quantum-libs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4f5d75aa",
   "metadata": {},
   "source": [
    "# QuanDocker: A docker container for quantum machine learning (QML) research.\n",
    "\n",
    "https://github.com/BoltzmannEntropy/QMLDocker "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3e3dbcab",
   "metadata": {},
   "outputs": [],
   "source": [
    "%reset -f\n",
    "import matplotlib.font_manager\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "font = {\n",
    "    'family':'SimHei',\n",
    "    'weight':'bold',\n",
    "    'size':'16'\n",
    "}\n",
    "matplotlib.rc(\"font\",**font)\n",
    "from IPython.display import display_pretty\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "889e7e73",
   "metadata": {},
   "source": [
    "## Qutip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "17aa251e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.37796447-0.37796447j, 0.37796447+0.75592895j]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip import *\n",
    "\n",
    "q = (1/np.sqrt(7))*Qobj(np.array([[1+ 1j], [1-2j]]).T)\n",
    "q.conj().full()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d6162153",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        -0.70710678j],\n",
       "       [0.70710678+0.j        ]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p=(1/np.sqrt(2))*Qobj(np.array([[-1j], [1]]))\n",
    "p.full()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f3ab1777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra $ \\\\ \\left(\\begin{matrix}0.267j\\\\\\end{matrix}\\right)$"
      ],
      "text/plain": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra\n",
       "Qobj data =\n",
       "[[0.+0.26726124j]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.conj()*p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bba55023",
   "metadata": {},
   "source": [
    "## SymPy Quantum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7b4f6e11",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family ['SimHei'] not found. Falling back to DejaVu Sans.\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2}\\\\- \\frac{1}{2}\\\\- \\frac{1}{2}\\\\\\frac{1}{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1/2 ⎤\n",
       "⎢    ⎥\n",
       "⎢-1/2⎥\n",
       "⎢    ⎥\n",
       "⎢-1/2⎥\n",
       "⎢    ⎥\n",
       "⎣1/2 ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix, symbols, sqrt, init_printing\n",
    "from sympy.physics.quantum import TensorProduct\n",
    "from IPython.display import display_pretty\n",
    "\n",
    "init_printing(use_latex=True)\n",
    "a1 = symbols('a_1')\n",
    "b1 = symbols('b_1')\n",
    "a2 = symbols('a_2')\n",
    "b2 = symbols('b_2')\n",
    "# psi1 = Matrix(2,1,[a1,b1])\n",
    "# psi2 = Matrix(2,1,[a2,b2])\n",
    "\n",
    "U_I = Matrix([[1,0],\n",
    "              [0,1]])\n",
    "U_H = 1/sqrt(2)*Matrix([[1, 1],\n",
    "                        [1,-1]])\n",
    "U_Z=Matrix(2,2,[1,0,0,-1])\n",
    "Cnot=Matrix([[1,0,0,0],\n",
    "             [0,1,0,0],\n",
    "             [0,0,0,1],\n",
    "             [0,0,1,0]])\n",
    "\n",
    "psi1 = Matrix(2,1,[1,0])\n",
    "psi2 = Matrix(2,1,[1,0])\n",
    "\n",
    "psi12 = TensorProduct(psi1,psi2)\n",
    "U_FINAL= Cnot*(TensorProduct(U_I,U_Z)*TensorProduct(U_H,U_H))*psi12\n",
    "\n",
    "U_FINAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "78f5ca6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sqrt{2}}{2}\\\\0\\\\0\\\\0\\\\- \\frac{\\sqrt{2}}{2}\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-√2 ⎤\n",
       "⎢────⎥\n",
       "⎢ 2  ⎥\n",
       "⎢    ⎥\n",
       "⎢ 0  ⎥\n",
       "⎢    ⎥\n",
       "⎢ 0  ⎥\n",
       "⎢    ⎥\n",
       "⎢ 0  ⎥\n",
       "⎢    ⎥\n",
       "⎢-√2 ⎥\n",
       "⎢────⎥\n",
       "⎢ 2  ⎥\n",
       "⎢    ⎥\n",
       "⎢ 0  ⎥\n",
       "⎢    ⎥\n",
       "⎢ 0  ⎥\n",
       "⎢    ⎥\n",
       "⎣ 0  ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix, symbols, sqrt, init_printing\n",
    "from sympy.physics.quantum import TensorProduct\n",
    "from IPython.display import display_pretty\n",
    "\n",
    "init_printing(use_latex=True)\n",
    "a1 = symbols('a_1')\n",
    "b1 = symbols('b_1')\n",
    "a2 = symbols('a_2')\n",
    "b2 = symbols('b_2')\n",
    "\n",
    "U_I = Matrix([[1,0],\n",
    "              [0,1]])\n",
    "U_H = 1/sqrt(2)*Matrix([[1, 1],\n",
    "                        [1,-1]])\n",
    "U_Z=Matrix(2,2,[1,0,0,-1])\n",
    "U_X=Matrix(2,2,[0,1,1,0])\n",
    "Cnot=Matrix([[1,0,0,0],\n",
    "             [0,1,0,0],\n",
    "             [0,0,0,1],\n",
    "             [0,0,1,0]])\n",
    "\n",
    "psi0 = Matrix(2,1,[1,0])\n",
    "psi1 = Matrix(2,1,[0,1])\n",
    "psi3 = a1*psi0 + b1*psi1\n",
    "\n",
    "psi3\n",
    "# psi1 = Matrix(2,1,[a1,b1])\n",
    "# psi2 = Matrix(2,1,[a2,b2])\n",
    "# psi12 = TensorProduct(psi1,psi2)\n",
    "# # psi12 = psi1+ psi2\n",
    "U_FINAL= TensorProduct(Cnot,U_I)*(TensorProduct(U_X,U_I,U_Z)*TensorProduct(Cnot,U_I))* TensorProduct(U_H,U_Z,U_I)\n",
    "U_FINAL * TensorProduct(psi0, psi1, psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0755fafc",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle X_{0} {\\left|0\\right\\rangle } = {\\left|1\\right\\rangle }$"
      ],
      "text/plain": [
       "X ⋅❘0⟩ = ❘1⟩\n",
       " 0          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle X_{0} {\\left|1\\right\\rangle } = {\\left|0\\right\\rangle }$"
      ],
      "text/plain": [
       "X ⋅❘1⟩ = ❘0⟩\n",
       " 0          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle Y_{0} {\\left|0\\right\\rangle } = i {\\left|1\\right\\rangle }$"
      ],
      "text/plain": [
       "Y ⋅❘0⟩ = ⅈ⋅❘1⟩\n",
       " 0            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle Y_{0} {\\left|1\\right\\rangle } = - i {\\left|0\\right\\rangle }$"
      ],
      "text/plain": [
       "Y ⋅❘1⟩ = -ⅈ⋅❘0⟩\n",
       " 0             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle Z_{0} {\\left|0\\right\\rangle } = {\\left|0\\right\\rangle }$"
      ],
      "text/plain": [
       "Z ⋅❘0⟩ = ❘0⟩\n",
       " 0          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'SimHei' not found.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle Z_{0} {\\left|1\\right\\rangle } = - {\\left|1\\right\\rangle }$"
      ],
      "text/plain": [
       "Z ⋅❘1⟩ = -❘1⟩\n",
       " 0           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import sqrt, symbols, Rational\n",
    "from sympy import expand, Eq, Symbol, simplify, exp, sin, srepr\n",
    "from sympy.physics.quantum import *\n",
    "from sympy.physics.quantum.qubit import *\n",
    "from sympy.physics.quantum.gate import *\n",
    "from sympy.physics.quantum.grover import *\n",
    "from sympy.physics.quantum.qft import QFT, IQFT, Fourier\n",
    "from sympy.physics.quantum.circuitplot import circuit_plot\n",
    "\n",
    "for gate in [X,Y,Z]:\n",
    "    for state in [Qubit('0'),Qubit('1')]:\n",
    "        lhs = gate(0)*state\n",
    "        rhs = qapply(lhs)\n",
    "        display(Eq(lhs,rhs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f65a9ba7",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from warnings import filterwarnings\n",
    "filterwarnings(action='ignore', category=DeprecationWarning)\n",
    "\n",
    "\n",
    "phi_plus = np.array([1, 0, 0, 1])/np.sqrt(2)   # | Phi^+ >\n",
    "phi_minus = np.array([1, 0, 0, -1])/np.sqrt(2) # | Phi^- >\n",
    "psi_plus = np.array([0, 1, 1, 0])/np.sqrt(2)   # | Psi^+ >\n",
    "psi_minus = np.array([0, 1, -1, 0])/np.sqrt(2) # | Psi^- >\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "243748ab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after X matrix, the state is  tensor([[0, 1]])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "initial_state = [1,0]   # Define initial_state as |0>\n",
    "# initial_state = [0,1]   # Define initial_state as |0>\n",
    "# initial_state = [1/np.sqrt(2), 1/np.sqrt(2)]  # Define state |q_0>\n",
    "\n",
    "initial_state_torch = torch.tensor([initial_state])\n",
    "x_gate_matrix = torch.tensor([[0,1],[1,0]])\n",
    "out_state_torch = torch.mm(x_gate_matrix,initial_state_torch.t()) \n",
    "print(\"after X matrix, the state is \",out_state_torch.t()) # Display the output state vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a1a6679",
   "metadata": {},
   "source": [
    "## Paddle-quantum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2553045c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "from numpy import pi as PI\n",
    "import paddle \n",
    "import paddle_quantum\n",
    "from paddle import matmul\n",
    "from paddle_quantum.ansatz import Circuit\n",
    "from paddle_quantum.qinfo import random_pauli_str_generator, pauli_str_to_matrix\n",
    "from paddle_quantum.linalg import dagger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "47da7fe7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Hamiltonian in Pauli string format = \n",
      " [[-0.003151539177421281, 'x0']]\n"
     ]
    }
   ],
   "source": [
    "N = 1  # Number of qubits\n",
    "SEED = np.random.randint(9999)  # Fixed random seed\n",
    "# Generate random Hamiltonian represented by Pauli string\n",
    "numpy.random.seed(SEED)\n",
    "hamiltonian = random_pauli_str_generator(N, terms=1)\n",
    "print(\"Random Hamiltonian in Pauli string format = \\n\", hamiltonian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1d77cbc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/qmuser/.local/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n",
       "       [[ 0j                       , (-0.003151539247483015+0j)],\n",
       "        [(-0.003151539247483015+0j),  0j                       ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate matrix representation of Hamiltonian\n",
    "complex_dtype = paddle_quantum.get_dtype()\n",
    "H = pauli_str_to_matrix(hamiltonian, N).astype(complex_dtype)\n",
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "080bb2c2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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   "file_extension": ".py",
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