notebooks/example.ipynb

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 "cells": [
  {
   "source": [
    "# Basic quantum calculator\n",
    "\n",
    "A %quantum magic command for evaluating basic quantum circuit calculations using `numpy`."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import quantum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "|0⟩",
      "text/latex": "$\\lvert0\\rangle$"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "# Zero\n",
    "%quantum |0>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "|1⟩",
      "text/latex": "$\\lvert1\\rangle$"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "# One\n",
    "%quantum |1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√2 |0⟩ + 1/√2 |1⟩",
      "text/latex": "$\\frac{1}{\\sqrt{2}} \\lvert0\\rangle + \\frac{1}{\\sqrt{2}} \\lvert1\\rangle$"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "# Plus\n",
    "%quantum |+>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0.70710678],\n       [0.70710678]])"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "import numpy as np\n",
    "_.view(np.ndarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "|1010101⟩",
      "text/latex": "$\\lvert1010101\\rangle$"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "# Multiple qubits\n",
    "%quantum |1010101>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√8 |000⟩ + 1/√8 |001⟩ + 1/√8 |010⟩ + 1/√8 |011⟩ + 1/√8 |100⟩ + 1/√8 |101⟩ + 1/√8 |110⟩ + 1/√8 |111⟩",
      "text/latex": "$\\frac{1}{\\sqrt{8}} \\lvert000\\rangle + \\frac{1}{\\sqrt{8}} \\lvert001\\rangle + \\frac{1}{\\sqrt{8}} \\lvert010\\rangle + \\frac{1}{\\sqrt{8}} \\lvert011\\rangle + \\frac{1}{\\sqrt{8}} \\lvert100\\rangle + \\frac{1}{\\sqrt{8}} \\lvert101\\rangle + \\frac{1}{\\sqrt{8}} \\lvert110\\rangle + \\frac{1}{\\sqrt{8}} \\lvert111\\rangle$"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "# Superposition\n",
    "%quantum |+++>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gate operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√2 |00⟩ + 1/√2 |11⟩",
      "text/latex": "$\\frac{1}{\\sqrt{2}} \\lvert00\\rangle + \\frac{1}{\\sqrt{2}} \\lvert11\\rangle$"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "# Bell state\n",
    "%quantum CX01 H0 |00>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√2 |00⟩ + 1/√2 |11⟩",
      "text/latex": "$\\frac{1}{\\sqrt{2}} \\lvert00\\rangle + \\frac{1}{\\sqrt{2}} \\lvert11\\rangle$"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "# Bell state, alternative |+> notation\n",
    "%quantum CX01 |+0>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "|101010⟩",
      "text/latex": "$\\lvert101010\\rangle$"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "# Apply multi-qubit gate\n",
    "# Index zero starts from left\n",
    "%quantum X0 X2 X4 |000000>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[farray([[0, 1],\n         [1, 0]]),\n farray([[1, 0],\n         [0, 1]]),\n farray([[     0,     1i],\n         [    1i,      0]]),\n farray([[  1/√2,   1/√2],\n         [  1/√2,   1/√2]])]"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "# One-qubit gate sequence\n",
    "%quantum X0 I0 Y0 H0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[farray([[0, 0, 0, 0, 0, 0, 0, 1],\n         [0, 0, 0, 0, 0, 0, 1, 0],\n         [0, 0, 0, 0, 0, 1, 0, 0],\n         [0, 0, 0, 0, 1, 0, 0, 0],\n         [0, 0, 0, 1, 0, 0, 0, 0],\n         [0, 0, 1, 0, 0, 0, 0, 0],\n         [0, 1, 0, 0, 0, 0, 0, 0],\n         [1, 0, 0, 0, 0, 0, 0, 0]])]"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "# Multi-qubit gate\n",
    "%quantum X0*X1*X2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[farray([[0, 1, 0, 0, 0, 0, 0, 0],\n         [1, 0, 0, 0, 0, 0, 0, 0],\n         [0, 0, 0, 1, 0, 0, 0, 0],\n         [0, 0, 1, 0, 0, 0, 0, 0],\n         [0, 0, 0, 0, 0, 1, 0, 0],\n         [0, 0, 0, 0, 1, 0, 0, 0],\n         [0, 0, 0, 0, 0, 0, 0, 1],\n         [0, 0, 0, 0, 0, 0, 1, 0]])]"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "# Multi-qubit gate\n",
    "%quantum X2"
   ]
  },
  {
   "source": [
    "\n",
    "## Variable assignments (wip)"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "foo = %quantum |00>\n",
    "bar = %quantum |11>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√2 |00⟩ + 1/√2 |11⟩",
      "text/latex": "$\\frac{1}{\\sqrt{2}} \\lvert00\\rangle + \\frac{1}{\\sqrt{2}} \\lvert11\\rangle$"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "baz = (foo + bar) / np.sqrt(2)\n",
    "baz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0.5, 0. , 0. , 0.5],\n       [0. , 0. , 0. , 0. ],\n       [0. , 0. , 0. , 0. ],\n       [0.5, 0. , 0. , 0.5]])"
     },
     "metadata": {},
     "execution_count": 42
    }
   ],
   "source": [
    "import numpy as np\n",
    "rho = np.dot(baz, baz.T)\n",
    "rho.view(np.ndarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def plot_density_matrix(rho, size_scale=1):\n",
    "    figsize=tuple(np.array([4,3]) * size_scale)\n",
    "    fig = plt.figure(figsize=figsize)\n",
    "    ax1 = fig.add_subplot(111, projection='3d')\n",
    "    num_qubits = int(np.log2(len(rho)))\n",
    "    num_elements = 2**num_qubits\n",
    "    xpos = np.array(list(range(num_elements)) * num_elements)\n",
    "    ypos = np.array([_n for n in range(num_elements) for _n in [n]*num_elements])\n",
    "    zpos = np.array([0] * num_elements**2)\n",
    "    dx = np.ones(num_elements**2)\n",
    "    dy = np.ones(num_elements**2)\n",
    "    dz = rho.flatten()\n",
    "    blue = '#00ceee'\n",
    "    red = '#ee3300'\n",
    "    colors = [blue if d >= 0 else red for d in dz]\n",
    "\n",
    "    ax1.bar3d(xpos, ypos, zpos, dx, dy, np.abs(dz), color=colors)\n",
    "    plt.xticks(np.arange(num_elements) + .5, [np.binary_repr(n, num_qubits) for n in range(num_elements)])\n",
    "    plt.yticks(np.arange(num_elements) + .5, [np.binary_repr(n, num_qubits) for n in range(num_elements)])\n",
    "    plt.title(\"$\\\\rho$ density matrix\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "rho = np.dot(foo, foo.T)\n",
    "plot_density_matrix(rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "rho = np.dot(bar, bar.T)\n",
    "plot_density_matrix(rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 288x216 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "rho = np.dot(baz, baz.T)\n",
    "plot_density_matrix(rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "state1 = %quantum |000>\n",
    "state2 = %quantum |111>\n",
    "state = (state1 + state2)/np.linalg.norm(state1 + state2)\n",
    "rho = np.dot(state, state.T)\n",
    "plot_density_matrix(rho, size_scale=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1/√2 |0⟩ + 1/√2i |1⟩",
      "text/latex": "$\\frac{1}{\\sqrt{2}} \\lvert0\\rangle + \\frac{1}{\\sqrt{2}}i \\lvert1\\rangle$"
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "source": [
    "state = %quantum T0 |+>\n",
    "state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RUS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RusArcTan2 = H0.H1.T0.T1.CX12.CX10.ConjT(T0).H0.H1.T2.Z2)\n",
    "\n",
    "RusArcTan2 *= (-1/I.353553) // MatrixForm / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "state = %quantum H1.T1.CNOT21.Z2.T2.H0.TD0.CNOT10.T0.H0*H1 |000>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "rho = np.dot(state, state.T)\n",
    "plot_density_matrix(rho, size_scale=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "RUS = %quantum H1*H0.T1.CNOT21.Z2.T2.TD0.CNOT10.T0.H0*H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(3/4+1/4i) |000⟩ + -√-1/√8i |010⟩ + -√-1/√8i |100⟩ + -√-1/√8i |110⟩",
      "text/latex": "$(\\frac{3}{4}+\\frac{1}{4}i) \\lvert000\\rangle + (\\frac{1}{4}-\\frac{1}{4}i) \\lvert010\\rangle + (\\frac{-1}{4}+\\frac{1}{4}i) \\lvert100\\rangle + (\\frac{1}{4}-\\frac{1}{4}i) \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "res = %quantum H1*H0.T1.CNOT21.Z2.T2.TD0.CNOT10.T0.H0*H1 |000>\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1/4-1/8i) |000⟩ + -1/8i |010⟩ + 1/8i |100⟩ + -1/8i |110⟩",
      "text/latex": "$(\\frac{1}{4}-\\frac{1}{8}i) \\lvert000\\rangle + \\frac{-1}{8}i \\lvert010\\rangle + \\frac{1}{8}i \\lvert100\\rangle + \\frac{-1}{8}i \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "source": [
    "res/(4/(1-1j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "RUSresult = np.round(RUS[0]*(4/(1-1j)), 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[(1+2i),      0,      1,      0,      1,      0,     -1,      0],\n        [     0, (1-2i),      0,      1,      0,     -1,      0,      1],\n        [     1,      0, (1+2i),      0,     -1,      0,      1,      0],\n        [     0,     -1,      0, (-1+2i),      0,     -1,      0,      1],\n        [    -1,      0,      1,      0,      1,      0, (1+2i),      0],\n        [     0,      1,      0,     -1,      0,      1,      0, (1-2i)],\n        [     1,      0,     -1,      0, (1+2i),      0,      1,      0],\n        [     0,      1,      0,     -1,      0, (-1+2i),      0,     -1]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 + 2.0 i & 0 & 1.0 & 0 & 1.0 & 0 & -1.0 & 0\\\\0 & 1.0 - 2.0 i & 0 & 1.0 & 0 & -1.0 & 0 & 1.0\\\\1.0 & 0 & 1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0 & 0\\\\0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0\\\\-1.0 & 0 & 1.0 & 0 & 1.0 & 0 & 1.0 + 2.0 i & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & 1.0 & 0 & 1.0 - 2.0 i\\\\1.0 & 0 & -1.0 & 0 & 1.0 + 2.0 i & 0 & 1.0 & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "source": [
    "import sympy as s\n",
    "s.init_printing()\n",
    "RUSresult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1+2i) |000⟩ + |010⟩ + -1 |100⟩ + |110⟩",
      "text/latex": "$(1+2i) \\lvert000\\rangle + \\lvert010\\rangle + -1 \\lvert100\\rangle + \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "source": [
    "state = %quantum |000>\n",
    "res = np.dot(RUSresult, state).view(quantum.formatter.dirac)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1+2i) |000⟩ + |010⟩ + -1 |100⟩ + |110⟩",
      "text/latex": "$(1+2i) \\lvert000\\rangle + \\lvert010\\rangle + -1 \\lvert100\\rangle + \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "source": [
    "from quantum.gates import I, Z\n",
    "np.dot(np.kron(I, np.kron(I, np.conjugate(Z))), res).view(quantum.formatter.dirac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[(1+2i),      0,      1,      0,      1,      0,     -1,      0],\n        [     0, (1-2i),      0,      1,      0,     -1,      0,      1],\n        [     1,      0, (1+2i),      0,     -1,      0,      1,      0],\n        [     0,     -1,      0, (-1+2i),      0,     -1,      0,      1],\n        [    -1,      0,      1,      0,      1,      0, (1+2i),      0],\n        [     0,      1,      0,     -1,      0,      1,      0, (1-2i)],\n        [     1,      0,     -1,      0, (1+2i),      0,      1,      0],\n        [     0,      1,      0,     -1,      0, (-1+2i),      0,     -1]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 + 2.0 i & 0 & 1.0 & 0 & 1.0 & 0 & -1.0 & 0\\\\0 & 1.0 - 2.0 i & 0 & 1.0 & 0 & -1.0 & 0 & 1.0\\\\1.0 & 0 & 1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0 & 0\\\\0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0\\\\-1.0 & 0 & 1.0 & 0 & 1.0 & 0 & 1.0 + 2.0 i & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & 1.0 & 0 & 1.0 - 2.0 i\\\\1.0 & 0 & -1.0 & 0 & 1.0 + 2.0 i & 0 & 1.0 & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 33
    }
   ],
   "source": [
    "RUSresult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1+2i) |000⟩ + |010⟩ + -1 |100⟩ + |110⟩",
      "text/latex": "$(1+2i) \\lvert000\\rangle + \\lvert010\\rangle + -1 \\lvert100\\rangle + \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 34
    }
   ],
   "source": [
    "\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[ 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]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & -1 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -1\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 35
    }
   ],
   "source": [
    "Zcorr, = %quantum Z2\n",
    "Zcorr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[(1+2i),      0,      1,      0,      1,      0,     -1,      0],\n        [     0, (-1+2i),      0,     -1,      0,      1,      0,     -1],\n        [     1,      0, (1+2i),      0,     -1,      0,      1,      0],\n        [     0,      1,      0, (1-2i),      0,      1,      0,     -1],\n        [    -1,      0,      1,      0,      1,      0, (1+2i),      0],\n        [     0,     -1,      0,      1,      0,     -1,      0, (-1+2i)],\n        [     1,      0,     -1,      0, (1+2i),      0,      1,      0],\n        [     0,     -1,      0,      1,      0, (1-2i),      0,      1]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 + 2.0 i & 0 & 1.0 & 0 & 1.0 & 0 & -1.0 & 0\\\\0 & -1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0 & 0 & -1.0\\\\1.0 & 0 & 1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0 & 0\\\\0 & 1.0 & 0 & 1.0 - 2.0 i & 0 & 1.0 & 0 & -1.0\\\\-1.0 & 0 & 1.0 & 0 & 1.0 & 0 & 1.0 + 2.0 i & 0\\\\0 & -1.0 & 0 & 1.0 & 0 & -1.0 & 0 & -1.0 + 2.0 i\\\\1.0 & 0 & -1.0 & 0 & 1.0 + 2.0 i & 0 & 1.0 & 0\\\\0 & -1.0 & 0 & 1.0 & 0 & 1.0 - 2.0 i & 0 & 1.0\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 36
    }
   ],
   "source": [
    "np.dot(Zcorr, RUSresult)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[ 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]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & -1 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -1\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 37
    }
   ],
   "source": [
    "\n",
    "Zcorr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "farray([[(1+2i),      0,      1,      0,      1,      0,     -1,      0],\n        [     0, (1-2i),      0,      1,      0,     -1,      0,      1],\n        [     1,      0, (1+2i),      0,     -1,      0,      1,      0],\n        [     0,     -1,      0, (-1+2i),      0,     -1,      0,      1],\n        [    -1,      0,      1,      0,      1,      0, (1+2i),      0],\n        [     0,      1,      0,     -1,      0,      1,      0, (1-2i)],\n        [     1,      0,     -1,      0, (1+2i),      0,      1,      0],\n        [     0,      1,      0,     -1,      0, (-1+2i),      0,     -1]])",
      "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 + 2.0 i & 0 & 1.0 & 0 & 1.0 & 0 & -1.0 & 0\\\\0 & 1.0 - 2.0 i & 0 & 1.0 & 0 & -1.0 & 0 & 1.0\\\\1.0 & 0 & 1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0 & 0\\\\0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0 & 0 & 1.0\\\\-1.0 & 0 & 1.0 & 0 & 1.0 & 0 & 1.0 + 2.0 i & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & 1.0 & 0 & 1.0 - 2.0 i\\\\1.0 & 0 & -1.0 & 0 & 1.0 + 2.0 i & 0 & 1.0 & 0\\\\0 & 1.0 & 0 & -1.0 & 0 & -1.0 + 2.0 i & 0 & -1.0\\end{matrix}\\right]$"
     },
     "metadata": {},
     "execution_count": 38
    }
   ],
   "source": [
    "RUSresult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1+2i) |000⟩ + |010⟩ + -1 |100⟩ + |110⟩",
      "text/latex": "$(1+2i) \\lvert000\\rangle + \\lvert010\\rangle + -1 \\lvert100\\rangle + \\lvert110\\rangle$"
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "source": [
    "np.dot(Zcorr, res).view(quantum.formatter.dirac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}