documentation/examples/preview-simulators-from-python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a21769ec",
   "metadata": {},
   "source": [
    "# Using Preview Simulators with Q# and Python"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7510c5c",
   "metadata": {},
   "source": [
    "The preview open systems and stabilizer simulators for the Quantum Development Kit use the [QuTiP](https://qutip.org) library for Python to help represent noise models, so we import it here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7430263c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qutip as qt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67abc680",
   "metadata": {},
   "source": [
    "To use the preview simulators, we start by importing Q# interoperability as normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "00c0728f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qsharp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a83cdd60",
   "metadata": {},
   "source": [
    "We can then use `qsharp.experimental.enable_noisy_simulation()` to add support for preview simulators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ad41d44b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qsharp.experimental\n",
    "qsharp.experimental.enable_noisy_simulation()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03daa4e4",
   "metadata": {},
   "source": [
    "Doing so adds the `.simulate_noise` method to Python representations of Q# callables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a97eefa7",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%qsharp\n",
    "\n",
    "operation DumpPlus() : Unit {\n",
    "    use q = Qubit();\n",
    "    H(q);\n",
    "    Microsoft.Quantum.Diagnostics.DumpMachine();\n",
    "    X(q);\n",
    "    Reset(q);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a7cb1504",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Data\":[0.5000000000000001,0.0,0.5000000000000001,0.0,0.5000000000000001,0.0,0.5000000000000001,0.0],\"NQubits\":1}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Mixed state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>1</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>\r\n",
       "                                $$\r\n",
       "                                \\left(\r\n",
       "                                    \\begin{matrix}\r\n",
       "                                        0.5000000000000001 + 0 i & 0.5000000000000001 + 0 i\\\\\n",
       "0.5000000000000001 + 0 i & 0.5000000000000001 + 0 i\r\n",
       "                                    \\end{matrix}\r\n",
       "                                \\right)\r\n",
       "                                $$\r\n",
       "                            </td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Mixed state on 1 qubits: [ [0.5000000000000001 + 0 i, 0.5000000000000001 + 0 i] [0.5000000000000001 + 0 i, 0.5000000000000001 + 0 i] ]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpPlus.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1fdf2e3",
   "metadata": {},
   "source": [
    "Looking at the output from the above, we notice two distinct differences with the output from `.simulate()`:\n",
    "\n",
    "- The preview simulators use quantum registers of a fixed size (by default, three qubits), and allocate qubits from that register.\n",
    "- By default, the preview simulators represent quantum states as density operators ($\\rho = \\left|\\psi\\right\\rangle\\left\\langle\\psi\\right|$) instead of as state vectors ($\\left|\\psi\\right\\rangle$).\n",
    "\n",
    "For example, in the output above, the preview simulator has output the density operator $\\rho = \\left|+00\\right\\rangle\\left\\langle+00\\right|$, as we can verify by using QuTiP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9a5bccc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[1.]\n",
       " [0.]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket_zero = qt.basis(2, 0)\n",
    "ket_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cd735ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.707\\\\0.707\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.70710678]\n",
       " [0.70710678]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket_one = qt.basis(2, 1)\n",
    "ket_plus = (ket_zero + ket_one).unit()\n",
    "ket_plus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02f7f83c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0 & 0.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.500 & 0.0 & 0.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.5 0.  0.  0.  0.5 0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
       " [0.5 0.  0.  0.  0.5 0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]\n",
       " [0.  0.  0.  0.  0.  0.  0.  0. ]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket_psi = qt.tensor(ket_plus, ket_zero, ket_zero)\n",
    "rho = ket_psi * ket_psi.dag()\n",
    "rho"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e1fd1cd",
   "metadata": {},
   "source": [
    "## Configuring Open Systems Noise Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9aa83aef",
   "metadata": {},
   "source": [
    "The preview simulators can be configured by the use of the `qsharp.config` object. For example, to change the size of the register used, we can modify the `experimental.simulators.nQubits` configuration setting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "865fa045",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.nQubits'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ff5b88d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Data\":[0.5000000000000001,0.0,0.5000000000000001,0.0,0.5000000000000001,0.0,0.5000000000000001,0.0],\"NQubits\":1}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Mixed state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>1</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>\r\n",
       "                                $$\r\n",
       "                                \\left(\r\n",
       "                                    \\begin{matrix}\r\n",
       "                                        0.5000000000000001 + 0 i & 0.5000000000000001 + 0 i\\\\\n",
       "0.5000000000000001 + 0 i & 0.5000000000000001 + 0 i\r\n",
       "                                    \\end{matrix}\r\n",
       "                                \\right)\r\n",
       "                                $$\r\n",
       "                            </td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Mixed state on 1 qubits: [ [0.5000000000000001 + 0 i, 0.5000000000000001 + 0 i] [0.5000000000000001 + 0 i, 0.5000000000000001 + 0 i] ]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpPlus.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "436a1534",
   "metadata": {},
   "source": [
    "We can modify the noise model used in simulating Q# programs by using several functions in the `qsharp.experimental` module. For instance, to initialize the noise model to an ideal model (that is, with no noise), we can use `set_noise_model_by_name` or the `%noise_model --set-by-name` magic command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4cfc0e13",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.experimental.set_noise_model_by_name('ideal')\n",
    "%noise_model --set-by-name ideal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fab9fb78",
   "metadata": {},
   "source": [
    "We can then access the noise model by using `get_noise_model`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "422a7ee2",
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = qsharp.experimental.get_noise_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3dba96a",
   "metadata": {},
   "source": [
    "This noise model is represented as a Python dictionary from preparations, measurements, and gates to Python objects representing the noise in each. For example, in the ideal noise model, the `Microsoft.Quantum.Intrinsic.H` operation is simulated by a unitary matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2774610",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.707 & 0.707\\\\0.707 & -0.707\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.70710678  0.70710678]\n",
       " [ 0.70710678 -0.70710678]]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model['h']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81c5310c",
   "metadata": {},
   "source": [
    "We can modify this to add depolarizing noise using QuTiP functions to build a depolarizing noise channel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b0a01d12",
   "metadata": {},
   "outputs": [],
   "source": [
    "I, X, Y, Z = [P.as_qobj() for P in qsharp.Pauli]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "938accec",
   "metadata": {},
   "outputs": [],
   "source": [
    "def depolarizing_noise(p=1.0):\n",
    "    return p * qt.to_super(I) + ((1 - p) / 4) * sum(map(qt.to_super, [I, X, Y, Z]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3add5aa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.495 & 0.495 & 0.500\\\\0.495 & -0.495 & 0.495 & -0.495\\\\0.495 & 0.495 & -0.495 & -0.495\\\\0.500 & -0.495 & -0.495 & 0.500\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.5    0.495  0.495  0.5  ]\n",
       " [ 0.495 -0.495  0.495 -0.495]\n",
       " [ 0.495  0.495 -0.495 -0.495]\n",
       " [ 0.5   -0.495 -0.495  0.5  ]]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model['h'] = depolarizing_noise(0.99) * qt.to_super(qt.qip.operations.hadamard_transform())\n",
    "noise_model['h']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d2a4a48a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[1.]\n",
       " [0.]]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket_zero = qt.basis(2, 0)\n",
    "ket_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "147c70db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[1. 0.]\n",
       " [0. 0.]]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho_zero = ket_zero * ket_zero.dag()\n",
    "rho_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b268e69b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.495\\\\0.495 & 0.500\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.5   0.495]\n",
       " [0.495 0.5  ]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model['h'](rho_zero)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6dc2da9",
   "metadata": {},
   "source": [
    "Once we have modified our noise model in this way, we can set it as the active noise model used in simulating Q# programs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "23379c8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.experimental.set_noise_model(noise_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05dbbef9",
   "metadata": {},
   "source": [
    "Using this model, we no longer get the exact $|+\\rangle\\langle+|$ state, but see that our Q# program has incurred some small error due to noise in the application of `Microsoft.Quantum.Intrinsic.H`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f791e6f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Data\":[0.5032581095356969,0.0,0.4951069263733158,0.0,0.4951069263733158,0.0,0.49667422634133085,0.0],\"NQubits\":1}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Mixed state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>1</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>\r\n",
       "                                $$\r\n",
       "                                \\left(\r\n",
       "                                    \\begin{matrix}\r\n",
       "                                        0.5032581095356969 + 0 i & 0.4951069263733158 + 0 i\\\\\n",
       "0.4951069263733158 + 0 i & 0.49667422634133085 + 0 i\r\n",
       "                                    \\end{matrix}\r\n",
       "                                \\right)\r\n",
       "                                $$\r\n",
       "                            </td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Mixed state on 1 qubits: [ [0.5032581095356969 + 0 i, 0.4951069263733158 + 0 i] [0.4951069263733158 + 0 i, 0.49667422634133085 + 0 i] ]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpPlus.simulate_noise()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c664c0c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       " Qobj data =\n",
       " [[ 0.06123724 -0.02041241]\n",
       "  [-0.02041241  0.02041241]],\n",
       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       " Qobj data =\n",
       " [[ 0.70445014  0.70445014]\n",
       "  [ 0.70445014 -0.70445014]],\n",
       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
       " Qobj data =\n",
       " [[ 0.05707046 -0.02948997]\n",
       "  [ 0.00190948  0.02948997]],\n",
       " Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\n",
       " Qobj data =\n",
       " [[-0.00103545  0.04950143]\n",
       "  [ 0.00197827  0.05044425]]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qt.to_kraus(noise_model['h'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c70d54",
   "metadata": {},
   "source": [
    "## Configuring Stabilizer Noise Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05d1a8f5",
   "metadata": {},
   "source": [
    "We can also configure the preview simulator to use stabilizer (_a.k.a._ CHP) simulation. This time, let's get a new noise model by using `get_noise_model_by_name`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a02721e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'initial_state': {'n_qubits': 1,\n",
       "  'data': {'Stabilizer': {'n_qubits': 1,\n",
       "    'table': array([[ True, False, False],\n",
       "           [False,  True, False]])}}},\n",
       " 'cnot': {'n_qubits': 2, 'data': {'ChpDecomposition': [{'Cnot': [0, 1]}]}},\n",
       " 'i': {'n_qubits': 1, 'data': {'Sequence': []}},\n",
       " 's': {'n_qubits': 1, 'data': {'ChpDecomposition': [{'Phase': 0}]}},\n",
       " 's_adj': {'n_qubits': 1, 'data': {'ChpDecomposition': [{'AdjointPhase': 0}]}},\n",
       " 't': {'n_qubits': 1, 'data': 'Unsupported'},\n",
       " 't_adj': {'n_qubits': 1, 'data': 'Unsupported'},\n",
       " 'h': {'n_qubits': 1, 'data': {'ChpDecomposition': [{'Hadamard': 0}]}},\n",
       " 'x': {'n_qubits': 1,\n",
       "  'data': {'ChpDecomposition': [{'Hadamard': 0},\n",
       "    {'Phase': 0},\n",
       "    {'Phase': 0},\n",
       "    {'Hadamard': 0}]}},\n",
       " 'y': {'n_qubits': 1,\n",
       "  'data': {'ChpDecomposition': [{'AdjointPhase': 0},\n",
       "    {'Hadamard': 0},\n",
       "    {'Phase': 0},\n",
       "    {'Phase': 0},\n",
       "    {'Hadamard': 0},\n",
       "    {'Phase': 0}]}},\n",
       " 'z': {'n_qubits': 1,\n",
       "  'data': {'ChpDecomposition': [{'Phase': 0}, {'Phase': 0}]}},\n",
       " 'z_meas': {'ZMeasurement': {'pr_readout_error': 0}}}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model = qsharp.experimental.get_noise_model_by_name('ideal_stabilizer')\n",
    "noise_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9f7791f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.experimental.set_noise_model(noise_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df293936",
   "metadata": {},
   "source": [
    "To make the best use of stabilizer noise models, we also need to configure the simulator to start off in the stabilizer representation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fe0142d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.representation'] = 'stabilizer'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4db703f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[2,3],\"Data\":[false,true,false,true,false,false],\"AsArray\":[false,true,false,true,false,false]},\"Data\":[false,true,false,true,false,false],\"NQubits\":1}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>1</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left\\langle X \\right\\rangle$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpPlus.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e340d9d",
   "metadata": {},
   "source": [
    "Notably, the stabilizer representation does not support operations outside of the stabilizer formalism, such as `T` and `CCNOT`. This allows the stabilizer representation to support significantly more qubits than other representations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5f24b886",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.nQubits'] = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5f4d45b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[20,21],\"Data\":[false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":10}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>10</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left\\langle X𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙, 𝟙Z𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙, 𝟙𝟙Z𝟙𝟙𝟙𝟙𝟙𝟙𝟙, 𝟙𝟙𝟙Z𝟙𝟙𝟙𝟙𝟙𝟙, 𝟙𝟙𝟙𝟙Z𝟙𝟙𝟙𝟙𝟙, 𝟙𝟙𝟙𝟙𝟙Z𝟙𝟙𝟙𝟙, 𝟙𝟙𝟙𝟙𝟙𝟙Z𝟙𝟙𝟙, 𝟙𝟙𝟙𝟙𝟙𝟙𝟙Z𝟙𝟙, 𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙Z𝟙, 𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙𝟙Z \\right\\rangle$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpPlus.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6e4795c",
   "metadata": {},
   "source": [
    "If we turn off visualization, we can get significantly more qubits still!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "138ff19b",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%qsharp\n",
    "open Microsoft.Quantum.Arrays;\n",
    "\n",
    "operation SampleRandomBitstring(nQubits : Int) : Result[] {\n",
    "    use register = Qubit[nQubits];\n",
    "    ApplyToEachCA(H, register);\n",
    "    return ForEach(M, register);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2f55cd3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.nQubits'] = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "92fc3ab1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2.79 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 0,\n",
       " 0,\n",
       " 1,\n",
       " 1,\n",
       " 0,\n",
       " 1]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time SampleRandomBitstring.simulate_noise(nQubits=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3534390d",
   "metadata": {},
   "source": [
    "For now, though, we'll turn back down the number of qubits just to make dumps easier to read!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f3587f4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.nQubits'] = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e96ca9",
   "metadata": {},
   "source": [
    "The visualization style for stabilizer states can be selected by using the `experimental.simulators.stabilizerStateStyle` configuration setting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2204f4ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%qsharp\n",
    "\n",
    "operation DumpBellPair() : Unit {\n",
    "    use left = Qubit();\n",
    "    use right = Qubit();\n",
    "    within {\n",
    "        H(left);\n",
    "        CNOT(left, right);\n",
    "    } apply {\n",
    "        Microsoft.Quantum.Diagnostics.DumpMachine();\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "70908857",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.stabilizerStateStyle'] = 'matrixWithoutDestabilizers'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "89b437a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>4</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left(\\begin{array}{cccc|cccc|c}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
       "0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0\\\\\n",
       "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
       "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\end{array}\\right)$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpBellPair.simulate_noise()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4708c2d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"div_id\":\"dump-machine-div-47a0d233-2a01-451a-9033-745fed57d860\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":[{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}]}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (little endian)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-86aa2894-03fa-4715-91d9-681385eaf148\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-86aa2894-03fa-4715-91d9-681385eaf148\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-01b201b9-db43-4b3c-ba33-0f5de6c0b149\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-01b201b9-db43-4b3c-ba33-0f5de6c0b149\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|2\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1e38e1be-152b-4b13-a762-c5e0a7ddd4da\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1e38e1be-152b-4b13-a762-c5e0a7ddd4da\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|3\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ba9b35aa-4469-4f99-9f85-59cbe5b5e5e3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ba9b35aa-4469-4f99-9f85-59cbe5b5e5e3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.7071067811865476 + 0𝑖\n",
       "|1⟩\t0 + 0𝑖\n",
       "|2⟩\t0 + 0𝑖\n",
       "|3⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpBellPair.simulate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "40431ed1",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.stabilizerStateStyle'] = 'denseGroupPresentation'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1cc366e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>4</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left\\langle XX𝟙𝟙, ZZ𝟙𝟙, 𝟙𝟙Z𝟙, 𝟙𝟙𝟙Z \\right\\rangle$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpBellPair.simulate_noise()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "07439931",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.config['experimental.simulators.stabilizerStateStyle'] = 'sparseGroupPresentation'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7f4560f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>4</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpBellPair.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58b9d547",
   "metadata": {},
   "source": [
    "So far, we've only used ideal stabilizer simulation, but what happens if one of our operations is followed by a mixed Pauli channel?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5b80e500",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SequenceProcess(n_qubits=1, processes=[ChpDecompositionProcess(n_qubits=1, operations=[Hadamard(idx_target=0)]), MixedPauliProcess(n_qubits=1, operators=[(0.9, 'I'), (0.1, 'Z')])])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noise_model['h'] = qsharp.experimental.SequenceProcess(1, \n",
    "    [\n",
    "        qsharp.experimental.ChpDecompositionProcess(1, [\n",
    "            qsharp.experimental.Hadamard(0)\n",
    "        ]),\n",
    "        qsharp.experimental.MixedPauliProcess(1, [\n",
    "            (0.9, 'I'),\n",
    "            (0.1, 'Z')\n",
    "        ])\n",
    "    ]\n",
    ")\n",
    "noise_model['h']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "94c8b146",
   "metadata": {},
   "outputs": [],
   "source": [
    "qsharp.experimental.set_noise_model(noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "c517bb74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": "{\"Table\":{\"SchemaVersion\":1,\"Dimensions\":[8,9],\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"AsArray\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false]},\"Data\":[false,false,false,false,true,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,false,false,false,false,false,false,true,false,false,false,false,false,false,false,false,false,true,false],\"NQubits\":4}",
      "text/html": [
       "\r\n",
       "                    <table>\r\n",
       "                        <caption>Stabilizer state</caption>\r\n",
       "                        <tr>\r\n",
       "                            <th># of qubits</th>\r\n",
       "                            <td>4</td>\r\n",
       "                        </tr>\r\n",
       "\r\n",
       "                        <tr>\r\n",
       "                            <th>State data</th>\r\n",
       "                            <td>$$\\left\\langle X_{0}X_{1}, Z_{0}Z_{1}, Z_{2}, Z_{3} \\right\\rangle$$</td>\r\n",
       "                        </tr>\r\n",
       "                    </table>\r\n",
       "                "
      ],
      "text/plain": [
       "Microsoft.Quantum.Experimental.StabilizerState"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DumpBellPair.simulate_noise()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64c1a27",
   "metadata": {},
   "source": [
    "## Epilogue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "56168b7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'iqsharp': LooseVersion ('0.17.210628040-alpha'),\n",
       " 'Jupyter Core': LooseVersion ('1.5.0.0'),\n",
       " '.NET Runtime': LooseVersion ('.NETCoreApp,Version=v3.1'),\n",
       " 'qsharp': LooseVersion ('0.17.2106.27950a1'),\n",
       " 'experimental': {'simulators': {'features': ['DEFAULT'],\n",
       "   'name': 'Microsoft.Quantum.Experimental.Simulators',\n",
       "   'opt_level': '3',\n",
       "   'target': 'x86_64-pc-windows-msvc',\n",
       "   'version': '0.17.210628040-alpha'}}}"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qsharp.component_versions()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85f8f2e8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}