoUcOYZjz9RuQCs12lfbkXEZDb/LEe3WWz2TRmzBjNnDlTDofD9D6hoaF68cUXNWbMGAUFBXk1HuAv/lyPy5cv19tvv+1Ue+SRR9SxY0cfPTog//HXmkxPT89xTp9//rlatWrl8mO4//779d133+mHH35wqs+bN0+HDx/O8XBZwGr8+R65bt06jRgxwhAIBgUFafTo0Xr66adVokQJw3Z33323Xn/9da1atUr333+/IZg7fvy4+vTpo02bNvE3pAUR1iEg3XzzzZowYYL++9//Gv743r17tyZMmOBSn44dO6pu3bqGbw0rVark9HtOL7xX+jDkCrPDFHihRX6T1+vRVRkZGZo4caJeeumlK15luWHDhvrss8/UtGlTj8YBrMQf6/HIkSMaPHiw03iNGjXiIi2A/LMmc/piqk2bNurVq5drE7/ESy+9ZAjrHA6HVqxYoQEDBrjdD/AXf6zH7OxsjRgxwrCTR3BwsL788kv17t37quO1adNGiYmJuuOOO7R06VKn27Zv367JkyfriSeecGnuyDscBouANXLkSM2aNUvh4eEebd+hQwfNmzdP+/btM9xWrVo1p9/Dw8NND4vz9sqtZgFCVFSUVz0Bf8jL9eiK+Ph41a9fX0888USOQV2xYsX0+uuvKzExkaAOBUperkeHw6EhQ4bIZrNdrBUpUsSr8YGCJq/fI3Ma5z//+Y9H4zdt2lSNGjUy1HO6IiZgZXm9HhcuXKht27YZ6s8//7xLQd0FERER+vrrr1WjRg3Dbe+++26uXJAN3iGsQ0C76667tGXLFt15550uH7pWsmRJvfnmm1qyZImKFi1qePEMDg42XC1IMg/RzK625Y5jx44ZatWrV/eqJ+Avebkec3Ly5EkNHz5ct9xyi/7880/T+wQFBWngwIHauXOnnnzySRUqVMjl/kB+kVfrcfbs2VqyZIlT7a233lK9evW8ewBAAZOX75E5HaXRrl079yf+/3Xq1MlQO3jwoMf9AH/Ky/U4e/ZsQ618+fIaPXq02/MuVqyYXnzxRUP98OHD+vnnn93uh9zFYbAIeLVr19bcuXP18ssva9GiRVq+fLn27Nmjo0eP6uTJk4qIiNA111yjJk2aqHPnzurVq9fFDzGnTp0ynGugbt26pn+816xZ0xCuXbongSfMtiesQ36WV+vRzI4dO9StWzft3r07x/u0atVK48ePV0xMjOcPEsgn8mI9HjlyxDDuyJEjNXLkSK/m/sILL+iFF14w1Ddv3qzGjRt71Rvwl7x6jyxbtqyhFh4ebji5vjvM9qwz+9IZyC/yaj2uW7fOUOvevbuKFCni0bx79eql8PBww+mY1q1bp2bNmnnUE7mDsA74/2rVqqVRo0Zp1KhRLm+zadMmw/kKmjdvnmP/DRs2ONWuFApczenTp9mzDgVWbq/HyyUkJKhXr146ceKE6e3Vq1fXm2++qT59+rg8H6CgyOv1CODKcntNVqhQwVArVaqUW3O8nFkAmNOV1YH8JDfXY1pamg4dOmSo33TTTW7P84IiRYqoadOm+vHHH53qycnJHvdE7iCsA7ywZs0aQy2nDz516tQx1LZu3erx2Dt37jTUrrvuOhUvXtzjnkB+5s56vNSvv/6q7t27m56bLiwsTE899ZTGjBmjwoUL+2SeQCDwdD0CyB3urMlatWoZahkZGV6Nb7Y951lGoHJ1PeYUaJcrV86r8c2uwpzTF9bwH8I6wAuXX01HMj8nhyTFxsYaaomJibLb7QoOdv/0kYmJiYZa69at3e4DFBTurMcLUlNTdeutt5oGdXXr1tWcOXNMD90BcGWerEcAucedNWl2zsjjx48rKytLoaGe/fl49OhRQ81sbzsgELi6HnM61NXV8+TlxOziGCVLlvSqJ3yPsA4B5a+//tK8efOcanXq1FHXrl3d7nXw4EFt3LjRqRYTE6OqVaua3r9169aKiIjQ2bNnL9ZSUlK0adMm0yDvauLj403HAPILf67HC8aMGWO623+HDh307bffsqcqAoa/1mOfPn28PofckiVL9MYbbzjVhgwZonvuucdw35o1a3o1FpBX/PkeWb9+fRUvXtzpiyy73a6ff/7Zo8+skkxPXs+FZJBf+Gs9RkVFqVChQsrMzHSqmx0a646UlBRDzdu99eB7hHUIKMnJyXrkkUecai1btvTohfbTTz81nGugb9++Od4/PDxcbdq00Q8//OBU//rrr93+4JOWlma4el7hwoXVrVs3t/oA/uTP9Sj9c0GJTz/91FBv166dFi5c6PGJe4H8yF/rsXLlyqpcubLbY1xq//79hlq1atXUtm1br/oC/uTP98iQkBC1bdtW3333nVN98eLFHod1y5cvN9Q6dOjgUS8gr/lzPVasWNFwMYrVq1fr3nvvdXtsSXI4HPrtt98M9fr163vUD7nH/WPvgHzM7IS527ZtM1wN52pOnjypKVOmONXCw8NNv8W/VL9+/Qy1adOmKS0tza3xZ8yYYThsr2fPnipRooRbfQB/8vd6/OCDDwwflipXrqwvv/ySoA4Bx9/rEYAzf69Js/Dgww8/1Pnz590aX/rnaJBdu3Y51SIjIzkiBPmGP9dj+/btDbV58+Z5fI65jRs3Gq7EXrhwYbVp08ajfsg9hHUIKFWrVjV8g3/y5El9+eWXbvV5/PHHDVdiHTRo0FV3H7777rsNL/YpKSmGw3eu5NChQxo3bpyh7um3K4C/+HM92u12/e9//zPUJ0yYoDJlyrg1PlAQ+Pv9EYAzf6/J3r17q3Tp0k61I0eO6JlnnnFrfLvdrtGjRxvq999/P1+MId/w53rs3r27oXb69Gm98MILbo19wXPPPWeo3XrrraxHCyKsQ741ffp0BQUFGX4SEhKuuN1tt91mqD3xxBMuH/v/1FNPGQ6di4iIMH3hu1xYWJj++9//GuqvvfbaVectSWfPnlXPnj0NJ+lt1aoVhxLAr/Lbety4caPhfB316tVT7969XRoXsLL8th6Bgi4/rsmIiAjDYX+SNH78eE2fPt2l8aV/5vvLL7841YoUKaJRo0a53APwpfy2Hm+99VbVqFHDUJ84caJmz57t0tgXjBkzRitWrHCqBQUF8T5tUYR1CDiPPfaY4UpWNptNbdq00YYNG3Lc7tChQ+rTp49ef/11w23PPvusrrnmGpfGf+ihh1StWjWnWlZWlm6//XZ99dVXOW73xx9/qHnz5tq0aZNTPSQkRO+++65LYwNW46/1aHaBlkaNGikhIcGnP7t373bxmQD8z9/vjwCc+XtNPv7446pTp45TzeFwaNiwYXryySdNr6R+wcmTJzV8+HC98847htvefvttRUdHuzQHwCr8tR7DwsJM/9ZzOBwaMGCAnn32WZ06deqKPfbv368ePXqYHs01aNAgry/0hNzBBSYQcGrVqqUHH3xQEydOdKrv3r1bN910k26++Wb17NlTVatWVXh4uA4ePKgVK1bo+++/17lz5wz9OnbsqCeeeMLl8YsWLarPPvtMnTp1UlZW1sV6Wlqa7rzzTrVo0UJ9+vRR3bp1Zbfb9ffff2vRokVasmSJ7Ha7od9zzz2nG2+80Y1nALAOf63HzZs3G2qzZ892+xvKq3n44Yc1YcIEn/YEcou/3x8BOPP3mgwPD9e3336rFi1aOIUBDodDb775pqZOnarbb79drVu3Vvny5RUcHCybzaa1a9dqwYIFSk1NNfS87bbb9MADD7jxLADW4M/12L17d40cOVKTJ092qjscDr3yyiuaMmWKunbtqpYtW6pChQqKjIzU6dOntWfPHq1cuVJLly5Vdna2oe/111+v999/341nAXmJsA4B6a233tLmzZu1evVqp7rD4dCqVau0atUql/o0atRIc+fOVUhIiFvjt2vXTpMmTdIDDzxgOMH9+vXrtX79epf6DBw4UGPHjnVrbMBq/LEet27d6tFcgYLO3++PAJz5e03Wq1dPy5cvV9euXQ3hW0pKimbMmKEZM2a41KtJkyam54sF8gt/rsdJkybJbrebhmsnTpxw+0vn6tWra8GCBSpatKjL2yBvcRgsAlKhQoX03XffmZ6w01WdOnXS6tWrFRUV5dH2I0aM0LRp01S4cGGPtn/44Yc1bdo0BQUFebQ9YBX+WI9JSUkejwUUZFZ4fwTwLyusyWbNmumnn35SkyZNPJ5Djx49lJCQoBIlSnjcA/A3f6/HKVOm6IsvvjBc/MVdN998s3766SfTc+HBOgjrELAiIyM1f/58ffDBB4ZzyF1JxYoV9cknn2jJkiWKjIz0ag5DhgzRL7/8os6dO7u8Tb169bR48WJNmDDBcN4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      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 497,
       "width": 629
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit.quantum_info import partial_trace, entropy\n",
    "entropy_list = [entropy(partial_trace(random_density_matrix(2**n).data, [0,1]), base=2) for _ in range(1000)]\n",
    "\n",
    "from utils import *\n",
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "ax.hist(entropy_list, bins=50, edgecolor='black')\n",
    "ax.set_xlabel('Entropy'); ax.set_ylabel('Frequency'); ax.set_title('Entropy distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2ef4296",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['IXIII'],\n",
       "              coeffs=[2.+0.j])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "commutator(SparsePauliOp(\"XIIZI\"), SparsePauliOp(\"XXIZI\")).simplify()\n",
    "anti_commutator(SparsePauliOp(\"XIIZI\"), SparsePauliOp(\"XXIZI\")).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b4b21ae",
   "metadata": {},
   "source": [
    "## Quantum circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "50a6ff1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 705.552x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "image/png": {
       "height": 625,
       "width": 563
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(9)\n",
    "for idx in range(4):\n",
    "   qc.h(idx)\n",
    "   qc.cx(idx, idx+5)\n",
    " \n",
    "qc.cx(1, 7)\n",
    "qc.x(8)\n",
    "qc.x(7)\n",
    "qc.x(6)\n",
    "qc.draw('mpl')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.8 ('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": "3.10.14"
  },
  "vscode": {
   "interpreter": {
    "hash": "4e8ef2f9fcac0817bca9a7ca376f64f20b4df5ea3bf7af756a50bda7d3557ea6"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}