PTM_Murao.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *\n",
    "import numpy as np\n",
    "from itertools import product\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import simple_exact_diagonalization_routines as spd\n",
    "from class_PTM_Murao import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functionality tests\n",
    "Explains the basic functions of the class and verify the correctness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 1: Pauli commutors\n",
    "1. Demonstrate the formalism of inputs\n",
    "2. Show that the pauli operations in class_PTM work as intended (compare with QuTiP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Commute by index (-2j, (0, 3, 3))\n",
      "QuTip produces the same result:  True\n"
     ]
    }
   ],
   "source": [
    "# Initialize class\n",
    "sys = pauli_transfer_matrix(3)\n",
    "\n",
    "# Note that the pauli operators are given as tuple\n",
    "# (0,1,2,3) correspond to id, X, Y, Z\n",
    "# number of elements must match ntls\n",
    "\n",
    "op1 = (1,3,2)\n",
    "op2 = (1,0,1)\n",
    "ind_com = sys.pauli_commute(op1,op2)\n",
    "print('Commute by index', ind_com)\n",
    "\n",
    "qutip_ops = sys.pauli_qutip_ops()\n",
    "comm_qutip = commutator(qutip_ops[op1], qutip_ops[op2])\n",
    "print('QuTip produces the same result: ', comm_qutip == -2j*qutip_ops[ind_com[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 2: Pauli transfer matrix equivalence to function\n",
    "\n",
    "Suppose function f(H) = [D,H], where D is diagonal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Index</th>\n",
       "      <th>Gamma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2064</th>\n",
       "      <td>((2, 0, 0), (1, 0, 0))</td>\n",
       "      <td>0.010417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2324</th>\n",
       "      <td>((2, 1, 0), (1, 1, 0))</td>\n",
       "      <td>0.010417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2519</th>\n",
       "      <td>((2, 1, 3), (1, 1, 3))</td>\n",
       "      <td>0.010417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1511</th>\n",
       "      <td>((1, 1, 3), (2, 1, 3))</td>\n",
       "      <td>0.010417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1771</th>\n",
       "      <td>((1, 2, 3), (2, 2, 3))</td>\n",
       "      <td>0.010417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>394</th>\n",
       "      <td>((0, 1, 2), (0, 2, 2))</td>\n",
       "      <td>0.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2596</th>\n",
       "      <td>((2, 2, 0), (2, 1, 0))</td>\n",
       "      <td>0.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3579</th>\n",
       "      <td>((3, 1, 3), (3, 2, 3))</td>\n",
       "      <td>0.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1499</th>\n",
       "      <td>((1, 1, 3), (1, 2, 3))</td>\n",
       "      <td>0.020833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>329</th>\n",
       "      <td>((0, 1, 1), (0, 2, 1))</td>\n",
       "      <td>0.020833</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>64 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Index     Gamma\n",
       "2064  ((2, 0, 0), (1, 0, 0))  0.010417\n",
       "2324  ((2, 1, 0), (1, 1, 0))  0.010417\n",
       "2519  ((2, 1, 3), (1, 1, 3))  0.010417\n",
       "1511  ((1, 1, 3), (2, 1, 3))  0.010417\n",
       "1771  ((1, 2, 3), (2, 2, 3))  0.010417\n",
       "...                      ...       ...\n",
       "394   ((0, 1, 2), (0, 2, 2))  0.020833\n",
       "2596  ((2, 2, 0), (2, 1, 0))  0.020833\n",
       "3579  ((3, 1, 3), (3, 2, 3))  0.020833\n",
       "1499  ((1, 1, 3), (1, 2, 3))  0.020833\n",
       "329   ((0, 1, 1), (0, 2, 1))  0.020833\n",
       "\n",
       "[64 rows x 2 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "D = [(1,(3,0,0)), (2,(0,3,0))]\n",
    "sys = commutator_type_dynamics(D)\n",
    "sys.show_prob_uw_distribution()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(pauli_test): [(-2j, (2, 2, 3)), (4j, (1, 1, 3))]\n",
      "PTM: [(4j, (1, 1, 3)), (-2j, (2, 2, 3))]\n"
     ]
    }
   ],
   "source": [
    "pauli_test = (1,2,3)\n",
    "# Commutator with D\n",
    "print('f(pauli_test):',sys.f(pauli_test, D))\n",
    "# Input to gamma\n",
    "f_ls = []\n",
    "gamma_uw_dict = sys.gamma_uw_dict\n",
    "for (u,w) in sys.perm_pairs:\n",
    "    if u == pauli_test and gamma_uw_dict[(u,w)]!=0:\n",
    "        f_ls.append((gamma_uw_dict[(u,w)], w))\n",
    "print('PTM:', f_ls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 3: Sampling routine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1400x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D = [(3,(0,3)),(1,(3,0))]\n",
    "sys = pauli_transfer_matrix(D)\n",
    "(v,vp) = sys.sample_vv()\n",
    "sampl_uw = sys.sample_uw(multi_sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 4: Controlled unitaries\n",
    "1. Check components Hadamard, controlled U correct\n",
    "2. Result in unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_fj using (v, vp) = ((3, 3),(3, 2)), (u, w) = ((2, 0),(1, 0)), gamma_uw = 2j\n",
      "Sign sf = 0\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = False $ \\\\ \\left(\\begin{matrix}0.0 & (-0.500-0.500j) & 0.0 & 0.0 & 0.0 & (-0.500+0.500j) & 0.0 & 0.0\\\\(0.500+0.500j) & 0.0 & 0.0 & 0.0 & (-0.500+0.500j) & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.500+0.500j) & 0.0 & 0.0 & 0.0 & (0.500+0.500j)\\\\0.0 & 0.0 & (0.500-0.500j) & 0.0 & 0.0 & 0.0 & (0.500+0.500j) & 0.0\\\\0.0 & (0.500-0.500j) & 0.0 & 0.0 & 0.0 & (0.500+0.500j) & 0.0 & 0.0\\\\(-0.500+0.500j) & 0.0 & 0.0 & 0.0 & (0.500+0.500j) & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & (0.500+0.500j) & 0.0 & 0.0 & 0.0 & (-0.500+0.500j)\\\\0.0 & 0.0 & (-0.500-0.500j) & 0.0 & 0.0 & 0.0 & (-0.500+0.500j) & 0.0\\\\\\end{matrix}\\right)$"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 0. +0.j  -0.5-0.5j  0. +0.j   0. +0.j   0. +0.j  -0.5+0.5j  0. +0.j\n",
       "   0. +0.j ]\n",
       " [ 0.5+0.5j  0. +0.j   0. +0.j   0. +0.j  -0.5+0.5j  0. +0.j   0. +0.j\n",
       "   0. +0.j ]\n",
       " [ 0. +0.j   0. +0.j   0. +0.j  -0.5+0.5j  0. +0.j   0. +0.j   0. +0.j\n",
       "   0.5+0.5j]\n",
       " [ 0. +0.j   0. +0.j   0.5-0.5j  0. +0.j   0. +0.j   0. +0.j   0.5+0.5j\n",
       "   0. +0.j ]\n",
       " [ 0. +0.j   0.5-0.5j  0. +0.j   0. +0.j   0. +0.j   0.5+0.5j  0. +0.j\n",
       "   0. +0.j ]\n",
       " [-0.5+0.5j  0. +0.j   0. +0.j   0. +0.j   0.5+0.5j  0. +0.j   0. +0.j\n",
       "   0. +0.j ]\n",
       " [ 0. +0.j   0. +0.j   0. +0.j   0.5+0.5j  0. +0.j   0. +0.j   0. +0.j\n",
       "  -0.5+0.5j]\n",
       " [ 0. +0.j   0. +0.j  -0.5-0.5j  0. +0.j   0. +0.j   0. +0.j  -0.5+0.5j\n",
       "   0. +0.j ]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = [(1,(3,0))]\n",
    "sys = commutator_type_dynamics(D)\n",
    "sys.run_PTM()\n",
    "sys.please_be_verbose = True\n",
    "V_fj = sys.V_fj(sys.sample_vv(), sys.sample_uw())\n",
    "V_fj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True $ \\\\ \\left(\\begin{matrix}1.000 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.000 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.000 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.000 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.000 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000\\\\\\end{matrix}\\right)$"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[1. 0. 0. 0. 0. 0. 0. 0.]\n",
       " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
       " [0. 0. 1. 0. 0. 0. 0. 0.]\n",
       " [0. 0. 0. 1. 0. 0. 0. 0.]\n",
       " [0. 0. 0. 0. 1. 0. 0. 0.]\n",
       " [0. 0. 0. 0. 0. 1. 0. 0.]\n",
       " [0. 0. 0. 0. 0. 0. 1. 0.]\n",
       " [0. 0. 0. 0. 0. 0. 0. 1.]]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_fj * V_fj.dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Components\n",
    "1. Hadamard\n",
    "2. Controlled U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# States for testing\n",
    "ket_0 = basis(2,0)\n",
    "ket_1 = basis(2,1)\n",
    "ket_c = ket_1\n",
    "ket_t = tensor(ket_0, ket_1)\n",
    "state = tensor(ket_c, ket_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/sn/4ym_qb8x0cs_f961d78kvvkc0000gn/T/ipykernel_14157/484745189.py:3: DeprecationWarning: Importing functions/classes of the qip submodule directly from the namespace qutip is deprecated. Please import them from the submodule instead, e.g.\n",
      "from qutip.qip.operations import cnot\n",
      "from qutip.qip.circuit import QubitCircuit\n",
      "\n",
      "  hadamard_c = tensor(hadamard_transform(1), sys.identity)\n",
      "/var/folders/sn/4ym_qb8x0cs_f961d78kvvkc0000gn/T/ipykernel_14157/484745189.py:7: DeprecationWarning: Importing functions/classes of the qip submodule directly from the namespace qutip is deprecated. Please import them from the submodule instead, e.g.\n",
      "from qutip.qip.operations import cnot\n",
      "from qutip.qip.circuit import QubitCircuit\n",
      "\n",
      "  ket_c_after = hadamard_transform(1) * ket_c\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True $ \\\\ \\left(\\begin{matrix}2.828 & 2.828\\\\2.828 & -2.828\\\\\\end{matrix}\\right)$"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 2.82842712  2.82842712]\n",
       " [ 2.82842712 -2.82842712]]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Hadamard\n",
    "# Hadamard in class\n",
    "hadamard_c = tensor(hadamard_transform(1), sys.identity)\n",
    "state_after = hadamard_c * state\n",
    "rho_c_class = (state_after * state_after.dag()).ptrace(0)\n",
    "# Hadamard by qutip\n",
    "ket_c_after = hadamard_transform(1) * ket_c\n",
    "rho_c_cal = ket_c_after * ket_c_after.dag()\n",
    "\n",
    "print(rho_c_cal == rho_c_class)\n",
    "hadamard_c.ptrace(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# Controlled U\n",
    "U = tensor(sigmax(), sigmaz())\n",
    "state_after = sys.controlled_U(U) * state\n",
    "rho_t_class = (state_after * state_after.dag()).ptrace([1,2])\n",
    "\n",
    "# Direct calculation\n",
    "if ket_c == ket_1:\n",
    "    ket_t_after = U * ket_t\n",
    "else:\n",
    "    ket_t_after = ket_t\n",
    "rho_t_cal = ket_t_after * ket_t_after.dag()\n",
    "\n",
    "print(rho_c_cal == rho_c_class)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 5: Local restriction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the knowledge that H belongs to a subspace $\\mathcal{L} (H)$ splanned by the set $\\{\\sigma_{\\vec v}\\}_{\\vec v \\in J}$ for some $J\\subset \\{0,1,2,3\\}^n$, we can set $\\gamma_{\\vec w, \\vec u} = 0$ when $\\vec u \\notin J$, so as to improve the complexity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "175\n",
      "{((0, 0, 0, 1), (3, 0, 3, 2)): (2+0j), ((0, 0, 0, 2), (3, 0, 3, 1)): (-2+0j), ((0, 0, 1, 0), (3, 0, 2, 3)): (2+0j), ((0, 0, 1, 3), (3, 0, 2, 0)): (2+0j), ((0, 0, 2, 0), (3, 0, 1, 3)): (-2+0j), ((0, 0, 2, 3), (3, 0, 1, 0)): (-2+0j), ((0, 0, 3, 1), (3, 0, 0, 2)): (2+0j), ((0, 0, 3, 2), (3, 0, 0, 1)): (-2+0j), ((0, 1, 0, 1), (3, 1, 3, 2)): (2+0j), ((0, 1, 0, 2), (3, 1, 3, 1)): (-2+0j), ((0, 1, 1, 0), (3, 1, 2, 3)): (2+0j), ((0, 1, 1, 3), (3, 1, 2, 0)): (2+0j), ((0, 1, 2, 0), (3, 1, 1, 3)): (-2+0j), ((0, 1, 2, 3), (3, 1, 1, 0)): (-2+0j), ((0, 1, 3, 1), (3, 1, 0, 2)): (2+0j), ((0, 1, 3, 2), (3, 1, 0, 1)): (-2+0j), ((0, 2, 0, 1), (3, 2, 3, 2)): (2+0j), ((0, 2, 0, 2), (3, 2, 3, 1)): (-2+0j), ((0, 2, 1, 0), (3, 2, 2, 3)): (2+0j), ((0, 2, 1, 3), (3, 2, 2, 0)): (2+0j), ((0, 2, 2, 0), (3, 2, 1, 3)): (-2+0j), ((0, 2, 2, 3), (3, 2, 1, 0)): (-2+0j), ((0, 2, 3, 1), (3, 2, 0, 2)): (2+0j), ((0, 2, 3, 2), (3, 2, 0, 1)): (-2+0j), ((0, 3, 0, 1), (3, 3, 3, 2)): (2+0j), ((0, 3, 0, 2), (3, 3, 3, 1)): (-2+0j), ((0, 3, 1, 0), (3, 3, 2, 3)): (2+0j), ((0, 3, 1, 3), (3, 3, 2, 0)): (2+0j), ((0, 3, 2, 0), (3, 3, 1, 3)): (-2+0j), ((0, 3, 2, 3), (3, 3, 1, 0)): (-2+0j), ((0, 3, 3, 1), (3, 3, 0, 2)): (2+0j), ((0, 3, 3, 2), (3, 3, 0, 1)): (-2+0j), ((1, 0, 0, 0), (2, 0, 3, 3)): (2+0j), ((1, 0, 0, 3), (2, 0, 3, 0)): (2+0j), ((1, 0, 1, 1), (2, 0, 2, 2)): (-2+0j), ((1, 0, 1, 2), (2, 0, 2, 1)): (2+0j), ((1, 0, 2, 1), (2, 0, 1, 2)): (2+0j), ((1, 0, 2, 2), (2, 0, 1, 1)): (-2+0j), ((1, 0, 3, 0), (2, 0, 0, 3)): (2+0j), ((1, 0, 3, 3), (2, 0, 0, 0)): (2+0j), ((1, 1, 0, 0), (2, 1, 3, 3)): (2+0j), ((1, 1, 0, 3), (2, 1, 3, 0)): (2+0j), ((1, 1, 3, 0), (2, 1, 0, 3)): (2+0j), ((1, 2, 0, 0), (2, 2, 3, 3)): (2+0j), ((1, 2, 0, 3), (2, 2, 3, 0)): (2+0j), ((1, 2, 3, 0), (2, 2, 0, 3)): (2+0j), ((1, 3, 0, 0), (2, 3, 3, 3)): (2+0j), ((1, 3, 0, 3), (2, 3, 3, 0)): (2+0j), ((1, 3, 3, 0), (2, 3, 0, 3)): (2+0j), ((2, 0, 0, 0), (1, 0, 3, 3)): (-2+0j), ((2, 0, 0, 3), (1, 0, 3, 0)): (-2+0j), ((2, 0, 1, 1), (1, 0, 2, 2)): (2+0j), ((2, 0, 1, 2), (1, 0, 2, 1)): (-2+0j), ((2, 0, 2, 1), (1, 0, 1, 2)): (-2+0j), ((2, 0, 2, 2), (1, 0, 1, 1)): (2+0j), ((2, 0, 3, 0), (1, 0, 0, 3)): (-2+0j), ((2, 0, 3, 3), (1, 0, 0, 0)): (-2+0j), ((2, 1, 0, 0), (1, 1, 3, 3)): (-2+0j), ((2, 1, 0, 3), (1, 1, 3, 0)): (-2+0j), ((2, 1, 3, 0), (1, 1, 0, 3)): (-2+0j), ((2, 2, 0, 0), (1, 2, 3, 3)): (-2+0j), ((2, 2, 0, 3), (1, 2, 3, 0)): (-2+0j), ((2, 2, 3, 0), (1, 2, 0, 3)): (-2+0j), ((2, 3, 0, 0), (1, 3, 3, 3)): (-2+0j), ((2, 3, 0, 3), (1, 3, 3, 0)): (-2+0j), ((2, 3, 3, 0), (1, 3, 0, 3)): (-2+0j), ((3, 0, 0, 1), (0, 0, 3, 2)): (2+0j), ((3, 0, 0, 2), (0, 0, 3, 1)): (-2+0j), ((3, 0, 1, 0), (0, 0, 2, 3)): (2+0j), ((3, 0, 1, 3), (0, 0, 2, 0)): (2+0j), ((3, 0, 2, 0), (0, 0, 1, 3)): (-2+0j), ((3, 0, 2, 3), (0, 0, 1, 0)): (-2+0j), ((3, 0, 3, 1), (0, 0, 0, 2)): (2+0j), ((3, 0, 3, 2), (0, 0, 0, 1)): (-2+0j), ((3, 1, 0, 1), (0, 1, 3, 2)): (2+0j), ((3, 1, 0, 2), (0, 1, 3, 1)): (-2+0j), ((3, 1, 1, 0), (0, 1, 2, 3)): (2+0j), ((3, 1, 2, 0), (0, 1, 1, 3)): (-2+0j), ((3, 2, 0, 1), (0, 2, 3, 2)): (2+0j), ((3, 2, 0, 2), (0, 2, 3, 1)): (-2+0j), ((3, 2, 1, 0), (0, 2, 2, 3)): (2+0j), ((3, 2, 2, 0), (0, 2, 1, 3)): (-2+0j), ((3, 3, 0, 1), (0, 3, 3, 2)): (2+0j), ((3, 3, 0, 2), (0, 3, 3, 1)): (-2+0j), ((3, 3, 1, 0), (0, 3, 2, 3)): (2+0j), ((3, 3, 2, 0), (0, 3, 1, 3)): (-2+0j)}\n",
      "344.0\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Index (u,w)</th>\n",
       "      <th>Gamma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14583</th>\n",
       "      <td>((0, 3, 2, 0), (3, 3, 1, 3))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29628</th>\n",
       "      <td>((1, 3, 0, 3), (2, 3, 3, 0))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13563</th>\n",
       "      <td>((0, 3, 1, 0), (3, 3, 2, 3))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17802</th>\n",
       "      <td>((1, 0, 1, 1), (2, 0, 2, 2))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23699</th>\n",
       "      <td>((1, 1, 3, 0), (2, 1, 0, 3))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62013</th>\n",
       "      <td>((3, 3, 0, 2), (0, 3, 3, 1))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57646</th>\n",
       "      <td>((3, 2, 0, 1), (0, 2, 3, 2))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>717</th>\n",
       "      <td>((0, 0, 0, 2), (3, 0, 3, 1))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57901</th>\n",
       "      <td>((3, 2, 0, 2), (0, 2, 3, 1))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45948</th>\n",
       "      <td>((2, 3, 0, 3), (1, 3, 3, 0))</td>\n",
       "      <td>0.011628</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>86 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Index (u,w)     Gamma\n",
       "14583  ((0, 3, 2, 0), (3, 3, 1, 3))  0.011628\n",
       "29628  ((1, 3, 0, 3), (2, 3, 3, 0))  0.011628\n",
       "13563  ((0, 3, 1, 0), (3, 3, 2, 3))  0.011628\n",
       "17802  ((1, 0, 1, 1), (2, 0, 2, 2))  0.011628\n",
       "23699  ((1, 1, 3, 0), (2, 1, 0, 3))  0.011628\n",
       "...                             ...       ...\n",
       "62013  ((3, 3, 0, 2), (0, 3, 3, 1))  0.011628\n",
       "57646  ((3, 2, 0, 1), (0, 2, 3, 2))  0.011628\n",
       "717    ((0, 0, 0, 2), (3, 0, 3, 1))  0.011628\n",
       "57901  ((3, 2, 0, 2), (0, 2, 3, 1))  0.011628\n",
       "45948  ((2, 3, 0, 3), (1, 3, 3, 0))  0.011628\n",
       "\n",
       "[86 rows x 2 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running circuit with N = 5917\n",
      "Running circuit with N = 5917\n",
      "Running circuit with N = 5917\n",
      "Running circuit with N = 5917\n",
      "Running circuit with N = 5917\n",
      "0.42829903862686713\n"
     ]
    }
   ],
   "source": [
    "H = tensor(sigmax(),sigmax(),qeye(2),qeye(2)) + tensor(qeye(2), sigmax(),sigmax(), qeye(2))\n",
    "D = tensor([sigmaz(),qeye(2),sigmaz(),sigmaz()])\n",
    "f_H = 1j * commutator(H, D)\n",
    "t = 0.1\n",
    "allowed_error = 1.0\n",
    "\n",
    "D_sys = [(1,(3,0,3,3))]\n",
    "sys = commutator_type_dynamics(D_sys)\n",
    "# sys.J = [(1,1,0,0), (0,1,1,0)]\n",
    "sys.J = sys.locality_restraint(3)\n",
    "print(len(sys.J))\n",
    "sys.local_restriction = True\n",
    "sys.run_PTM()\n",
    "filtered_PTM = sys.filter_out_zeros(sys.gamma_uw_dict)\n",
    "print(filtered_PTM)\n",
    "print(sys.beta)\n",
    "sys.show_prob_uw_distribution()\n",
    "\n",
    "H_exact = (-1j * f_H * t).expm()\n",
    "nmb_samples = 5\n",
    "error_list = []\n",
    "for i in range(nmb_samples):\n",
    "    U_m = sys.complete_circuit(H, t, allowed_error)\n",
    "    error = sys.approximtion_error(H, U_m, f_H, t)\n",
    "    error_list.append(error)\n",
    "print(np.mean(error_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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