tutorial/3_ftqc/02_pea3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Phase Estimation of Random 4x4 Hermitian Matrix\n",
    "\n",
    "Authors: Takumi Kato (Blueqat inc.), Maho Nakata (Riken), Shinya Morino, Seiya Sugo (Quemix inc.), Yuichiro Minato (Blueqat inc.)\n",
    "\n",
    "[Last time](114_pea2_en.ipynb), we calculated the eigenvalues of 2x2 Hermitian matrix. This time, we perform the quantum phase estimation of a random generated 4x4 Hermitian matrix.\n",
    "\n",
    "Calculating eigenvalues of Hermitian matrices is useful for finding physical quantities in quantum mechanics. It has wide range of applications in fields such as quantum chemistry and quantum simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "First, we import required libraries. In this time, we use [qgate](https://github.com/shinmorino/qgate) backend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import cmath\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "from blueqat import *\n",
    "from blueqat.pauli import X, Y, Z, I\n",
    "\n",
    "BlueqatGlobalSetting.set_default_backend('qgate')\n",
    "pi = math.pi\n",
    "\n",
    "# Version check for Blueqat\n",
    "try:\n",
    "    Circuit().r(0.1)[0].run()\n",
    "except AttributeError:\n",
    "    raise ImportError('Blueqat version is old.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Qgate installation check\n",
    "try:\n",
    "    Circuit().x[0].run_with_qgate()\n",
    "except ModuleNotFoundError:\n",
    "    raise ImportError('Qgate is not installed.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If ImportError is occured, you didn't install Qgate.\n",
    "# You can use Qgate without CUDA, but it's recommended on Linux environment.\n",
    "# https://github.com/shinmorino/qgate#build--install\n",
    "\n",
    "# To install pre-built package, run following command.\n",
    "\n",
    "# For Python 3.8 user:\n",
    "# !pip install https://github.com/shinmorino/qgate/raw/gh-pages/packages/0.2/qgate-0.2.2-cp38-cp38-manylinux1_x86_64.whl\n",
    "\n",
    "# For Python 3.7 user:\n",
    "# !pip install https://github.com/shinmorino/qgate/raw/gh-pages/packages/0.2/qgate-0.2.2-cp37-cp37m-manylinux1_x86_64.whl\n",
    "\n",
    "# For Python 3.6 user:\n",
    "# !pip install https://github.com/shinmorino/qgate/raw/gh-pages/packages/0.2/qgate-0.2.2-cp36-cp36m-manylinux1_x86_64.whl\n",
    "\n",
    "# Don't install and use numba backend\n",
    "# BlueqatGlobalSetting.set_default_backend('numba')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we make a random Hermitian matrix $\\hat H$.\n",
    "\n",
    "To obtain the eigenvalue by quantum phase estimation, we also need\n",
    "- A quantum circuit which gives the eigenvector of $\\hat H$ corresponding with desired eigenvalue\n",
    "- A quantum circuit which gives Controlled-$e^{i2\\pi \\hat H 2^n}$.\n",
    "\n",
    "We will create them.\n",
    "\n",
    "A Hermitian matrix can be decomposed into $\\hat H = P D P^\\dagger$\n",
    "where $P$ is a unitary matrix, $D$ is a real diagonal matrix.\n",
    "\n",
    "In this case, diagonal elements of $D$ are eigenvalues of $\\hat H$ and each column of $P$ are eigenvalues of $\\hat H$. Now, we're considering a 4x4 Hermitian. Thus, we need random generated SU(4) circuit. Such a SU(4) circuit can be generated from 4 SU(2) matrices and a matrix with 3 parameters. (Refer [arXiv:quant-ph/0507171](https://arxiv.org/abs/quant-ph/0507171))\n",
    "\n",
    "![circuit](img/115_1.png)\n",
    "\n",
    "Where $e^{iH} = e^{i(k_1 \\sigma_{XX} + k_2 \\sigma_{YY} + k_3 \\sigma_{ZZ})}$,\n",
    "$k_i$ are parameters and $\\sigma_{**}$ are Kronecker product of Pauli matrices.\n",
    "\n",
    "Now, we can define the function which returns\n",
    "\n",
    "- A Hermitian matrix $\\hat H$\n",
    "- eigenvalues, which we desired to calculate\n",
    "- A circuit, which gives the eigenvector of $\\hat H$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_hermitian(mat):\n",
    "    \"\"\"Check whether mat is Hermitian\"\"\"\n",
    "    return np.allclose(mat, mat.T.conjugate())\n",
    "\n",
    "def circuit_to_unitary(c):\n",
    "    \"\"\"Get a unitary matrix from circuit\"\"\"\n",
    "    n_qubits = c.n_qubits\n",
    "    def bits(n):\n",
    "        return tuple(i for i in range(8) if (1 << i) & n)\n",
    "    vecs = []\n",
    "    for i in range(2**n_qubits):\n",
    "        c0 = Circuit().x[bits(i)]\n",
    "        c0 += c\n",
    "        vecs.append(c0.run().reshape((-1, 1)))\n",
    "    return np.hstack(vecs)\n",
    "\n",
    "def rand_2pi():\n",
    "    return random.random() * 2 * pi\n",
    "\n",
    "def rand_eigval():\n",
    "    return random.random() * 2 - 1\n",
    "\n",
    "def random_su4_circuit():\n",
    "    c = Circuit()\n",
    "    c.u(rand_2pi(), rand_2pi(), rand_2pi())[0]\n",
    "    c.u(rand_2pi(), rand_2pi(), rand_2pi())[1]\n",
    "    c.cx[0, 1].rx(rand_2pi())[0].h[0].rz(rand_2pi())[1]\n",
    "    c.cx[0, 1].s[0].h[0].rz(rand_2pi())[1]\n",
    "    c.cx[0, 1].sdg[0].h[0].sdg[0].s[1].h[1].s[1]\n",
    "    c.u(rand_2pi(), rand_2pi(), rand_2pi())[0]\n",
    "    c.u(rand_2pi(), rand_2pi(), rand_2pi())[1]\n",
    "    return c\n",
    "\n",
    "def random_hermitian():\n",
    "    \"\"\"Make random Hermitian and returns triplet\n",
    "    (Hermitian, eigenvalues, Circuit for making eigenvectors).\n",
    "    \"\"\"\n",
    "    # Generate random eigenvalue\n",
    "    eigvals = [rand_eigval(), rand_eigval(), rand_eigval(), rand_eigval()]\n",
    "    eigvals.sort()\n",
    "    su4 = random_su4_circuit()\n",
    "    # Make Hermitian from them\n",
    "    p = circuit_to_unitary(su4)\n",
    "    hermitian = p @ np.diag(eigvals) @ p.T.conjugate()\n",
    "    # Check it is Hermitian\n",
    "    assert is_hermitian(hermitian)\n",
    "    # returns Hermitian, eigenvalue, circuit\n",
    "    return hermitian, eigvals, su4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK. We will make a Hermitian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H:\n",
      "[[-0.3602787 +6.93889390e-18j -0.16847036+4.50532033e-01j\n",
      "  -0.07103875-2.17509961e-01j -0.09194124-2.17742115e-01j]\n",
      " [-0.16847036-4.50532033e-01j  0.39806629+0.00000000e+00j\n",
      "   0.12594163-1.67494694e-01j  0.0500555 +1.22112697e-02j]\n",
      " [-0.07103875+2.17509961e-01j  0.12594163+1.67494694e-01j\n",
      "   0.07977263+2.77555756e-17j  0.58716814+4.58725159e-02j]\n",
      " [-0.09194124+2.17742115e-01j  0.0500555 -1.22112697e-02j\n",
      "   0.58716814-4.58725159e-02j -0.24505159+0.00000000e+00j]]\n",
      "\n",
      "Eigenvalues:\n",
      "[-0.7056969713621091, -0.7054962616978162, 0.6190267913204479, 0.6646750744522858]\n",
      "\n",
      "Eigenvectors (P = [v1 v2 v3 v4]):\n",
      "[[ 0.5243647 +0.02788284j -0.00403505+0.68144135j  0.47805499-0.09155162j\n",
      "  -0.14915106-0.02685705j]\n",
      " [ 0.05219516+0.32248169j -0.24825946+0.13123448j -0.31959717-0.4095473j\n",
      "  -0.05539297+0.7358575j ]\n",
      " [ 0.53159258-0.12789668j  0.12553904-0.32121597j -0.15515137+0.49456818j\n",
      "  -0.47902153+0.28979434j]\n",
      " [-0.561247  -0.05999184j  0.21686463+0.53925516j -0.13127266+0.45531115j\n",
      "  -0.26623217+0.21944488j]]\n",
      "\n",
      "P D P† = H? (D = diagonal matrix of eigenvalues): True\n"
     ]
    }
   ],
   "source": [
    "H, eigvals, su4 = random_hermitian()\n",
    "print('H:')\n",
    "print(H)\n",
    "print()\n",
    "print('Eigenvalues:')\n",
    "print(eigvals)\n",
    "print()\n",
    "print('Eigenvectors (P = [v1 v2 v3 v4]):')\n",
    "P = circuit_to_unitary(su4)\n",
    "print(P)\n",
    "print()\n",
    "print('P D P† = H? (D = diagonal matrix of eigenvalues):', np.allclose(P @ np.diag(eigvals) @ P.T.conjugate(), H))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make an eigenvector using `theta, phi, lam` and U gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.5243647 +0.02788284j  0.05219516+0.32248169j  0.53159258-0.12789668j\n",
      " -0.561247  -0.05999184j]\n"
     ]
    }
   ],
   "source": [
    "vec = su4.run()\n",
    "print(vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check `H vec = E vec`, it means, `E, vec` is a pair of eigenvalue and eigenvector of H."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.dot(H, vec), eigvals[0] * vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preparation is done. We will implement quantum phase estimation. We make the quantum circuit and calculate `E` by quantum phase estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def iqft(c, q0, n_qubits):\n",
    "    \"\"\"Add inversed quantum Fourier transform operations to q0-th - (q0 + n_qubits)-th qubits of the circuit `c`\"\"\"\n",
    "    for i in reversed(range(n_qubits)):\n",
    "        angle = -0.5\n",
    "        for j in range(i + 1, n_qubits):\n",
    "            c.cr(angle * pi)[q0 + j, q0 + i]\n",
    "            angle *= 0.5\n",
    "        c.h[q0 + i]\n",
    "    return c\n",
    "\n",
    "\n",
    "def apply_cu(c, ctrl, su4, eigvals, n):\n",
    "    \"\"\"Append Controlled-U^(2^n) to the circuit `c`.\n",
    "    Controll qubit is `ctrl`, target qubit is 0 and 1.\n",
    "    \n",
    "    This function requires eigenvalue `eigval` as an argument.\n",
    "    We make Controlled-U^(2^n) by using eigenvalue. You may feel we're cheating.\n",
    "    You can make approximate Controlled-U^(2^n) circuit without eigenvalue,\n",
    "    for example by using Suzuki-Trotter decomposition. In this case, you have to consider about precision.\n",
    "    Generally, making efficient and high-precision Controlled-U^(2^n) circuit without cheating is difficult.\n",
    "    \"\"\"\n",
    "    bias = 0.25 * sum(eigvals)\n",
    "    p, q, r, s = [v - bias for v in eigvals]\n",
    "    p1 = pi * (r + s)\n",
    "    p2 = pi * (q + s)\n",
    "    p3 = pi * (q + r)\n",
    "    c += su4.dagger()\n",
    "    c.crz(p1 * (2**n))[ctrl, 1]\n",
    "    c.crz(p2 * (2**n))[ctrl, 0]\n",
    "    c.ccx[ctrl, 1, 0].crz(p3 * (2**n))[ctrl, 0].ccx[ctrl, 1, 0]\n",
    "    c.rz(pi * bias * (2**n))[ctrl]\n",
    "    c += su4\n",
    "    return c\n",
    "\n",
    "def qpe_circuit(initial_circuit, eigvals, su4, precision):\n",
    "    \"\"\"Returns quantum phase estimation circuit\"\"\"\n",
    "    c = initial_circuit + su4\n",
    "    c.h[2:2 + precision]\n",
    "    for i in range(precision):\n",
    "        apply_cu(c, i + 2, su4, eigvals, i)\n",
    "    iqft(c, 2, precision)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the quantum circuit of quantum phase estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D1naPJx+y+fkBI1UwyfHcHbnKcbEwXi58zejuirppZGv+qXNJGvdZHx04tl0/jE+Rp6dzUlN89aWw4+BqRYffJElqHdZD2w+syjO/aqWa+d4wdjnjknYcXK3Ihp3zlff71m/VpcWdBW7PVnk5aldrrIuXUiVJqWnJCqxgHdV7456levLDrprzW8E7Hi/PK6/F8PbyVfXK+Z/58fepoGqBtXTk1J7caUs3fKXY6+8rsFxcUVgd58xLS09R6F8XCYV91wBQmHUJC9W99QN649ElmjxyhZJTjmtf0hajwzIlV6nroo7jtf46R0hLT1EF30BJhZ+PXO1s6klduHhONas2LHC7mVmZqlopRAF+gapbPVypF89KktLSz6uif5UCy/52+WSN+fAGrd+V/2ZPTtkXL6UotFZUkbE4SlF1W9D514I/pummNn8r07YLOocrKCZ7bLOwMmxtt6DPD6B8cpXjIoyRc6Pk7RHLJUkJifFFzg8MCNLEYYvVrH6HfOU5EgmwUkhJS1bAXyeSFfwqKyUtuch1fo2fru6tH8g3PSPzsvYd3aKwuq1LFUud4DDtOLBKD0+KVEJivJo36KSgwFr67F8JmvToUq3ftUh7j2wucP2V277XI5NaKPn8MZsnL2fOH9PB43/q0LEdkqyPPUSFxsji4aIPS7ugwur4xel36JlPblbrsIIfQQGAq23aE6c7Xqiqp6bEauArDfTCZ9ZeF5v3LlOnyL7y8faTJHlavGUp4vXwKJw71HVhx5jOLe7Q8Mmt9Njb16tv59GSCj4fudbc5ZPVt/OoAuf/tPpjPTQxQoEB1eTj5auI+u3005qP9dAb1kf3ala1/Ubuzi36aeqYzXrhwTn6+MenlZmVt3f/5YxLeuKDLnr/u9Fq1qBDsWJxlMLq1tb5V0bmZW3aE6dWTW4s9TaLOoe7NiZ7bLM4ZVy7XVufH4D5ucNxEc5X1E0jW/N9vP1UKaCq02LMQQKsFCr4VdaF9HOSpNT0c4Xe5ZSkzMwMxe/8Re2a9so3b9OeOLVsHFvqWBbGf64OzW/Tp09vU/umt2rx+hny8fKVv08FeXp6qUOzPtp/bGuB63eKvF2fPL1VwVXqavX2H/PMe6T3RL3y5X36eslrav7XneKf//hUt7QdUup4y6PC6vjFwd/qvdFr9J+fnzMoOgDu5rpGNyiiXju9OTxOUaExevzOD5Wdna2Ll1Ll72t91dXeI5t1NvWEGtRsbnC07s0d6rqwY8yMhf/Wp09v17R/7LCO2VXI+cjVUtKSdSL5kBqGRBa4zK0dhumzfybo5NlE7T68QbOXvakHeryg//xjhyr4V9bmvbbHZ63oX0UWi0VVKlZX3erhOnP+WJ753l4+mjxyhcYNmqXPf3mhWLGUxelzR/XUlNg8f6/MsPZyL6xubZ1/LVr3X93Y6v4ybbOoc7hrY7LHNotTxrXbtfX5AZifOxwXYYyiOtYUNd9Z3GYMMFfSvEFH/bR6qmJa3qMNuxbp5jaDC13+TMoxHU8+qGc/6akjp3ZrzY6fFFY3WpUCqur3rd/meZzw3IXT8vX2l6+3f7FiyVa2KgUESZICKwQr9eJZXbh4XgF+1lfcbdv/u/p2sd71PXn2sIIrX3kVyqWM9NwBSwN8A/Nts3nDjpr02FIlntileSvflyQlnkjQ/03vp5PnDkvZ2WrRqEvu4PjIr7A6zpnn71tRfj4VjAoRgIvKGVT8akGVQjS453jVCgqVJJ04e0jBleto9+GNuY9Sn7twWu9/N0rPP/A/p8fsrty1ros6jvt4+crPO0Dy8FBG5qUCz0cysi6rkn/V3Du0h07sVOKJBD37SU/tO7pFJ88mauKji/Jt12KxyM+ngny8/aXsq85HAqop9eJZpV9OU/rlNAX+NV2SUi+eUwW/QKVfTtPhk7vyjCmanZ2tzKwMeXl6536eomIpq6DAEL05PK7EdWvr/OvE2UTtObJRP676SAeObdN3K97TbR2H69yFU6paqWaR25RU4DlcQTHtOLi6zNs8dGJnvjL6FbFdW58fgHm463ERjlVQuxj7wNfqFHm7OkXerve/G63V239Ul+vuyLNcUfOdhQRYKYTVbS1vbz89+WFXNa59vZrWb6fT547q57XTNLD7WP38xzT9sPJDnb9wWucvnNHjd36gD/6+VpL0xa8vqkXDLqoUUFXZ2dnafmCVRvV7P7fsOb+9pbYRvdSi0ZWxOWyV9/WS19QjepBubHW/xs+4V4vW/Vdent4a+8A32rJvuT7/ZZy8vXzVolFXNavfXpmZGXrjm8F6fdjC3HLj/1yg2cvfkmTtyh8dfnOez/Hl4le0YdciBQZU0xN3TZWk3DdV/rJ2ujKzMkh+FeHaOm5UK0pfLn5FA7uP1Ssz7lVKWrKysjM1tNerkmx/1wDKp4IuWFdunacGIZHKzMqUh4e1I/f6XQsVHXaTMjMz9NrMBzSszyQFBYY4OWL35a51XdRxvE/H4XriA+v5RO/2wxRcuY7N85HXvnpAD9/6eu5Nsmb12+vd0dbxTSd+PVgDezwvSfpw3hN69LY39cvazxS38WtlZWeqZWis6tdoqts6jdDEb/6mGYv+rcCAahpw43Pasvc37Ti0RgO7j82Nee5vb2vtzgXKzs7Sfd2ekZent3Yf3qhdh9epe6uBevbTnvLw8JCHPDTqjg/UoGYzm7EYXbe2zr+uTvQ98UEX9esyWodP7tY3S1/XmP6fFGu7ts7hcrbbqGaLfDG1bXrl1bWl3eYjt76er4yrP6uturiQfi7f5wdgHu56XIRjlfamUVHznYkEWCmN7PtOnn8HBYbknuD1ajdUvdoNtbnegze/mPv/Hh4e+ujJDXnmp148q+YNOuaZZqu8+258Jvf/X3vklzzz2jfrrfbNeueZtidpk7pdPyDPtE4t+uZ7Y8/Vn2Ng97F5TlqvdkvbwTanIy9bdZxTpy8N/i7f8oW1HQCQpP3Htql5g466nJGu5JTjOnUuSQmJ8br7hqcUt+kbJRxaq09++qckaWivV9W8YcciSkRBXL2uizqO39J2cIHH66vPRwL8AvP0EL/aP++bnvv/I/pOliTd1vEx3dbxsTzLhQQ11FvDl+WZtu/oFsW2vDfPtEE3/58G3fx/eaY1qXO9mtS5XpIK7KV0bSyOVlTdVvSvku/862qTR66QJO09skndWg0ocLlr2TqHu3q7hb1psbTbtFXGtdu8drtFfX4A5uTqx0UYo6ibRrbmZ2Re1nOf9tLepE165tNb9FCvCWrmhLc9kwBzMaP6veeQcsPrRiu8brRDygYAOM/93a+MGfjJU9Y3LHW97i5ZLBbd2GqAbizlhS/yKy91/fidHzqk3LtueNIh5bqTrlF3lYttAigfystxESVT1E0jW/Mtsth1SIPiYhB8AADcXEzLe4wOodygrgEAuILjItwJPcCKqVINoyNwfeW1joz63GXZbh3nv3HWJbZtBHesa3eM2V0Zud90x31IWbbrrnXtyLLMoKT1Qf05XlF17K7HGHfc77lrXbsjd61rd7yOcVfuuA8xy7nT1UiAFVPEjUZHAFfljm3jzjZGR1B+uGNdu2PM7sod9x+Se7YRd63ra5nlcxiF+jOeO+4/JPeM2x1jdlfuWtfsE53HHduIGdsHj0ACAAAAAADA1EiAAQAAAAAAwNRIgAEAAAAAAMDUSIABAAAAAADA1EiAAQAAAAAAwNRIgAEAAAAAAMDUSIABAAAAAADA1EiAAQAAAAAAwNRIgAEAAAAAAMDUSIABAAAAAADA1EiAAQAAAAAAwNRIgAEAAAAAAMDUSIABAAAAAADA1LyMDsCV7VwinT9udBTuqVINKeJGo6NwDqPaSXmqY3dm5H6ENuL65sZLh88Ys+06VaU725RuXaPidseYpbLFfS3OTfIq6X6O+nO8or4Tdz0uuuN+z13r2h1R1ygK14yugQRYIc4fl5ITjY4Cro52gsLQPlCYw2ekPW54Me6OcbtjzLawTykb6s947voduOM+xF3r2h1R1ygKbcQ18AgkAAAAAAAATI0EGAAAAAAAAEyNRyDhli5nSpsPWruiHzp9Zfo7v0h1q0nhNaXmdSRPUrzlUna2tP+ktO2wdOjUlemv/yjVrio1DJZaNZAq+hkXI4x1Nk3asF86cEpKSr4yfepSqV6QFFVPqhtkVHQAAKA4ki9IGw5IB07mPZ5/vFSqV01qWc967ofy6XKmtOWQtPu4lHjVNePkX6zne2EhUiTXjOUKCTC4lYxMaeE2aUWClJqef/6+k9a/5TulKgFS9+ZS53DJ4uH8WK/21JRY7TiwSp6e3rJYPBVStZHu7z5WMS37GxuYCW0/LP20yfZAtUlnrX/r9kvz1kutG0q3tZIqGZwIo304T/IF63e/6aCUlZ1//o4j1r9ft0oNqlnbR5Oazo8TAAAU7FSK9P16aUui7eP59iPWv1+2SKHVrcfzRtWdH+e1OOdzjoxMafF26bedtq8Z95+0/i1PkCr7S92aSzeESxaDE2G0D8cj1+lGHpjQUIvWzSj2dLM5ckaa9LP1QGZrR3at5AvSnHjp/YXSmVTHx1eUgT3G6YdXUjT3xVO6pe1gvfrV/Tp8crfRYZnGpQxp5mrp47jivaUpI0v6Y6/02o/WO0NGo304Xvw+6/e94YDtk+VrHTglvb/I+uavzCzHxwe4uvJ+HuIs1LNtT02JVe9nfHXb2IrqO66yHnu7lZZvnmN0WKbjDvW8eo808Sdp06HiHc/3npDe/VX6foNrHM8553Oso2eltxZIP28u3jXj2TTpu3XSewul0ymOj68otA/HIgEGt3DwlPTuQusOraT2npDe+dV6p8gVeHp6qVf7R5SZlaE9RzYaHY4pXMqwPrq2Zk/J101Nl/7zW+nWdQTah2Ms+1OasVK6eLnk6/6209pGMjLtHxcAoPiuvjDsdv0Ajf/yXiWeSDA6LNNx5XpeuFX6erWUnlGy9bIlLdku/fd310iCSZzzOULiaet135Hkkq+776R13RPn7R5WqdA+HIMEGFze2TRrcqM0F645ki9Yy7hUwoOlI1zOuKQfV06RJNUNDjc4GnOYubpsrybPlvVkatcxu4VUarQP+9t8SPp2XdnK2HZYmlvGMgAA9uHp6aXbO41QVlam9iVtMToc03K1el633zrMRVlsPCj9sMEu4ZQZ53z2df6i9NESKe1S6cs4myZNXSKll+G6015oH47BGGBwadnZ0qw/iu6+Onmg9b9PfFnwMsfPWQ+ad0TbL76S+GrxK5q1bJLS0s/L09NbY/p/qtDaUZKkn/+YpkXr/pu7bNLpvbquUVc9e38hHwiSrI+zbThQ+DLFaR85SbB/9pZ8ve0WXrHRPhwjNV363x9FL1ecNrJyl3Uw3Yha9okNAFA6lzMuad7KD+Tl6a3Q2i2NDse0XKmez6VJs9cWvVxxjufL/rS+7Ca0hn1iKynO+Rxj9lopxQ7XjCdTpB82Sne3tVtoJUL7cCyX7gGWlZWlSZMmKSwsTH5+fmrZsqWWLVumiIgIDRs2zOjw4AS7j0lbE+1X3m9/SicN6tZ6f/ex+u7lZM1+8aTaNe2tTbuX5s7r1W6o3hwepzeHx2nswK/l51NBQ3q+YkygbiQzyzqgub2cSrE+7mYE2odjLNompVy0X3nfrrMm5o129vhe/fRuf30yMkQfDq2oaY/X049v36HMjDLc9nSg2eNj9cd344s93ZW4W10DZvbV4lfUb1wV3T++rlZtm6cXHpyjOsFNjA7LJnfe77liPf+ypWw9e66WLek7O54/lhTnfPa397j1BUf2siJBOnbOfuWVBO3DsVy6B9jQoUM1d+5cjRs3TtHR0Vq5cqUGDBigEydOaMyYMUaH53Sent7KyMrfHzMj87K8PA3osuIEK3bZt7xsSSt3S7e3sm+5JVEpoKrG9P9Uf3utsVZunadOLfrmzsvKytKrMwdqaK9XFRLU0Lgg3cS2w9bHW+3p913Wt4ca9RYY2of9XMqwDpRrT0fPWk+yGhv8Zsh5b/RW/etu1oNv7JSPf6BSTh/Wvo0/KtsVsnMmQ11fUR7PQ4xAPRfs/u5jNbDH80aHYXquVs8XL1tfZGNPB09Z/+pXs2+5JcE5n/2scMAQdSt3GffkkET7cBSX7QE2c+ZMTZ8+Xd9//72efvppdevWTWPHjlXHjh2VkZGh1q1bGx2i04VUbagj17wBIi09RWfOH1WtaqEGReU4lzPt2/srR1GPyzlDYECQ7uo6Rv9Z8Jyysq6MxPnfhS+pUch16tyin3HBuRFHfJfJF6yvRTYS7cM+dh21393iqxm9D0k7f0pnknbquu6PyTegsjw8PFSpWl1FdX9MXt6+xgZnMtR1XuXtPMQo1DOQ144jJR/0vjiMPp5LnPPZQ2aWdbxXe6N9mJPLJsAmTJignj17KiYmJs/0Jk2ayNvbW1FR1udgX3jhBYWHh8tisWj27NlGhOo0N7cZrPlrPtaWvcuVmZWp8xfO6MN5f1fDkOvUpLaBXZocJCnZMW9pOZNq30eiSuuOrn/X6XNJWrjuC0nS+l2LtS7hVz1y60SDI3Mfh067V7klQfsou4MmbR/+laqpWt1ILf70Ye1Y/oVOHd5eLnsjOQN1nVd5Ow8xCvUM5HXolGPKTXSB8z2Jc76ySkqWMhxwzXguzToovtFoH/blke2CZ3KJiYmqV6+epk2bpoceeijPvAEDBujPP//Uhg3W13esXLlSISEheuihhzRq1CjdfffdxdqGh4dHkctMemypWjaOLXH8jjR/zSf6bsV7OpZ8QP4+FRUVGqOHb31dNarUMzq0PDbtidPTH3UrUxlNuwzSLY99kWdazsCFJXXtQIezXu6qIztXlDKyvOzRTk6fO6qnp3bThKE/F7sbqz3q2J1ZPL00+vPLys7Ozv0926t9bFn8kZZ8NryMEVoZ1T4k2kiv0d8ovP09eabZo42kp53TR49ULkNkV9w1dqnqNost8Xpp509q/fy3dGDzAp1K3CrfClXU8qbRatfv+WId3yQpcUec5rxSuvZR0rhnj4/V0T1r5HlNr6nLF1PU4c4X1a5f8R61cWbMOYyu62sZfW7iauchJd3PGV1/xeVq9VwSRX0npf0OnpoSq9ZhPcr0aF5ZjovuuN8rTV3bo54l+56D3P7UD2rUqk+eafY4nqcmH9Wno+zzZht77Vu4Jii58I73qdfImXmm2euaYM6EG5W4fanthUuIa0bHKUlKyyXHAEtMtD73FhISkmd6Wlqali1bpl69euVO69Spk1NjM1rv9o+od/tHjA7DKby8/dyy7NKYsehlpV48qze+GZw7rV71CD1x91TjgnJxnl7WE8riXoCWqGwXe7SJ9lE6jvqdu8L+w79SsDrfO0Gd752gy+kXtGvN/7R42iOqGFRHkTEPFV2AAdr1HZvvgm/2+FhjgikBd6xrRypP5yFGop7ze3N4nNEhlJg77vdcsZ49TXw8vxbnfCXHNSPtoyRcMgEWHBwsSUpISFDv3r1zp0+cOFFJSUmKji77aHQ5j1bGxcUVuEz811KyA8agKg9iYmKVPaVsnQvj90kzVuadVtAra4vzSturxS1ZqEbVSx/b1ezRTh6/8wM9fucHJVrHHnXszjKzpKdnWl9skMNe7WPY0CH6deqQMsWXw6j2IdFGPl+Rf/wGe7SRigE+dnsM7r2F0p7jZSvD2zdAzW8YrE2/vqcTBzYWe72YmFjNHl+6z2GPuEvD6JiNqOtrcW6SV0n3c9Sf4xX1nRj5HZTluOiO+z13retrfbos/7jA9jie1wiuYrfjub3qmmuCklu/X/ri97zT7HVN8Osv8xVmpxcfcc1of7GxsSVexyXHAAsNDVVUVJQmTJigL774QosXL9bw4cP1n//8R5LskgCD6wuxzxNGTi8bzuFpkWoEOqbskCqOKRfOVauKg8o1eP9xMfWMfv/mWZ08tFWZGZeVlZmhXX/M0anEraoT0dXY4EyGugYA4znquMv5njk46nxPMv6cD/bnkj3ALBaLZs2apUcffVTDhw9XtWrV9Le//U0jR47Uc889lzsAPsytVhXJ29P6Nkh7ql5J8vexb5kwRv1q0rFzjikX7s9R32M9g9uHp6ePLpw7rp/euVOpyUmyWLwUWL2hYga9q7D2/Y0NzmSoawAwnqOOu/WDHFMunKtmoOTrZf83hVatIFV0rScgYQcumQCTpPDwcC1dmnfAuUGDBql58+by9/c3KCo4k6dFur6BtHavfcuNbmjf8mCc6EbS2n32LbNGoFSPEyJTCKspBfpJ5+z81tc2De1bXkl5+1XQTY9MMzaIErr7+bgSTXcV7ljXAFyDu+73XFHTWlKAj3Thkn3LjW5k3/JgDItFatVAWr3HvuUafb4Hx3DZBJgt8fHx6tChQ55p48aN02effaYTJ05oy5YteuKJJ7Rs2TI1btzYITHM+e1tLd8yR5NH5n+DYPrlNA2a0EjPDJih1uE99MqM+3T6/FFdzkhX+uU0TR2z0WaZ+45u1TtzHlN2drb+fucUhdbO28NtyvdPKiExXk3qtNbIvu/YjGXf0a2aPHuYLBZP1a7WRE/f8x9lZWXqtZkP6EzKMUXUbatH+th+VeqOg2v00fdPysPDooh6bTX89rfzzP/vry9p7c4FkqTBPcerdVh3HTi2XW/Nsg7O2qrJjRrc8+Vi12FJdAmzbwLM4iF1aGK/8opSWN1+8euL+n3rt6roX1Udm9+uu2PGOK1ezSI8xNqj78R5+5XZOUxywLj6BTp59ojGfdZHB45t1w/jU+TpeWW3bGsf8uG8J7TnyEZJ0t6kTfr232ecF6yb8bRIHcOkX7bYr8z61YzvAQbkOHp6v0a/1171azSTl6ePXh/2a575to4zv6ydrq+XvqqgSrXUtF67As8N/vjzZ330/ZMKrBCc75zn9LmjeuXL+yRJZ1KOqU34LRrRd7Ik6dS5JD34aqg+fmqL6gTbPuAuXv+lvl/5gSoFBOnZ+79SBb8rz7P/tPpjLVhrHfLiji6P68ZW92v34Q16/esHlZZ+XjOe21+aqgLgxny8pA6NpSU77Fdmk5oMiWImXcLtmwCzeEidwuxXHlyH2yTAUlJSlJCQoBEjRuSZ/vLLL+vll52TJLiUkZ574WnLz2s+VaNa1+X+e+wDX0uSVmz5VrsOrytwvc8XjNNzA2fK4mHRu3NH6N9D5uXO25W4XmnpKXp7xHK9M2e4dh5aq4h6bfPFUq96hN4ZZR0x/o1vhighMV5HT+9XaO2WGnDjs3r/u9Hac2STGtdumW/7Nas00BuPLpGPt59e/Wqg9iVtyfM5erR5UINu/j+lpCXrhc9uV+uw7vpx1Uca2vtVRYXeoH99fJNS0pJV0b9KUVVYYg2Cpbah9kuC3XydVCXAPmUVR1F1+2ifN9U6vEfuv51Vr2Zh8ZDuait9tMQ+5dWqbE2AOVNgQJAmDlusFz+/I988W/uQnIvM3Yc3aPayN50Wp7u6sZl1/3E6texleUi6q03ZywHsKTrsJj1z/4wC5197nJGk/jH/UO/2DxdabrP6HfTRmE3659Tu+eYFBYbkvinug3l/V4dmfXLnzV0+WU3rty+w3IzMy/px9Ud6a/hvWr5ljn5aPVX3xP7jyucJv1m3dhimjMzLevy9Drqx1f2qXa2J3h29Ws9+ckuhMdtTUclFW/OLWqe4CrrxaeumWmE3UYqrsDLW/rlAXy99TZKUeGKnHr9zijq36Cep8JvCznLy7GG9NethpV48W+CNXNiH0XXdo4W0br90Nq3sZVk8pDsMHFK6pL85Hy+/An+HsKobZE2S2isJ1iPS+giksxXVMcXWcebipQt6+b/9dfFSqir4Vdbzg/4nHy/XeqO9K3HJQfBtqVixojIzMzV69GjDYljwxzTd1OZvNuddzrikHQdXK7Jh53zzft/6rbq0uLPAcs+nnVGNKvUUXLmOUi4m55m34+BqRYffJElqHdZD2w+sshmLl6d37v97e/mqeuV6Sjq9V6G1rL3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      "text/plain": [
       "<Figure size 1591.6x3335.08 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpe_circuit(Circuit(), eigvals, su4, 4).run_with_ibmq(returns='draw', output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we make a function for calculating the eigenvalue from observed result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_qpe(c, shots=1000, max_candidates=5):\n",
    "    \"\"\"Run the circuit for quantum phase estimation and returns candidates of eigenvalue.\n",
    "    shots: The number of running quantum circuit, max_candidates: Maximum number of candidates\n",
    "    \"\"\"\n",
    "    cnt = c.m[2:].run(shots=shots)\n",
    "\n",
    "    # Convert measured result to floating point value\n",
    "    def to_value(k):\n",
    "        k = k[2:] # Drop unnecessary element\n",
    "        val = 0 # Value\n",
    "        a = 1.0 \n",
    "        for ch in k:\n",
    "            if ch == '1':\n",
    "                val += a\n",
    "            a *= 0.5\n",
    "        if val > 1:\n",
    "            # When the phase > π, subtract 2π (phase is negative).\n",
    "            val = val - 2\n",
    "        return val\n",
    "\n",
    "    return [(to_value(k), v) for k, v in cnt.most_common(max_candidates)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can perform the quantum phase estimation. Let's see the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue (expected): -0.7945019526444816\n",
      "3 bit precision:\n",
      "906  -0.75             (deviation:  4.450e-02)\n",
      "36   1.0               (deviation:  1.795e+00)\n",
      "22   -0.5              (deviation:  2.945e-01)\n",
      "\n",
      "4 bit precision:\n",
      "650  -0.75             (deviation:  4.450e-02)\n",
      "185  -0.875            (deviation: -8.050e-02)\n",
      "48   -0.625            (deviation:  1.695e-01)\n",
      "\n",
      "5 bit precision:\n",
      "731  -0.8125           (deviation: -1.800e-02)\n",
      "121  -0.75             (deviation:  4.450e-02)\n",
      "47   -0.875            (deviation: -8.050e-02)\n",
      "\n",
      "6 bit precision:\n",
      "548  -0.78125          (deviation:  1.325e-02)\n",
      "292  -0.8125           (deviation: -1.800e-02)\n",
      "43   -0.84375          (deviation: -4.925e-02)\n",
      "\n",
      "7 bit precision:\n",
      "915  -0.796875         (deviation: -2.373e-03)\n",
      "37   -0.78125          (deviation:  1.325e-02)\n",
      "21   -0.8125           (deviation: -1.800e-02)\n",
      "\n",
      "8 bit precision:\n",
      "695  -0.796875         (deviation: -2.373e-03)\n",
      "165  -0.7890625        (deviation:  5.439e-03)\n",
      "45   -0.8046875        (deviation: -1.019e-02)\n",
      "\n",
      "9 bit precision:\n",
      "617  -0.79296875       (deviation:  1.533e-03)\n",
      "213  -0.796875         (deviation: -2.373e-03)\n",
      "38   -0.7890625        (deviation:  5.439e-03)\n",
      "\n",
      "10 bit precision:\n",
      "845  -0.794921875      (deviation: -4.199e-04)\n",
      "68   -0.79296875       (deviation:  1.533e-03)\n",
      "28   -0.796875         (deviation: -2.373e-03)\n",
      "\n",
      "11 bit precision:\n",
      "514  -0.794921875      (deviation: -4.199e-04)\n",
      "302  -0.7939453125     (deviation:  5.566e-04)\n",
      "49   -0.7958984375     (deviation: -1.396e-03)\n",
      "\n",
      "12 bit precision:\n",
      "929  -0.79443359375    (deviation:  6.836e-05)\n",
      "37   -0.794921875      (deviation: -4.199e-04)\n",
      "13   -0.7939453125     (deviation:  5.566e-04)\n",
      "\n",
      "13 bit precision:\n",
      "758  -0.79443359375    (deviation:  6.836e-05)\n",
      "131  -0.794677734375   (deviation: -1.758e-04)\n",
      "34   -0.794189453125   (deviation:  3.125e-04)\n",
      "\n",
      "14 bit precision:\n",
      "512  -0.7945556640625  (deviation: -5.371e-05)\n",
      "301  -0.79443359375    (deviation:  6.836e-05)\n",
      "47   -0.794677734375   (deviation: -1.758e-04)\n",
      "\n",
      "15 bit precision:\n",
      "949  -0.79449462890625 (deviation:  7.324e-06)\n",
      "23   -0.7945556640625  (deviation: -5.371e-05)\n",
      "9    -0.79443359375    (deviation:  6.836e-05)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue (expected):', eigvals[0]) # It's expected value. We desire a value closed to it.\n",
    "# We'll run small to high precision for comparison.\n",
    "for precision in range(3, 16):\n",
    "    print(precision, 'bit precision:')\n",
    "    c = qpe_circuit(Circuit(), eigvals, su4, precision)\n",
    "    result = run_qpe(c, 1000, 3)\n",
    "    for value, count in result:\n",
    "        # Display a number of observation, obtained eigenvalue and a deviation from true eigenvalue.\n",
    "        print(f'{count:<5}{value:<18}(deviation: {value - eigvals[0]: .3e})')\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtained value are near by true eigenvalue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we calculate 2nd eigenvalue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue (expected): 0.28570068909309354\n",
      "3 bit precision:\n",
      "926  0.25              (deviation: -3.570e-02)\n",
      "32   0.5               (deviation:  2.143e-01)\n",
      "21   0                 (deviation: -2.857e-01)\n",
      "\n",
      "4 bit precision:\n",
      "749  0.25              (deviation: -3.570e-02)\n",
      "131  0.375             (deviation:  8.930e-02)\n",
      "38   0.125             (deviation: -1.607e-01)\n",
      "\n",
      "5 bit precision:\n",
      "534  0.3125            (deviation:  2.680e-02)\n",
      "296  0.25              (deviation: -3.570e-02)\n",
      "39   0.375             (deviation:  8.930e-02)\n",
      "\n",
      "6 bit precision:\n",
      "932  0.28125           (deviation: -4.451e-03)\n",
      "30   0.3125            (deviation:  2.680e-02)\n",
      "19   0.25              (deviation: -3.570e-02)\n",
      "\n",
      "7 bit precision:\n",
      "761  0.28125           (deviation: -4.451e-03)\n",
      "128  0.296875          (deviation:  1.117e-02)\n",
      "34   0.265625          (deviation: -2.008e-02)\n",
      "\n",
      "8 bit precision:\n",
      "533  0.2890625         (deviation:  3.362e-03)\n",
      "291  0.28125           (deviation: -4.451e-03)\n",
      "49   0.296875          (deviation:  1.117e-02)\n",
      "\n",
      "9 bit precision:\n",
      "945  0.28515625        (deviation: -5.444e-04)\n",
      "19   0.2890625         (deviation:  3.362e-03)\n",
      "12   0.28125           (deviation: -4.451e-03)\n",
      "\n",
      "10 bit precision:\n",
      "776  0.28515625        (deviation: -5.444e-04)\n",
      "110  0.287109375       (deviation:  1.409e-03)\n",
      "40   0.283203125       (deviation: -2.498e-03)\n",
      "\n",
      "11 bit precision:\n",
      "494  0.2861328125      (deviation:  4.321e-04)\n",
      "330  0.28515625        (deviation: -5.444e-04)\n",
      "44   0.287109375       (deviation:  1.409e-03)\n",
      "\n",
      "12 bit precision:\n",
      "959  0.28564453125     (deviation: -5.616e-05)\n",
      "20   0.28515625        (deviation: -5.444e-04)\n",
      "9    0.2861328125      (deviation:  4.321e-04)\n",
      "\n",
      "13 bit precision:\n",
      "842  0.28564453125     (deviation: -5.616e-05)\n",
      "81   0.285888671875    (deviation:  1.880e-04)\n",
      "24   0.285400390625    (deviation: -3.003e-04)\n",
      "\n",
      "14 bit precision:\n",
      "482  0.28564453125     (deviation: -5.616e-05)\n",
      "337  0.2857666015625   (deviation:  6.591e-05)\n",
      "46   0.285888671875    (deviation:  1.880e-04)\n",
      "\n",
      "15 bit precision:\n",
      "976  0.28570556640625  (deviation:  4.877e-06)\n",
      "11   0.28564453125     (deviation: -5.616e-05)\n",
      "5    0.2857666015625   (deviation:  6.591e-05)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue (expected):', eigvals[1]) # It's expected value. We desire a value closed to it.\n",
    "# We'll run small to high precision for comparison.\n",
    "for precision in range(3, 16):\n",
    "    print(precision, 'bit precision:')\n",
    "    c = qpe_circuit(Circuit().x[0], eigvals, su4, precision)\n",
    "    result = run_qpe(c, 1000, 3)\n",
    "    for value, count in result:\n",
    "        # Display a number of observation, obtained eigenvalue and a deviation from true eigenvalue.\n",
    "        print(f'{count:<5}{value:<18}(deviation: {value - eigvals[1]: .3e})')\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok. Let's calculate 3rd one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue (expected): 0.3578678227869243\n",
      "3 bit precision:\n",
      "511  0.25              (deviation: -1.079e-01)\n",
      "298  0.5               (deviation:  1.421e-01)\n",
      "58   0.75              (deviation:  3.921e-01)\n",
      "\n",
      "4 bit precision:\n",
      "936  0.375             (deviation:  1.713e-02)\n",
      "23   0.25              (deviation: -1.079e-01)\n",
      "15   0.5               (deviation:  1.421e-01)\n",
      "\n",
      "5 bit precision:\n",
      "763  0.375             (deviation:  1.713e-02)\n",
      "114  0.3125            (deviation: -4.537e-02)\n",
      "45   0.4375            (deviation:  7.963e-02)\n",
      "\n",
      "6 bit precision:\n",
      "504  0.34375           (deviation: -1.412e-02)\n",
      "320  0.375             (deviation:  1.713e-02)\n",
      "44   0.40625           (deviation:  4.838e-02)\n",
      "\n",
      "7 bit precision:\n",
      "973  0.359375          (deviation:  1.507e-03)\n",
      "10   0.375             (deviation:  1.713e-02)\n",
      "9    0.34375           (deviation: -1.412e-02)\n",
      "\n",
      "8 bit precision:\n",
      "874  0.359375          (deviation:  1.507e-03)\n",
      "55   0.3515625         (deviation: -6.305e-03)\n",
      "34   0.3671875         (deviation:  9.320e-03)\n",
      "\n",
      "9 bit precision:\n",
      "601  0.359375          (deviation:  1.507e-03)\n",
      "220  0.35546875        (deviation: -2.399e-03)\n",
      "53   0.36328125        (deviation:  5.413e-03)\n",
      "\n",
      "10 bit precision:\n",
      "838  0.357421875       (deviation: -4.459e-04)\n",
      "63   0.359375          (deviation:  1.507e-03)\n",
      "30   0.35546875        (deviation: -2.399e-03)\n",
      "\n",
      "11 bit precision:\n",
      "463  0.357421875       (deviation: -4.459e-04)\n",
      "354  0.3583984375      (deviation:  5.306e-04)\n",
      "43   0.3564453125      (deviation: -1.423e-03)\n",
      "\n",
      "12 bit precision:\n",
      "975  0.35791015625     (deviation:  4.233e-05)\n",
      "8    0.357421875       (deviation: -4.459e-04)\n",
      "8    0.3583984375      (deviation:  5.306e-04)\n",
      "\n",
      "13 bit precision:\n",
      "917  0.35791015625     (deviation:  4.233e-05)\n",
      "34   0.357666015625    (deviation: -2.018e-04)\n",
      "15   0.358154296875    (deviation:  2.865e-04)\n",
      "\n",
      "14 bit precision:\n",
      "648  0.35791015625     (deviation:  4.233e-05)\n",
      "186  0.3577880859375   (deviation: -7.974e-05)\n",
      "54   0.3580322265625   (deviation:  1.644e-04)\n",
      "\n",
      "15 bit precision:\n",
      "726  0.35784912109375  (deviation: -1.870e-05)\n",
      "140  0.35791015625     (deviation:  4.233e-05)\n",
      "34   0.3577880859375   (deviation: -7.974e-05)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue (expected):', eigvals[2]) # It's expected value. We desire a value closed to it.\n",
    "# We'll run small to high precision for comparison.\n",
    "for precision in range(3, 16):\n",
    "    print(precision, 'bit precision:')\n",
    "    c = qpe_circuit(Circuit().x[1], eigvals, su4, precision)\n",
    "    result = run_qpe(c, 1000, 3)\n",
    "    for value, count in result:\n",
    "        # Display a number of observation, obtained eigenvalue and a deviation from true eigenvalue.\n",
    "        print(f'{count:<5}{value:<18}(deviation: {value - eigvals[2]: .3e})')\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last eigenvalue is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue (expected): 0.8041869501627237\n",
      "3 bit precision:\n",
      "837  0.75              (deviation: -5.419e-02)\n",
      "88   1.0               (deviation:  1.958e-01)\n",
      "28   0.5               (deviation: -3.042e-01)\n",
      "\n",
      "4 bit precision:\n",
      "500  0.75              (deviation: -5.419e-02)\n",
      "337  0.875             (deviation:  7.081e-02)\n",
      "54   0.625             (deviation: -1.792e-01)\n",
      "\n",
      "5 bit precision:\n",
      "934  0.8125            (deviation:  8.313e-03)\n",
      "32   0.75              (deviation: -5.419e-02)\n",
      "12   0.875             (deviation:  7.081e-02)\n",
      "\n",
      "6 bit precision:\n",
      "809  0.8125            (deviation:  8.313e-03)\n",
      "77   0.78125           (deviation: -2.294e-02)\n",
      "42   0.84375           (deviation:  3.956e-02)\n",
      "\n",
      "7 bit precision:\n",
      "475  0.796875          (deviation: -7.312e-03)\n",
      "345  0.8125            (deviation:  8.313e-03)\n",
      "41   0.78125           (deviation: -2.294e-02)\n",
      "\n",
      "8 bit precision:\n",
      "983  0.8046875         (deviation:  5.005e-04)\n",
      "5    0.796875          (deviation: -7.312e-03)\n",
      "3    0.8125            (deviation:  8.313e-03)\n",
      "\n",
      "9 bit precision:\n",
      "946  0.8046875         (deviation:  5.005e-04)\n",
      "22   0.80078125        (deviation: -3.406e-03)\n",
      "13   0.80859375        (deviation:  4.407e-03)\n",
      "\n",
      "10 bit precision:\n",
      "791  0.8046875         (deviation:  5.005e-04)\n",
      "105  0.802734375       (deviation: -1.453e-03)\n",
      "36   0.806640625       (deviation:  2.454e-03)\n",
      "\n",
      "11 bit precision:\n",
      "443  0.8037109375      (deviation: -4.760e-04)\n",
      "376  0.8046875         (deviation:  5.005e-04)\n",
      "55   0.8056640625      (deviation:  1.477e-03)\n",
      "\n",
      "12 bit precision:\n",
      "998  0.80419921875     (deviation:  1.227e-05)\n",
      "1    0.8046875         (deviation:  5.005e-04)\n",
      "1    0.80517578125     (deviation:  9.888e-04)\n",
      "\n",
      "13 bit precision:\n",
      "995  0.80419921875     (deviation:  1.227e-05)\n",
      "2    0.804443359375    (deviation:  2.564e-04)\n",
      "1    0.803955078125    (deviation: -2.319e-04)\n",
      "\n",
      "14 bit precision:\n",
      "966  0.80419921875     (deviation:  1.227e-05)\n",
      "12   0.8040771484375   (deviation: -1.098e-04)\n",
      "8    0.8043212890625   (deviation:  1.343e-04)\n",
      "\n",
      "15 bit precision:\n",
      "878  0.80419921875     (deviation:  1.227e-05)\n",
      "54   0.80413818359375  (deviation: -4.877e-05)\n",
      "26   0.80426025390625  (deviation:  7.330e-05)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Eigenvalue (expected):', eigvals[3]) # It's expected value. We desire a value closed to it.\n",
    "# We'll run small to high precision for comparison.\n",
    "for precision in range(3, 16):\n",
    "    print(precision, 'bit precision:')\n",
    "    c = qpe_circuit(Circuit().x[0, 1], eigvals, su4, precision)\n",
    "    result = run_qpe(c, 1000, 3)\n",
    "    for value, count in result:\n",
    "        # Display a number of observation, obtained eigenvalue and a deviation from true eigenvalue.\n",
    "        print(f'{count:<5}{value:<18}(deviation: {value - eigvals[3]: .3e})')\n",
    "    print('')"
   ]
  }
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