constraint_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8a58e9e8",
   "metadata": {},
   "source": [
    "## The symmetric 4-city problem\n",
    "\n",
    "solving the bottleneck travelling salesman problem using phase estimation.\n",
    "\n",
    "### testing contraint:\n",
    "\n",
    " - 6 qubits for phase estimation.\n",
    " - 8 qubits initialized to the eigenvalue of the of the matrix $U$.\n",
    " - There are 3 hamilonian cycles, so we need eigenvalue and estimation qubits for each.\n",
    " - To solve the constraint problem we need a new operator $U$ satifying a max edge weight."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "b07b856d",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"attachment:image.png\" width=\"400\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47a2443f",
   "metadata": {},
   "source": [
    "### we can assign arbitrary weights\n",
    "\n",
    "$$\\Large 1: A\\xrightarrow{\\gamma_1}B \\xrightarrow{\\gamma_4}C \\xrightarrow{\\gamma_5}D\\xrightarrow{\\gamma_3}A: 4 + 4 + \\mathbf{5} + 4 = 17$$\n",
    "\n",
    "$$\\Large 2: A\\xrightarrow{\\gamma_1}B \\xrightarrow{\\gamma_6}D \\xrightarrow{\\gamma_5}C\\xrightarrow{\\gamma_2}A: 4 + \\mathbf{6} + 5 + 2 = 17$$\n",
    "\n",
    "$$\\Large 3: A\\xrightarrow{\\gamma_2}C \\xrightarrow{\\gamma_4}B \\xrightarrow{\\gamma_6}D\\xrightarrow{\\gamma_3}A: 2 + 4 + \\mathbf{6} + 4 = 16$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0129dbf8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 2 4 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import math\n",
    "\n",
    "gamma_1 = 4 # a <-> b\n",
    "gamma_2 = 2 # a <-> c\n",
    "gamma_3 = 4 # a <-> d\n",
    "gamma_4 = 4 # b <-> c\n",
    "gamma_5 = 5 # c <-> d\n",
    "gamma_6 = 6 # b <-> d\n",
    "\n",
    "\n",
    "# gamma_1 = 1 # a <-> b\n",
    "# gamma_2 = 2 # a <-> c\n",
    "# gamma_3 = 3 # a <-> d\n",
    "# gamma_4 = 4 # b <-> c\n",
    "# gamma_5 = 5 # c <-> d\n",
    "# gamma_6 = 6 # b <-> d\n",
    "\n",
    "weights = []\n",
    "\n",
    "for i in range(1, 7):\n",
    "    variable_name = \"gamma_\" + str(i)\n",
    "    # Assuming you have variables like number_1, number_2, etc.\n",
    "    current_number = locals()[variable_name]\n",
    "    weights.append(current_number)\n",
    "\n",
    "weights = np.array(weights)\n",
    "print(weights)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c932b220",
   "metadata": {},
   "source": [
    "we need to normalize the weights, $w$, so we only have values in $(0, 2\\pi)$. We can do this by:\n",
    "\n",
    "$$\\Large w = \\frac{w}{\\mathrm{max}(w) + \\epsilon} \\times 2\\pi$$\n",
    "\n",
    "The addition of $\\epsilon$ is included to avoid a max normalized weight of $2\\pi$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d62393",
   "metadata": {},
   "source": [
    "**edit: normalizing by max does not work, we need to normalize by largest hamiltonian cycle, then multiply by $2\\pi$**\n",
    "\n",
    "we can just use the values we have above for now, but might be worth considering what strategy works best.\n",
    " - simplest solution would be to normalize based on the sum of all edge weights\n",
    " \n",
    " $$\\Large w = \\frac{w}{\\mathrm{sum}(w)} \\times 2\\pi$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "77d2711e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "normalized weights: [0.50265482 0.25132741 0.50265482 0.50265482 0.62831853 0.75398224]\n",
      "solution 1: 2.1362830044410597\n",
      "solution 2: 2.1362830044410592\n",
      "solution 3: 2.0106192982974678\n",
      "solutions after max weight removed\n",
      "solution 1: 2.1362830044410597\n",
      "solution 2: 1.3823007675795091\n",
      "solution 3: 1.2566370614359172\n"
     ]
    }
   ],
   "source": [
    "eps = 1\n",
    "#weights = weights / (max(weights) + eps) * 2 * np.pi\n",
    "weights = weights / np.sum(weights) * np.pi\n",
    "\n",
    "print('normalized weights: {}'.format(weights))\n",
    "\n",
    "## solutions\n",
    "print('solution 1: {}'.format(weights[0] + weights[3] + weights[4] + weights[2]))\n",
    "print('solution 2: {}'.format(weights[0] + weights[5] + weights[4] + weights[1]))\n",
    "print('solution 3: {}'.format(weights[1] + weights[3] + weights[5] + weights[2]))\n",
    "\n",
    "print('solutions after max weight removed')\n",
    "print('solution 1: {}'.format(weights[0] + weights[3] + weights[4] + weights[2]))\n",
    "print('solution 2: {}'.format(weights[0]  + weights[4] + weights[1]))\n",
    "print('solution 3: {}'.format(weights[1] + weights[3] + weights[2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3db9d140",
   "metadata": {},
   "source": [
    "To construct $U$, we need to compute the tensor product of diagonal matrices $U_j$, where $ 1 \\leq j \\leq N$. $N$ denotes the number of cities in total.\n",
    "\n",
    "$$\\Large\\left[U_j \\right]_{kk} = \\frac{1}{\\sqrt{N}}e^{i\\gamma_{jk}}$$\n",
    "\n",
    "\n",
    "$$\\Large U = \\bigotimes_j^N U_j$$\n",
    "\n",
    "\n",
    "for our contstraint test, we simply need a tensor product of 4 matrices:\n",
    "\n",
    "$$\\Large U = U_1 \\otimes U_2 \\otimes U_3 \\otimes U_4$$\n",
    "\n",
    "lets have a closer look at the matrix $U_1$\n",
    "$$ \\Large\n",
    "\\begin{bmatrix}\n",
    "  1 & 0 & 0 & 0 \\\\\n",
    "  0 & e^{i\\gamma_{12}} & 0 & 0 \\\\\n",
    "  0 & 0 & e^{i\\gamma_{13}} & 0 \\\\\n",
    "  0 & 0 & 0 & e^{i\\gamma_{14}} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "constructing the large matrix U is straight forward. I am a little confused on how to construct a controlled-U operation such that we have the appropriate phase kickback. The 2018 paper does a decomposition, and claims that a $CU$ matrix can simply be achieved by the tensor product of the smaller $CU_J$ matrices. Need to confirm how this works."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d1293ea",
   "metadata": {},
   "source": [
    "A control gate can simply be constructed:\n",
    "\n",
    "$$ \\Large\n",
    "\\begin{bmatrix}\n",
    "  \\mathbb{1} & 0 \\\\\n",
    "  0 & U \\\\\n",
    "\\end{bmatrix}\n",
    "$$ \n",
    "\n",
    "\n",
    "#### January 16th clarification:\n",
    "\n",
    "to construct a control gate, we need an equal amount of diagonal elements for the identity matrix above as we have in the diagonal of U, implying we double the size of U and store 1s in the first half of the diagonal "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "127dcaa1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://github.com/qiskit-community/qiskit-textbook/blob/main/content/ch-algorithms/quantum-phase-estimation.ipynb\n",
    "# https://www.youtube.com/watch?v=zFgyMGklANM (how to create a custom gate)  \n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, Aer, transpile, assemble\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit.circuit.library import QFT\n",
    "\n",
    "# for creating custom gates\n",
    "from qiskit import quantum_info as qi\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4ef6be1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "## create and set up quantum circuits\n",
    "\n",
    "# initialization\n",
    "draw = 0\n",
    "\n",
    "n = 5 # estimation qubits\n",
    "m = 8 # eigenvalue qubits\n",
    "\n",
    "qpe = QuantumCircuit(n + m, n)\n",
    "\n",
    "# Apply H-Gates to counting qubits:\n",
    "for qubit in range(n):\n",
    "    qpe.h(qubit)\n",
    "\n",
    "# Prepare our eigenstate |psi>:\n",
    "eig = '11000110'\n",
    "\n",
    "for ind, val in enumerate(eig):\n",
    "    if(int(val)):\n",
    "        qpe.x(ind + n)\n",
    "    \n",
    "if draw:\n",
    "    qpe.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6d744c8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating our CU matrix (example just as the identity to draw the rest of the circuit)\n",
    "#CU = qi.Operator(np.diag(np.ones(2**(m+1))))\n",
    "#CU"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96ebd62f",
   "metadata": {},
   "source": [
    "## recreating CU matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "142d8da9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True False False ... False False False]\n",
      " [False  True False ... False False False]\n",
      " [False False  True ... False False False]\n",
      " ...\n",
      " [False False False ...  True False False]\n",
      " [False False False ... False  True False]\n",
      " [False False False ... False False  True]]\n",
      "(512, 512)\n"
     ]
    }
   ],
   "source": [
    "### need the four values for each sub distance matrix:\n",
    "\n",
    "U111 = 1\n",
    "U122 = np.exp(1j * weights[0])\n",
    "U133 = np.exp(1j * weights[1])\n",
    "U144 = np.exp(1j * weights[2])\n",
    "U1 = np.diag([U111, U122, U133, U144])\n",
    "\n",
    "U211 = np.exp(1j * weights[0])\n",
    "U222 = 1\n",
    "U233 = np.exp(1j * weights[3])\n",
    "U244 = np.exp(1j * weights[4])\n",
    "U2 = np.diag([U211, U222, U233, U244])\n",
    "\n",
    "U311 = np.exp(1j * weights[1])\n",
    "U322 = np.exp(1j * weights[3])\n",
    "U333 = 1\n",
    "U344 = np.exp(1j * weights[4])\n",
    "U3 = np.diag([U311, U322, U333, U344])\n",
    "\n",
    "U411 = np.exp(1j * weights[2])\n",
    "U422 = np.exp(1j * weights[5])\n",
    "U433 = np.exp(1j * weights[4])\n",
    "U444 = 1\n",
    "U4 = np.diag([U411, U422, U433, U444])\n",
    "\n",
    "## tensor product all of them\n",
    "## Add ones to the diagonal (first half)\n",
    "\n",
    "U = np.kron(np.kron(np.kron(U1,U2),U3),U4)\n",
    "print(U != 0)# confirming only the diagonal is being used.\n",
    "\n",
    "##CUdiag = np.append(np.ones(2**m), np.diag(U))\n",
    "CUdiag = np.append(np.diag(U), np.ones(2**m))\n",
    "\n",
    "\n",
    "CU = qi.Operator(np.diag(CUdiag))\n",
    "print(np.shape(CU))  ### needs to work on m + 1 qubits (2^(m+1) x 2^(m+1) matrix)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b19b235c",
   "metadata": {},
   "source": [
    "## Confirming where the solutions are:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e8f7f364",
   "metadata": {},
   "outputs": [],
   "source": [
    "U_angles = np.around(np.diag(np.angle(U)), 4)\n",
    "#solutions = [4.27,4.27,4.02]\n",
    "#U_angles = U_angles[U_angles > 2] ## range here is -pi to pi. Changing it to 0 to 2pi\n",
    "#U_angles = U_angles[U_angles < 4.5]\n",
    "#np.where(U_angles==1.9448)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "24977a80",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([198]), array([0]))\n",
      "[2.136283]\n",
      "(array([454]), array([0]))\n",
      "[2.136283]\n"
     ]
    }
   ],
   "source": [
    "#manual multiplication for confirmation\n",
    "eigstate = np.zeros(256)\n",
    "eigstate[198] = 1   # where the solution is |111000110>\n",
    "eigstate = eigstate.reshape(-1,1) # changing to a column vector\n",
    "product = np.matmul(U,eigstate)\n",
    "print(np.where(np.angle(product) != 0)) ## confirming only same index has a nonzero value\n",
    "print(np.angle(product)[198])\n",
    "\n",
    "\n",
    "### how would this work with CU\n",
    "\n",
    "CU_check = np.append(np.ones(2**m), np.diag(U))\n",
    "CU_check = np.diag(CU_check)\n",
    "\n",
    "eigstate = np.zeros(512)\n",
    "eigstate[454] = 1   # where the solution is |1>|111000110>\n",
    "eigstate = eigstate.reshape(-1,1) # changing to a column vector\n",
    "product = np.matmul(CU_check,eigstate)\n",
    "print(np.where(np.angle(product) != 0)) ## confirming only same index has a nonzero value\n",
    "print(np.angle(product)[454])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c89bd9f",
   "metadata": {},
   "source": [
    "### *we were able to retrieve the eigenvalue correctly, the algorithm seems to be failing. Possibly the construction of the CU matrix?* ###Jan 28th"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7100318d",
   "metadata": {},
   "source": [
    "## Creating CU Prime matrix (removing max edge weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9798bc51",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True False False ... False False False]\n",
      " [False  True False ... False False False]\n",
      " [False False  True ... False False False]\n",
      " ...\n",
      " [False False False ...  True False False]\n",
      " [False False False ... False  True False]\n",
      " [False False False ... False False  True]]\n",
      "(512, 512)\n"
     ]
    }
   ],
   "source": [
    "### need the four values for each sub distance matrix:\n",
    "\n",
    "max_index = np.where(weights == np.max(weights))[0][0] ## largest weight in weights index\n",
    "weights[max_index] = 0                                 ## setting the largest weight to zero\n",
    "\n",
    "U111 = 1\n",
    "U122 = np.exp(1j * weights[0])\n",
    "U133 = np.exp(1j * weights[1])\n",
    "U144 = np.exp(1j * weights[2])\n",
    "U1 = np.diag([U111, U122, U133, U144])\n",
    "\n",
    "U211 = np.exp(1j * weights[0])\n",
    "U222 = 1\n",
    "U233 = np.exp(1j * weights[3])\n",
    "U244 = np.exp(1j * weights[4])\n",
    "U2 = np.diag([U211, U222, U233, U244])\n",
    "\n",
    "U311 = np.exp(1j * weights[1])\n",
    "U322 = np.exp(1j * weights[3])\n",
    "U333 = 1\n",
    "U344 = np.exp(1j * weights[4])\n",
    "U3 = np.diag([U311, U322, U333, U344])\n",
    "\n",
    "U411 = np.exp(1j * weights[2])\n",
    "U422 = np.exp(1j * weights[5])\n",
    "U433 = np.exp(1j * weights[4])\n",
    "U444 = 1\n",
    "U4 = np.diag([U411, U422, U433, U444])\n",
    "\n",
    "## tensor product all of them\n",
    "## Add ones to the diagonal (first half)\n",
    "\n",
    "Up = np.kron(np.kron(np.kron(U1,U2),U3),U4)\n",
    "print(U != 0)# confirming only the diagonal is being used.\n",
    "\n",
    "CUdiag = np.append(np.ones(2**m), np.diag(Up))\n",
    "\n",
    "CUP = qi.Operator(np.diag(CUdiag))\n",
    "print(np.shape(CUP))  ### needs to work on m + 1 qubits (2^(m+1) x 2^(m+1) matrix)\n",
    "#CUP_check = UnitaryGate(np.diag(CUdiag), label='cupcheck')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "91a89d78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([], dtype=int64),)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Up_angles = np.around(np.diag(np.angle(U)), 4)\n",
    "#solutions = [4.27,4.27,4.02]\n",
    "#U_angles = U_angles[U_angles > 2] ## range here is -pi to pi. Changing it to 0 to 2pi\n",
    "#U_angles = U_angles[U_angles < 4.5]\n",
    "np.where(Up_angles==1.9448)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8e4a73f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "eig_qubits = np.arange(0,m) + n\n",
    "\n",
    "repetitions = 1\n",
    "for counting_qubit in range(n):\n",
    "    applied_qubits = np.append([counting_qubit], [eig_qubits])\n",
    "    for i in range(repetitions):\n",
    "        qpe.unitary(CU, list(applied_qubits), label = \"CU\"); # This is CU\n",
    "    repetitions *= 2\n",
    "    \n",
    "draw=1\n",
    "if draw:\n",
    "    qpe.draw()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6e039f42",
   "metadata": {},
   "outputs": [],
   "source": [
    "def qft_dagger(qc, n):\n",
    "    \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n",
    "    # Don't forget the Swaps!\n",
    "    for qubit in range(n//2):\n",
    "        qc.swap(qubit, n-qubit-1)\n",
    "    for j in range(n):\n",
    "        for m in range(j):\n",
    "            qc.cp(-math.pi/float(2**(j-m)), m, j)\n",
    "        qc.h(j)\n",
    "\n",
    "        \n",
    "# def qft_dagger(qc, n, k):\n",
    "#     \"\"\"n-qubit QFTdagger the first n qubits in circ\n",
    "#         rewriting to account for a bit shift\n",
    "#     \"\"\"\n",
    "#     # Don't forget the Swaps!\n",
    "#     for qubit in range(n//2):\n",
    "#         qc.swap(k + qubit, k + n-qubit-1)\n",
    "#     for j in range(n):\n",
    "#         for m in range(j):\n",
    "#             qc.cp(-math.pi/float(2**(j-m)), m, j)\n",
    "#         qc.h(j)\n",
    "        \n",
    "\n",
    "qpe.barrier()\n",
    "# Apply inverse QFT\n",
    "qft_dagger(qpe, n)\n",
    "# Measure\n",
    "qpe.barrier()\n",
    "for i in range(n):\n",
    "    qpe.measure(i,i) \n",
    "    \n",
    "if draw:\n",
    "    qpe.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9e9242ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/raveel/miniconda3/lib/python3.10/site-packages/qiskit/visualization/circuit/matplotlib.py:266: FutureWarning: The default matplotlib drawer scheme will be changed to \"iqp\" in a following release. To silence this warning, specify the current default explicitly as style=\"clifford\", or the new default as style=\"iqp\".\n",
      "  self._style, def_font_ratio = load_style(self._style)\n"
     ]
    }
   ],
   "source": [
    "if draw:\n",
    "    qpe.draw(output = 'mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "46e8ae4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#qpe.draw(output = 'latex') did not work\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "d5b3bc63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                ┌───┐\n",
       "       phase_0: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_1: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_2: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_3: ┤ H ├\n",
       "                ├───┤\n",
       "  eigenstate_0: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_1: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_2: ─────\n",
       "                     \n",
       "  eigenstate_3: ─────\n",
       "                     \n",
       "  eigenstate_4: ─────\n",
       "                ┌───┐\n",
       "  eigenstate_5: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_6: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_7: ─────\n",
       "                ┌───┐\n",
       "   phase two_0: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_1: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_2: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_3: ┤ H ├\n",
       "                ├───┤\n",
       "eigstate two_0: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_1: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_2: ─────\n",
       "                     \n",
       "eigstate two_3: ─────\n",
       "                     \n",
       "eigstate two_4: ─────\n",
       "                ┌───┐\n",
       "eigstate two_5: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_6: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_7: ─────\n",
       "                     \n",
       "      output: 4/═════\n",
       "                     \n",
       "  output two: 4/═════\n",
       "                     </pre>"
      ],
      "text/plain": [
       "                ┌───┐\n",
       "       phase_0: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_1: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_2: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_3: ┤ H ├\n",
       "                ├───┤\n",
       "  eigenstate_0: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_1: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_2: ─────\n",
       "                     \n",
       "  eigenstate_3: ─────\n",
       "                     \n",
       "  eigenstate_4: ─────\n",
       "                ┌───┐\n",
       "  eigenstate_5: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_6: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_7: ─────\n",
       "                ┌───┐\n",
       "   phase two_0: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_1: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_2: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_3: ┤ H ├\n",
       "                ├───┤\n",
       "eigstate two_0: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_1: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_2: ─────\n",
       "                     \n",
       "eigstate two_3: ─────\n",
       "                     \n",
       "eigstate two_4: ─────\n",
       "                ┌───┐\n",
       "eigstate two_5: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_6: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_7: ─────\n",
       "                     \n",
       "      output: 4/═════\n",
       "                     \n",
       "  output two: 4/═════\n",
       "                     "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(n, name = 'phase')\n",
    "qr2 = QuantumRegister(m, name = 'eigenstate')\n",
    "cr = ClassicalRegister(n, 'output')\n",
    "\n",
    "qrp = QuantumRegister(n, name = 'phase two')\n",
    "qr2p = QuantumRegister(m, name = 'eigstate two')\n",
    "crp = ClassicalRegister(n, 'output two')\n",
    "\n",
    "qc = QuantumCircuit(qr,qr2,cr,qrp,qr2p,crp)\n",
    "\n",
    "\n",
    "# Apply H-Gates to counting qubits:\n",
    "for qubit in range(2*n):\n",
    "    if qubit < n:\n",
    "        qc.h(qubit)\n",
    "    else:\n",
    "        qc.h(qubit + m)\n",
    "\n",
    "# Prepare our eigenstate |psi>: state 198\n",
    "eig = '11000110'\n",
    "\n",
    "eigstatelist = ['11000110', '01101100', '10001101',\n",
    "                '01110010', '11100001', '10110100']\n",
    "\n",
    "for ind, val in enumerate(eig):\n",
    "    if(int(val)):\n",
    "        qc.x(ind + n)\n",
    "        qc.x(ind + 2*n + m)\n",
    "\n",
    "draw = 1        \n",
    "if draw:    \n",
    "    qc.draw()\n",
    "    \n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "2fc64e90",
   "metadata": {},
   "outputs": [],
   "source": [
    "eig_qubits = np.arange(0,m) + n\n",
    "eig_qubits2 = np.arange(0,m) + 2*n + m\n",
    "\n",
    "repetitions = 1\n",
    "for counting_qubit in range(n):\n",
    "    applied_qubits = np.append([counting_qubit], [eig_qubits])\n",
    "    applied_qubits2 = np.append([counting_qubit + m + n], [eig_qubits2])\n",
    "    for i in range(repetitions):\n",
    "        qc.unitary(CU, list(applied_qubits), label = \"CU\"); # This is CU\n",
    "        qc.unitary(CUP, list(applied_qubits2), label = \"CU'\");\n",
    "    repetitions *= 2\n",
    "    \n",
    "qc.append(QFT(num_qubits = n, inverse = True), qr)\n",
    "qc.append(QFT(num_qubits = n, inverse = True), qrp)\n",
    "\n",
    "qc.measure(qr,cr)\n",
    "qc.measure(qrp,crp)\n",
    "if draw:\n",
    "    qc.draw()\n",
    "#qc.qubits good for printing out all qubits\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "895c347f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                ┌───┐┌─────┐                                                 »\n",
       "       phase_0: ┤ H ├┤0    ├─────────────────────────────────────────────────»\n",
       "                ├───┤│     │ ┌─────┐ ┌─────┐                                 »\n",
       "       phase_1: ┤ H ├┤     ├─┤0    ├─┤0    ├─────────────────────────────────»\n",
       "                ├───┤│     │ │     │ │     │ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "       phase_2: ┤ H ├┤     ├─┤     ├─┤     ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "       phase_3: ┤ H ├┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_0: ┤ X ├┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_1: ┤ X ├┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "                └───┘│  CU │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_2: ─────┤3    ├─┤3 CU ├─┤3 CU ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "                     │     │ │     │ │     │ │  CU │ │  CU │ │  CU │ │  CU │ »\n",
       "  eigenstate_3: ─────┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─»\n",
       "                     │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_4: ─────┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "                ┌───┐│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_5: ┤ X ├┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_6: ┤ X ├┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "                └───┘│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_7: ─────┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "                ┌───┐├─────┴┐└─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "   phase two_0: ┤ H ├┤0     ├────────────────────────────────────────────────»\n",
       "                ├───┤│      │┌──────┐┌──────┐                                »\n",
       "   phase two_1: ┤ H ├┤      ├┤0     ├┤0     ├────────────────────────────────»\n",
       "                ├───┤│      ││      ││      │┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "   phase two_2: ┤ H ├┤      ├┤      ├┤      ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "   phase two_3: ┤ H ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_0: ┤ X ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_1: ┤ X ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "                └───┘│  CU' ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_2: ─────┤3     ├┤3 CU' ├┤3 CU' ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "                     │      ││      ││      ││  CU' ││  CU' ││  CU' ││  CU' │»\n",
       "eigstate two_3: ─────┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├»\n",
       "                     │      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_4: ─────┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "                ┌───┐│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_5: ┤ X ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_6: ┤ X ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "                └───┘│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_7: ─────┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "                     └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "      output: 4/═════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "  output two: 4/═════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "«                                                                        »\n",
       "«       phase_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_1: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_2: ────────────────────────────────────────────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "«       phase_3: ┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_3: ┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "«                └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "«   phase two_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«   phase two_1: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«   phase two_2: ────────────────────────────────────────────────────────»\n",
       "«                ┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_3: ┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_3: ┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "«      output: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«  output two: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«                        ┌───────┐┌─┐         ┌─────┐                     »\n",
       "«       phase_0: ────────┤0      ├┤M├─────────┤0    ├─────────────────────»\n",
       "«                        │       │└╥┘┌─┐      │     │┌─────┐┌─────┐       »\n",
       "«       phase_1: ────────┤1      ├─╫─┤M├──────┤     ├┤0    ├┤0    ├───────»\n",
       "«                        │  IQFT │ ║ └╥┘┌─┐   │     ││     ││     │┌─────┐»\n",
       "«       phase_2: ────────┤2      ├─╫──╫─┤M├───┤     ├┤     ├┤     ├┤0    ├»\n",
       "«                ┌─────┐ │       │ ║  ║ └╥┘┌─┐│     ││     ││     ││     │»\n",
       "«       phase_3: ┤0    ├─┤3      ├─╫──╫──╫─┤M├┤     ├┤     ├┤     ├┤     ├»\n",
       "«                │     │ └───────┘ ║  ║  ║ └╥┘│     ││     ││     ││     │»\n",
       "«  eigenstate_0: ┤1    ├───────────╫──╫──╫──╫─┤1    ├┤1    ├┤1    ├┤1    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_1: ┤2    ├───────────╫──╫──╫──╫─┤2    ├┤2    ├┤2    ├┤2    ├»\n",
       "«                │     │           ║  ║  ║  ║ │  CU ││     ││     ││     │»\n",
       "«  eigenstate_2: ┤3    ├───────────╫──╫──╫──╫─┤3    ├┤3 CU ├┤3 CU ├┤3    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││  CU │»\n",
       "«  eigenstate_3: ┤4 CU ├───────────╫──╫──╫──╫─┤4    ├┤4    ├┤4    ├┤4    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_4: ┤5    ├───────────╫──╫──╫──╫─┤5    ├┤5    ├┤5    ├┤5    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_5: ┤6    ├───────────╫──╫──╫──╫─┤6    ├┤6    ├┤6    ├┤6    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_6: ┤7    ├───────────╫──╫──╫──╫─┤7    ├┤7    ├┤7    ├┤7    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_7: ┤8    ├───────────╫──╫──╫──╫─┤8    ├┤8    ├┤8    ├┤8    ├»\n",
       "«                └─────┘ ┌───────┐ ║  ║  ║  ║ └─┬─┬─┘└─────┘└─────┘└─────┘»\n",
       "«   phase two_0: ────────┤0      ├─╫──╫──╫──╫───┤M├───────────────────────»\n",
       "«                        │       │ ║  ║  ║  ║   └╥┘    ┌─┐                »\n",
       "«   phase two_1: ────────┤1      ├─╫──╫──╫──╫────╫─────┤M├────────────────»\n",
       "«                        │  IQFT │ ║  ║  ║  ║    ║     └╥┘    ┌─┐         »\n",
       "«   phase two_2: ────────┤2      ├─╫──╫──╫──╫────╫──────╫─────┤M├─────────»\n",
       "«                ┌──────┐│       │ ║  ║  ║  ║    ║      ║     └╥┘    ┌─┐  »\n",
       "«   phase two_3: ┤0     ├┤3      ├─╫──╫──╫──╫────╫──────╫──────╫─────┤M├──»\n",
       "«                │      │└───────┘ ║  ║  ║  ║    ║      ║      ║     └╥┘  »\n",
       "«eigstate two_0: ┤1     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_1: ┤2     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_2: ┤3     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_3: ┤4 CU' ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_4: ┤5     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_5: ┤6     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_6: ┤7     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_7: ┤8     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                └──────┘          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«      output: 4/══════════════════╩══╩══╩══╩════╬══════╬══════╬══════╬═══»\n",
       "«                                  0  1  2  3    ║      ║      ║      ║   »\n",
       "«  output two: 4/════════════════════════════════╩══════╩══════╩══════╩═══»\n",
       "«                                                0      1      2      3   »\n",
       "«                                                                        »\n",
       "«       phase_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_1: ────────────────────────────────────────────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐                                 »\n",
       "«       phase_2: ┤0    ├─┤0    ├─┤0    ├─────────────────────────────────»\n",
       "«                │     │ │     │ │     │ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "«       phase_3: ┤     ├─┤     ├─┤     ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "«                │  CU │ │  CU │ │  CU │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_3: ┤4    ├─┤4    ├─┤4    ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "«                ├─────┴┐└─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "«   phase two_0: ┤0     ├────────────────────────────────────────────────»\n",
       "«                │      │┌──────┐┌──────┐                                »\n",
       "«   phase two_1: ┤      ├┤0     ├┤0     ├────────────────────────────────»\n",
       "«                │      ││      ││      │┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_2: ┤      ├┤      ├┤      ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«   phase two_3: ┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "«                │  CU' ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3 CU' ├┤3 CU' ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││  CU' ││  CU' ││  CU' ││  CU' │»\n",
       "«eigstate two_3: ┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "«      output: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«  output two: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«                                                ┌───────┐                »\n",
       "«       phase_0: ────────────────────────────────┤0      ├────────────────»\n",
       "«                                                │       │                »\n",
       "«       phase_1: ────────────────────────────────┤1      ├────────────────»\n",
       "«                                                │  IQFT │                »\n",
       "«       phase_2: ────────────────────────────────┤2      ├────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │       │                »\n",
       "«       phase_3: ┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤3      ├────────────────»\n",
       "«                │     │ │     │ │     │ │     │ └───────┘                »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_3: ┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├──────────────────────────»\n",
       "«                └─────┘ └─────┘ └─────┘ └─────┘                          »\n",
       "«   phase two_0: ─────────────────────────────────────────────────────────»\n",
       "«                                                                         »\n",
       "«   phase two_1: ─────────────────────────────────────────────────────────»\n",
       "«                                                                         »\n",
       "«   phase two_2: ─────────────────────────────────────────────────────────»\n",
       "«                ┌──────┐┌──────┐┌──────┐┌──────┐ ┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_3: ┤0     ├┤0     ├┤0     ├┤0     ├─┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├─┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├─┤2     ├┤2     ├┤2     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3     ├┤3     ├┤3     ├─┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_3: ┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├─┤4 CU' ├┤4 CU' ├┤4 CU' ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├─┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├─┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├─┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├─┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘ └──────┘└──────┘└──────┘»\n",
       "«      output: 4/═════════════════════════════════════════════════════════»\n",
       "«                                                                         »\n",
       "«  output two: 4/═════════════════════════════════════════════════════════»\n",
       "«                                                                         »\n",
       "«                                 ┌─┐                     \n",
       "«       phase_0: ─────────────────┤M├─────────────────────\n",
       "«                                 └╥┘┌─┐                  \n",
       "«       phase_1: ──────────────────╫─┤M├──────────────────\n",
       "«                                  ║ └╥┘┌─┐               \n",
       "«       phase_2: ──────────────────╫──╫─┤M├───────────────\n",
       "«                                  ║  ║ └╥┘┌─┐            \n",
       "«       phase_3: ──────────────────╫──╫──╫─┤M├────────────\n",
       "«                                  ║  ║  ║ └╥┘            \n",
       "«  eigenstate_0: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_1: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_2: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_3: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_4: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_5: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_6: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_7: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                        ┌───────┐ ║  ║  ║  ║ ┌─┐         \n",
       "«   phase two_0: ────────┤0      ├─╫──╫──╫──╫─┤M├─────────\n",
       "«                        │       │ ║  ║  ║  ║ └╥┘┌─┐      \n",
       "«   phase two_1: ────────┤1      ├─╫──╫──╫──╫──╫─┤M├──────\n",
       "«                        │  IQFT │ ║  ║  ║  ║  ║ └╥┘┌─┐   \n",
       "«   phase two_2: ────────┤2      ├─╫──╫──╫──╫──╫──╫─┤M├───\n",
       "«                ┌──────┐│       │ ║  ║  ║  ║  ║  ║ └╥┘┌─┐\n",
       "«   phase two_3: ┤0     ├┤3      ├─╫──╫──╫──╫──╫──╫──╫─┤M├\n",
       "«                │      │└───────┘ ║  ║  ║  ║  ║  ║  ║ └╥┘\n",
       "«eigstate two_0: ┤1     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_1: ┤2     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_2: ┤3     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_3: ┤4 CU' ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_4: ┤5     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_5: ┤6     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_6: ┤7     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_7: ┤8     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                └──────┘          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«      output: 4/══════════════════╩══╩══╩══╩══╬══╬══╬══╬═\n",
       "«                                  0  1  2  3  ║  ║  ║  ║ \n",
       "«  output two: 4/══════════════════════════════╩══╩══╩══╩═\n",
       "«                                              0  1  2  3 </pre>"
      ],
      "text/plain": [
       "                ┌───┐┌─────┐                                                 »\n",
       "       phase_0: ┤ H ├┤0    ├─────────────────────────────────────────────────»\n",
       "                ├───┤│     │ ┌─────┐ ┌─────┐                                 »\n",
       "       phase_1: ┤ H ├┤     ├─┤0    ├─┤0    ├─────────────────────────────────»\n",
       "                ├───┤│     │ │     │ │     │ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "       phase_2: ┤ H ├┤     ├─┤     ├─┤     ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "       phase_3: ┤ H ├┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─┤     ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_0: ┤ X ├┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_1: ┤ X ├┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "                └───┘│  CU │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_2: ─────┤3    ├─┤3 CU ├─┤3 CU ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "                     │     │ │     │ │     │ │  CU │ │  CU │ │  CU │ │  CU │ »\n",
       "  eigenstate_3: ─────┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─┤4    ├─»\n",
       "                     │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_4: ─────┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "                ┌───┐│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_5: ┤ X ├┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "                ├───┤│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_6: ┤ X ├┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "                └───┘│     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "  eigenstate_7: ─────┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "                ┌───┐├─────┴┐└─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "   phase two_0: ┤ H ├┤0     ├────────────────────────────────────────────────»\n",
       "                ├───┤│      │┌──────┐┌──────┐                                »\n",
       "   phase two_1: ┤ H ├┤      ├┤0     ├┤0     ├────────────────────────────────»\n",
       "                ├───┤│      ││      ││      │┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "   phase two_2: ┤ H ├┤      ├┤      ├┤      ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "   phase two_3: ┤ H ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_0: ┤ X ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_1: ┤ X ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "                └───┘│  CU' ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_2: ─────┤3     ├┤3 CU' ├┤3 CU' ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "                     │      ││      ││      ││  CU' ││  CU' ││  CU' ││  CU' │»\n",
       "eigstate two_3: ─────┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├»\n",
       "                     │      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_4: ─────┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "                ┌───┐│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_5: ┤ X ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "                ├───┤│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_6: ┤ X ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "                └───┘│      ││      ││      ││      ││      ││      ││      │»\n",
       "eigstate two_7: ─────┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "                     └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "      output: 4/═════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "  output two: 4/═════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "«                                                                        »\n",
       "«       phase_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_1: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_2: ────────────────────────────────────────────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "«       phase_3: ┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_3: ┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "«                └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "«   phase two_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«   phase two_1: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«   phase two_2: ────────────────────────────────────────────────────────»\n",
       "«                ┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_3: ┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_3: ┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "«      output: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«  output two: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«                        ┌───────┐┌─┐         ┌─────┐                     »\n",
       "«       phase_0: ────────┤0      ├┤M├─────────┤0    ├─────────────────────»\n",
       "«                        │       │└╥┘┌─┐      │     │┌─────┐┌─────┐       »\n",
       "«       phase_1: ────────┤1      ├─╫─┤M├──────┤     ├┤0    ├┤0    ├───────»\n",
       "«                        │  IQFT │ ║ └╥┘┌─┐   │     ││     ││     │┌─────┐»\n",
       "«       phase_2: ────────┤2      ├─╫──╫─┤M├───┤     ├┤     ├┤     ├┤0    ├»\n",
       "«                ┌─────┐ │       │ ║  ║ └╥┘┌─┐│     ││     ││     ││     │»\n",
       "«       phase_3: ┤0    ├─┤3      ├─╫──╫──╫─┤M├┤     ├┤     ├┤     ├┤     ├»\n",
       "«                │     │ └───────┘ ║  ║  ║ └╥┘│     ││     ││     ││     │»\n",
       "«  eigenstate_0: ┤1    ├───────────╫──╫──╫──╫─┤1    ├┤1    ├┤1    ├┤1    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_1: ┤2    ├───────────╫──╫──╫──╫─┤2    ├┤2    ├┤2    ├┤2    ├»\n",
       "«                │     │           ║  ║  ║  ║ │  CU ││     ││     ││     │»\n",
       "«  eigenstate_2: ┤3    ├───────────╫──╫──╫──╫─┤3    ├┤3 CU ├┤3 CU ├┤3    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││  CU │»\n",
       "«  eigenstate_3: ┤4 CU ├───────────╫──╫──╫──╫─┤4    ├┤4    ├┤4    ├┤4    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_4: ┤5    ├───────────╫──╫──╫──╫─┤5    ├┤5    ├┤5    ├┤5    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_5: ┤6    ├───────────╫──╫──╫──╫─┤6    ├┤6    ├┤6    ├┤6    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_6: ┤7    ├───────────╫──╫──╫──╫─┤7    ├┤7    ├┤7    ├┤7    ├»\n",
       "«                │     │           ║  ║  ║  ║ │     ││     ││     ││     │»\n",
       "«  eigenstate_7: ┤8    ├───────────╫──╫──╫──╫─┤8    ├┤8    ├┤8    ├┤8    ├»\n",
       "«                └─────┘ ┌───────┐ ║  ║  ║  ║ └─┬─┬─┘└─────┘└─────┘└─────┘»\n",
       "«   phase two_0: ────────┤0      ├─╫──╫──╫──╫───┤M├───────────────────────»\n",
       "«                        │       │ ║  ║  ║  ║   └╥┘    ┌─┐                »\n",
       "«   phase two_1: ────────┤1      ├─╫──╫──╫──╫────╫─────┤M├────────────────»\n",
       "«                        │  IQFT │ ║  ║  ║  ║    ║     └╥┘    ┌─┐         »\n",
       "«   phase two_2: ────────┤2      ├─╫──╫──╫──╫────╫──────╫─────┤M├─────────»\n",
       "«                ┌──────┐│       │ ║  ║  ║  ║    ║      ║     └╥┘    ┌─┐  »\n",
       "«   phase two_3: ┤0     ├┤3      ├─╫──╫──╫──╫────╫──────╫──────╫─────┤M├──»\n",
       "«                │      │└───────┘ ║  ║  ║  ║    ║      ║      ║     └╥┘  »\n",
       "«eigstate two_0: ┤1     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_1: ┤2     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_2: ┤3     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_3: ┤4 CU' ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_4: ┤5     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_5: ┤6     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_6: ┤7     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                │      │          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«eigstate two_7: ┤8     ├──────────╫──╫──╫──╫────╫──────╫──────╫──────╫───»\n",
       "«                └──────┘          ║  ║  ║  ║    ║      ║      ║      ║   »\n",
       "«      output: 4/══════════════════╩══╩══╩══╩════╬══════╬══════╬══════╬═══»\n",
       "«                                  0  1  2  3    ║      ║      ║      ║   »\n",
       "«  output two: 4/════════════════════════════════╩══════╩══════╩══════╩═══»\n",
       "«                                                0      1      2      3   »\n",
       "«                                                                        »\n",
       "«       phase_0: ────────────────────────────────────────────────────────»\n",
       "«                                                                        »\n",
       "«       phase_1: ────────────────────────────────────────────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐                                 »\n",
       "«       phase_2: ┤0    ├─┤0    ├─┤0    ├─────────────────────────────────»\n",
       "«                │     │ │     │ │     │ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ »\n",
       "«       phase_3: ┤     ├─┤     ├─┤     ├─┤0    ├─┤0    ├─┤0    ├─┤0    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─┤1    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─┤2    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─┤3    ├─»\n",
       "«                │  CU │ │  CU │ │  CU │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_3: ┤4    ├─┤4    ├─┤4    ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─┤5    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─┤6    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─┤7    ├─»\n",
       "«                │     │ │     │ │     │ │     │ │     │ │     │ │     │ »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─┤8    ├─»\n",
       "«                ├─────┴┐└─────┘ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ »\n",
       "«   phase two_0: ┤0     ├────────────────────────────────────────────────»\n",
       "«                │      │┌──────┐┌──────┐                                »\n",
       "«   phase two_1: ┤      ├┤0     ├┤0     ├────────────────────────────────»\n",
       "«                │      ││      ││      │┌──────┐┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_2: ┤      ├┤      ├┤      ├┤0     ├┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«   phase two_3: ┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├┤      ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├┤2     ├»\n",
       "«                │  CU' ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3 CU' ├┤3 CU' ├┤3     ├┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││  CU' ││  CU' ││  CU' ││  CU' │»\n",
       "«eigstate two_3: ┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├┤4     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      ││      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘└──────┘└──────┘└──────┘»\n",
       "«      output: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«  output two: 4/════════════════════════════════════════════════════════»\n",
       "«                                                                        »\n",
       "«                                                ┌───────┐                »\n",
       "«       phase_0: ────────────────────────────────┤0      ├────────────────»\n",
       "«                                                │       │                »\n",
       "«       phase_1: ────────────────────────────────┤1      ├────────────────»\n",
       "«                                                │  IQFT │                »\n",
       "«       phase_2: ────────────────────────────────┤2      ├────────────────»\n",
       "«                ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │       │                »\n",
       "«       phase_3: ┤0    ├─┤0    ├─┤0    ├─┤0    ├─┤3      ├────────────────»\n",
       "«                │     │ │     │ │     │ │     │ └───────┘                »\n",
       "«  eigenstate_0: ┤1    ├─┤1    ├─┤1    ├─┤1    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_1: ┤2    ├─┤2    ├─┤2    ├─┤2    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_2: ┤3    ├─┤3    ├─┤3    ├─┤3    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_3: ┤4 CU ├─┤4 CU ├─┤4 CU ├─┤4 CU ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_4: ┤5    ├─┤5    ├─┤5    ├─┤5    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_5: ┤6    ├─┤6    ├─┤6    ├─┤6    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_6: ┤7    ├─┤7    ├─┤7    ├─┤7    ├──────────────────────────»\n",
       "«                │     │ │     │ │     │ │     │                          »\n",
       "«  eigenstate_7: ┤8    ├─┤8    ├─┤8    ├─┤8    ├──────────────────────────»\n",
       "«                └─────┘ └─────┘ └─────┘ └─────┘                          »\n",
       "«   phase two_0: ─────────────────────────────────────────────────────────»\n",
       "«                                                                         »\n",
       "«   phase two_1: ─────────────────────────────────────────────────────────»\n",
       "«                                                                         »\n",
       "«   phase two_2: ─────────────────────────────────────────────────────────»\n",
       "«                ┌──────┐┌──────┐┌──────┐┌──────┐ ┌──────┐┌──────┐┌──────┐»\n",
       "«   phase two_3: ┤0     ├┤0     ├┤0     ├┤0     ├─┤0     ├┤0     ├┤0     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_0: ┤1     ├┤1     ├┤1     ├┤1     ├─┤1     ├┤1     ├┤1     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_1: ┤2     ├┤2     ├┤2     ├┤2     ├─┤2     ├┤2     ├┤2     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_2: ┤3     ├┤3     ├┤3     ├┤3     ├─┤3     ├┤3     ├┤3     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_3: ┤4 CU' ├┤4 CU' ├┤4 CU' ├┤4 CU' ├─┤4 CU' ├┤4 CU' ├┤4 CU' ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_4: ┤5     ├┤5     ├┤5     ├┤5     ├─┤5     ├┤5     ├┤5     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_5: ┤6     ├┤6     ├┤6     ├┤6     ├─┤6     ├┤6     ├┤6     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_6: ┤7     ├┤7     ├┤7     ├┤7     ├─┤7     ├┤7     ├┤7     ├»\n",
       "«                │      ││      ││      ││      │ │      ││      ││      │»\n",
       "«eigstate two_7: ┤8     ├┤8     ├┤8     ├┤8     ├─┤8     ├┤8     ├┤8     ├»\n",
       "«                └──────┘└──────┘└──────┘└──────┘ └──────┘└──────┘└──────┘»\n",
       "«      output: 4/═════════════════════════════════════════════════════════»\n",
       "«                                                                         »\n",
       "«  output two: 4/═════════════════════════════════════════════════════════»\n",
       "«                                                                         »\n",
       "«                                 ┌─┐                     \n",
       "«       phase_0: ─────────────────┤M├─────────────────────\n",
       "«                                 └╥┘┌─┐                  \n",
       "«       phase_1: ──────────────────╫─┤M├──────────────────\n",
       "«                                  ║ └╥┘┌─┐               \n",
       "«       phase_2: ──────────────────╫──╫─┤M├───────────────\n",
       "«                                  ║  ║ └╥┘┌─┐            \n",
       "«       phase_3: ──────────────────╫──╫──╫─┤M├────────────\n",
       "«                                  ║  ║  ║ └╥┘            \n",
       "«  eigenstate_0: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_1: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_2: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_3: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_4: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_5: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_6: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                                  ║  ║  ║  ║             \n",
       "«  eigenstate_7: ──────────────────╫──╫──╫──╫─────────────\n",
       "«                        ┌───────┐ ║  ║  ║  ║ ┌─┐         \n",
       "«   phase two_0: ────────┤0      ├─╫──╫──╫──╫─┤M├─────────\n",
       "«                        │       │ ║  ║  ║  ║ └╥┘┌─┐      \n",
       "«   phase two_1: ────────┤1      ├─╫──╫──╫──╫──╫─┤M├──────\n",
       "«                        │  IQFT │ ║  ║  ║  ║  ║ └╥┘┌─┐   \n",
       "«   phase two_2: ────────┤2      ├─╫──╫──╫──╫──╫──╫─┤M├───\n",
       "«                ┌──────┐│       │ ║  ║  ║  ║  ║  ║ └╥┘┌─┐\n",
       "«   phase two_3: ┤0     ├┤3      ├─╫──╫──╫──╫──╫──╫──╫─┤M├\n",
       "«                │      │└───────┘ ║  ║  ║  ║  ║  ║  ║ └╥┘\n",
       "«eigstate two_0: ┤1     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_1: ┤2     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_2: ┤3     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_3: ┤4 CU' ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_4: ┤5     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_5: ┤6     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_6: ┤7     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                │      │          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«eigstate two_7: ┤8     ├──────────╫──╫──╫──╫──╫──╫──╫──╫─\n",
       "«                └──────┘          ║  ║  ║  ║  ║  ║  ║  ║ \n",
       "«      output: 4/══════════════════╩══╩══╩══╩══╬══╬══╬══╬═\n",
       "«                                  0  1  2  3  ║  ║  ║  ║ \n",
       "«  output two: 4/══════════════════════════════╩══╩══╩══╩═\n",
       "«                                              0  1  2  3 "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#draw = 1\n",
    "if draw:\n",
    "    draw = 0\n",
    "qc.draw() #'clifford"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b2989fea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Qiskit\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit import Aer, transpile\n",
    "from qiskit.tools.visualization import plot_histogram, plot_state_city\n",
    "import qiskit.quantum_info as qi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0d16e241",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " AerSimulator('aer_simulator'),\n",
       " QasmSimulator('qasm_simulator'),\n",
       " StatevectorSimulator('statevector_simulator'),\n",
       " UnitarySimulator('unitary_simulator')]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Aer.backends()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0face5e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('aer_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "50d76e90",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "qc = transpile(qc, simulator)  #### Doesnt like the inverse Quantum Fourier transform without decomposition\n",
    "\n",
    "if draw:\n",
    "    qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c1a0b17",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run and get counts\n",
    "result = simulator.run(qc).result()\n",
    "counts = result.get_counts(qc)\n",
    "plot_histogram(counts, title='check')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40738e51",
   "metadata": {},
   "source": [
    "## attempt 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "4137815e",
   "metadata": {},
   "outputs": [],
   "source": [
    "## https://www.youtube.com/watch?v=455pmYaZXKw&t=614s\n",
    "\n",
    "\n",
    "from qiskit.circuit import QuantumRegister, ClassicalRegister\n",
    "from qiskit.circuit.library import PhaseEstimation, RZGate\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "82f1573a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">             ┌──────┐\n",
       "eval_0: ─────┤0     ├\n",
       "             │      │\n",
       "eval_1: ─────┤1     ├\n",
       "             │      │\n",
       "eval_2: ─────┤2 QPE ├\n",
       "             │      │\n",
       "eval_3: ─────┤3     ├\n",
       "        ┌───┐│      │\n",
       "     q: ┤ X ├┤4     ├\n",
       "        └───┘└──────┘\n",
       "   c: 4/═════════════\n",
       "                     </pre>"
      ],
      "text/plain": [
       "             ┌──────┐\n",
       "eval_0: ─────┤0     ├\n",
       "             │      │\n",
       "eval_1: ─────┤1     ├\n",
       "             │      │\n",
       "eval_2: ─────┤2 QPE ├\n",
       "             │      │\n",
       "eval_3: ─────┤3     ├\n",
       "        ┌───┐│      │\n",
       "     q: ┤ X ├┤4     ├\n",
       "        └───┘└──────┘\n",
       "   c: 4/═════════════\n",
       "                     "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evr = QuantumRegister(4,'eval')\n",
    "qr = QuantumRegister(1, 'q')\n",
    "cr = ClassicalRegister(4, 'c')\n",
    "\n",
    "pe_circ = QuantumCircuit(evr, qr, cr)\n",
    "pe_circ.x(qr)\n",
    "\n",
    "#### estimating 0.42 #######\n",
    "pe_circ.append(PhaseEstimation(4, RZGate(2*np.pi*2*0.42)), range(5))\n",
    "pe_circ.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5845f865",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TS295ymGf2SNNRHS/hcFPLa3j6qQu2Wxw/DDknwK7DbyaQEA7sHg6uzKR2pGaeYBVv3zB9gM/cPT4QaxFBbTxb8e13YZxxzWP4e3p6+wSpQYpULkAjVCJOyu2wpFtkLYbzuaUbzN7QJvOEHEFNPZzTn0iteU/Wz/iu/++w1Wdb+P6S0ZgNnuw6+BaPvnPC2zY9RVv/vNnvDy8nV2m1JAGccrParUyd+5c+vfvT8uWLfHy8qJ9+/Y8++yz5OT88Qq/fPlyTCYT7dq1O+/2+vbti8lkIi4urtzy5ORkZs6cyU033US7du3w9fXFx8eHbt26MW3aNKxWq8PtufMIlTRs1nzY/hUc+m/FMAVQXAipu2DLl5CdWff1idSma2KGMv/5VGLv+ZIhV/+TW6/6By+MXMA91z/PoaO7+X7Lh84uUWqQ2weqpKQkevTowYMPPsj69esJCAggMjKSI0eOMH36dPr06UNeXh4AMTExQEkwys/Pd7i95cuXs379ejp27Mjo0aPLtU2ePJlnnnmGH3/8EbPZTJcuXQgMDGT37t3ExsZy9913V9jeyZMnSUlJwdfXl/bt29fw3os4j60Ydi2GMxkX7mvNhR1fQ0F2rZclUmcuDuuJr3ezCsv7dhsOQHLGr3VdktQitw5UJ06cYODAgcTHx/PAAw+QlpbG/v372bt3LwkJCXTq1IlffvmF119/HYCwsDCaNWuGzWZj3759FbZns9mIjY0FYOrUqZjN5nLtN9xwA9u3byc7O5sDBw6wZcsWkpOT2bp1K61bt2bRokXs2bOn3Dqlo1MxMTE0auS+P44iax752VkOv8Q9/Z4Ip9Mq39+aW3JqUMTdZZ5OBaBFk9ZOrkRqkvu+gwPjx48nKSmJ8ePHM3fuXAIDA8vaoqKieOuttwBYvHhx2fLo6GgAEhISKmxv3rx57N69m169ejFkyJAK7cOHD6dHjx6YTKZyy3v27MmAAQMAiI+PL9fWUOZP/bzwReLGtnL4Je4pdWfV1zn6a8mcKxF3VWwr5stVkzE3snDdJfc4uxypQW47KT0+Pp558+YRFBTE1KlTHfYpDTFpaX/8GR0TE8OmTZsqBCqr1crEiRMBmDFjhsPtnT17lu+++47169dz+PBhsrOzsdlsZfUAeHqWv6TJ0fyp1NRUpk2bxpYtW9i1axdWqxW73V7JPXdN0f0eJOqKYQ7bvpk2oI6rkdp2NgdOpVZ9vaKzcDwZAjvUeEkiLmHOd4+RcOQn7h/4CmGBFzu7HKlBbhuo5s+fj81mo7i4uGx06K9KJ4n7+v5x6eq5RqjmzJlDcnIygwcPpnfv3hW2tXr1akaNGkVKSsp564qMjCz3fWmg+vMIVVJSEgsXLuSyyy7D09OTTZs2nXebldGzZ08yMioxmeX/mD28uf3lRMOPW6p5UBTh0f1rbHuOdIiKorjQ8dw3V/La6K34N23D0aNHCQ29zNnl1IqwgE5MHrmyWus++Vgsa3d/XsMVidQ8T4s3cY9W/nXyk/9M5NtNb3PLFQ9y93WxtViZe4vqEIW1qHZe64OCgti2rXpzD9w2UK1ZswaAzMxMMjPPf/lQRERE2f9LJ6b/OVBlZ2czZcoUzGazw9GuzZs3c/PNN1NYWMjo0aMZMWIE0dHRtGjRAovFwr59++jUqRMWi4VOnTqVrVdYWMjevXtp1KgRXbt2LVt+7bXXcvToUQAmTZpUI4EqIyOj3EjchVi8fAw/Zl1LP5pO0dk8Z5dxQcXFxWX/VuVnUp9YiipOxK2s48cz3fa4iHtp7FH518nPfpjEl6tf5sbLRjH+b+/VYlXu72h6OgWFrvda77aBKjW15HxDcnIyF110UaXXKx2hOnjwIFarFU9PT2bNmkVmZiZjxowpF4hKxcbGYrVamTZtGhMmTKjQvmzZMgA6d+6Ml5dX2fKEhASsVisdOnTAx+ePX8zamJweFBRUpf7menhvlOA2wfVihKr0Ygaz2UxISIiTq6kdFs9iCosK8LA0rvQ6drsdk8nEWU657XER9+Jpqdzr5Gc/TOLzlS8x4NJ7eWLoBxXm2UrVtAkOrtURqupy20CVm5sLQEFBQZXW8/f3Jzg4mPT0dPbv309gYCCvvfYaPj4+TJo0qUL/4uJiNmzYAMCoUaMqtNtsNr788ksALrnkknJtdTkhvapDmGeLYMKCWiqmlhxITMSrHjyjN75XMseoTZs2ZcHfHcUvh6MVr+04J5PJhI8/rPr5a/R+I/VBsRXWvnn+Pp+v/F8+X/kS/Xv8nafu/Mitr+auK4kHEjG74Ccs1IO3n+oJDw/nxIkTrFq1iosvrtrEv5iYGNLT00lISOD9998nJyeH5557juDg4Ap9c3Nzy07hOApvr776Kjt27AAqBird0FPcWeglVQtUAKHdUJgSt/Htpnf47IcXCWweTo+o/qzZMa9ce4umrbm0gy7KcRduG6iGDh3Kzp07iY2NpXXr1gwdOrRce1JSEl9++SV9+vShb9++5dqio6NZsWIFS5Ys4auvviIgIMDhqTwAPz8/QkJCSEtLY8qUKbz77ruYzWasViuzZ89m4sSJWCwWioqKnDpCJVLXmrWBiy6HI1sq19//IgjtXqslidSp/SlbAfj91G/MWHBvhfaukX0UqNyI2waqJ554ghUrVrBx40aGDRuGv78/ERER2Gw2UlJSOH78OACHDh2qsG7pxPTSU3UvvPACfn7n/qCx559/nocffpi4uDi+/fZbwsLCSExMJC8vj3feeYexY8diMpkqBKfSQOXOI1Shnfsy/ovz3/LhQu1Sf7W/pmTEKXnz+fsFREL0IGhkPn8/kfrkmbs+4Zm7PnF2GVJH3DZQeXt7s3r1aubMmcP8+fNJSEhgz549BAQEEBERwciRIxk0aBBt27atsG5poAJo27YtY8eOPe9jjR07FovFwsyZM0lOTsZsNjNo0CAmTJhQduuGdu3alQtlqampHD9+nICAAE3AFbdlMpWEqsAOkLar5BSgreiP9oB2JaNSLSN0qk9E6je3DVQAHh4ejBs3jnHjxlVpvR49elT5RppjxoxhzJgxDtscbSs0NLTe36xTpLL8WoPfDdChH2yaC9Y88PSF7rc7uzIRkZrh1oGqPvv666+BP+6HVfp9REQEPXv2dFpdIkaYPcD0fxc5aURKRNyJApWLGjZsmMPv7733Xj755BMnVCQiIiLnokDlonQ6UEREpP7QHcZEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCB9lp845GmG6cOdXUXVeJqdXYGIiDRUClTikMkEXnp2iIhIDVix9RNmfTWKWf9YS7d2fZ1dTq3QW6aIiIgL2HVwHU+9148Hb5nJsL5PlS232Wys+uVzVm77lINHd1FwNofmTVvTLbIvw/o8RWRw1wrbGvlKBMdOHnH4OLdc+RApv+9j96H1larrqTs/5sbL7qvWPjUkClQiIiIuKt+ay6RPbueXxJV0DL+Cu/o9S1Mff1IzD/DD1o9Zs3Me425/l1uufLDCuq2ahXL/wKkVloe26kBuwWkGXv5A2bIzeVnM+e5xYtpew81XlN9Wl4heNb9jbkiBSkRExEXNXvgPfklcyd3XPcf9A6eUa7uz79M88/71vLloLMEB7bmk/XXl2n0bN6P/pSMr9TgZJ5KZ893jBPlHVnodKU9X+YmIiLigQ+m7Wf3LF3QMv4JRN71cob2ZbwCx98zDjp0Plk1wQoWOLd88l/tndOTmZ724d1p7Fm18Azt2h30Ppe9mQtwN3PqcL3e82JIZ/7qX07lZDHjaxIx/3Ve3hRukESoREREXtHHPQgAGXv4AJpPJYZ+IoC50Cr+KhCP/5feTvxHYIrysrdhezOncrArrNPMNqJ2CgUUb32DOd48T2aYbowa+wllrHv9eP4vmTQIr9E3NTOTxOddgt9sYcvU4WjYLYcu+5cR+cFOt1VebFKhERERcUHLGrwBEhfQ4b78OoZeScOS/HDq6u1ygSvl9H0MntarQf9kr+Xh6NK7ZYoGc/FN8/P3zhAd2Yvaj/6Wxpw8AN142ivtndqzQ/+P/PE9ewRlef/hHotv2BmBI70d5+YvhJKZur/H6apsClYiIiAvKO3sGKJkLdT4+jf3+r392ueVBLSJ4fOjcCv0tZs8aqrC87Qd+oKAwj9t6PVIWpgBaNQ/l+ktGsGxzXNmyYlsxW/Ytp2PY5WVhqtTQa59k/a6vaqXG2qRAJSIi4oJ8vEqCUm7B6fP2yysoCV4tmrYut7yxpy89OvSvneIcOHr8EABhgRVHo8Jbdy73/emcTAqsuYS2urhC3zAHy+oDTUoXERFxQRFB0QAkpv1y3n6l7SEt29d6TXJuClQiIiIu6JqYvwHwny0fYrc7vkruyLEEEo78l5i215SbP+UMbVpGAiVzt/7qt2MJ5b5v1qQVjT19Sc3cX6FvioNl9YEClYiIiAuKDO7K9T1Gsve3n/nsh0kV2s/knWDa/JGYTI34nxteqvsC/6JH1AC8PLz57r/vUGDNK1ueeSqVNTvnletrbmTmso4D2ZeyhV8PbyrX9vWGV+uk3pqmOVQiIiIuavwdcziZfYwvVv0vvySu5OroO0rulJ51gBVbPyY3/xTj73iP7u37ObtUmvq04N4bJxO39CnGv92LAZf+D2cL81j683uEBESRlLajXP9RN77M9v0reO7Dmxjc61ECmoWyed8yTudkApzzVhGuSoFKRETERXl7NeGVB75n1fbPWbn9U+aveYXs/JMAeFoa8874bbRtE+PkKv8wrM+TeHs2YeHG1/jo+1haNQ9jWJ+n8GncjFe/ur9c37DAi3l17Abilj7FNz/OxtPSmCs6DeKft7/D/0yNxMvD20l7UT0m+7lOzIpIrdj4HpzNAa8mcM0/nF1N3Wvo+y/uo9gKa990zmP/e90s4pY9zdXRd/DCyAWYze4zPnIgdTuPzO7J6IFTueu6Zyu09xsHtXTnB0M0h0pERKSeGdb3Ke67cTI//rqIGQvuxWazObukajlbmF/ue7vdzlfrZgDQo8MAZ5RUbe4TaUVERBqQEf1fYET/F2r9cc7knaCoyHrePl4e3vh6n/8GpI784/XudG93HW3bxFBgzeXnhCXsObyRvt2G0yH00uqW7BQKVCIiInJOL316B7sPrT9vnwGX3sszd31S5W336jyYn/YuYdUvn1NsKyLIvy333TiZ4f1c58OeK0uBShyy28Fa7OwqqsbTDPXsohAREZf30K2vkpN38rx9WjYLrta2xwyawZhBM6q1rqtRoBKHrMUwYYGzq6ia6cPBS89oEZEaVd9OvTmLJqWLiIiIGKRAJSIiImKQApWIiIiIQQpUIiIiIgYpUImIiIgYpEAlIiIiYpAClYiIiIhBClQiIiIiBilQiYiIiBikQCUiIiJikAKVC7Db7fj5+WEymcjKynJ2OSIiIlJFClQu4ODBg2RnZxMSEkJAQICzyxEREZEqUqByAbt27QKge/fuzi1EREREqkWBygXs3LkTgG7dujm3kFqQmrCO2SNNbF8265x9Zo808e2sQXVYlYjz2IrAml/yr7i3+Wum8r+fD+PvUyMZ8LSJka9EOLskqUUWZxcgGqEScXfFRXBsP6TuhDNH/1jerA2EXgKBHcCsV2O389H3z9HUx5+okB7k5p9ydjlSyxrECJXVamXu3Ln079+fli1b4uXlRfv27Xn22WfJyckp67d8+XJMJhPt2rU77/b69u2LyWQiLi6u3PLk5GRmzpzJTTfdRLt27fD19cXHx4du3boxbdo0rFarw+258wiVSEOXkwk/fQgJ35cPUwCnj0L8cvjpI8jR9Shu57NnD7LopeNMf3AlLf2CnV2O1DK3/5soKSmJIUOGEB8fj8ViITIyksDAQJKSkpg+fTorV65k48aN+Pj4EBMTA5QEo/z8fLy9vStsb/ny5axfv56OHTsyevTocm2TJ0/mo48+wtfXl+DgYLp06cLvv//O7t272b17N1u3bmXhwoXl1jl58iQpKSn4+vrSvn372jsQIlLnck/AtgVQVHD+fgVnYPsCuOwe8GlRN7VJ7WvTMtLZJUgdcusRqhMnTjBw4EDi4+N54IEHSEtLY//+/ezdu5eEhAQ6derEL7/8wuuvvw5AWFgYzZo1w2azsW/fvgrbs9lsxMbGAjB16lTMZnO59htuuIHt27eTnZ3NgQMH2LJlC8nJyWzdupXWrVuzaNEi9uzZU26d0tGpmJgYGjVy3x9HkTWP/Owsh18i7shuh/hlFw5TpQrzS0arRKR+ct93cGD8+PEkJSUxfvx45s6dS2BgYFlbVFQUb731FgCLFy8uWx4dHQ1AQkJChe3NmzeP3bt306tXL4YMGVKhffjw4fTo0QOTyVRuec+ePRkwYAAA8fHx5doayvypnxe+SNzYVg6/RNzRmQw4c6xq65w+WrKeiNQ/bnvKLz4+nnnz5hEUFMTUqVMd9ikNMWlpaWXLYmJi2LRpU4VAZbVamThxIgAzZsxwuL2zZ8/y3XffsX79eg4fPkx2djY2m62sHgBPT89y6ziaP/X1118zf/58tm3bRmZmJuHh4fztb38jNjaWJk2aVPIIuJbofg8SdcUwh23fTBtQx9WI1L7UXdVbL203+AXVbC0iUvvcNlDNnz8fm81GcXFx2ejQX5VOEvf19S1bdq4Rqjlz5pCcnMzgwYPp3bt3hW2tXr2aUaNGkZKSct66IiPLn1MvDVR/HqGaNWsW4eHhvPLKK4SGhrJz505eeukl1q9fz4YNG6p1arBnz55kZFT+T1+zhze3v5xY5cc5l+ZBUYRH96+x7TnSISqK4sL8Wn2MmvDa6K34N23D0aNHCQ29zNnl1LmGsv8T71pCu6BLqrze2u+3MOD+O2qhIqlpnhZv4h6tuddJqZyoDlFYi2rntT4oKIht27ZVa123DVRr1qwBIDMzk8zMzPP2jYiIKPt/6cT0Pweq7OxspkyZgtlsdjjatXnzZm6++WYKCwsZPXo0I0aMIDo6mhYtWmCxWNi3bx+dOnXCYrHQqVOnsvUKCwvZu3cvjRo1omvXrmXLlyxZQqtWf5wK69OnD61atWLEiBH8+OOPXHvttVU7GEBGRka5kbgLsXj5VPkxnC39aDpFZ/OcXcYFFRcXl/1blZ+Ju2gw+28zXbiPA3abyb2Pixtp7FH/XifdwdH0dAoKXe+13m0DVWpqKlByxd5FF11U6fVKR6gOHjyI1WrF09OTWbNmkZmZyZgxY8oFolKxsbFYrVamTZvGhAkTKrQvW7YMgM6dO+Pl5VW2PCEhAavVSocOHfDx+eMX889hqlTPnj0Bqv1CGxRUtXMIZo+KVzi6uuA2wfVihKr0Ygaz2UxISIiTq6l7DWX/C4qyq7Xe2eIctz4u7sTTUv9eJ91Bm+DgWh2hqi63DVS5ubkAFBRU8hKb/+Pv709wcDDp6ens37+fwMBAXnvtNXx8fJg0aVKF/sXFxWzYsAGAUaNGVWi32Wx8+eWXAFxySfnh/6pMSF+7di2Aw0BXGVUdwjxbBBMWVOuhnOZAYiJe9eAZvfE9OJsDbdq0KQv+DUlD2f/UnbBvVdXXG/5QP554232PizsptsLaN51dRcOTeCARs+eF+9W1evD2Uz3h4eGcOHGCVatWcfHFF1dp3ZiYGNLT00lISOD9998nJyeH5557juDgijdmy83NLTuF4Si8vfrqq+zYsQOoGKgqe0PPtLQ0Jk6cyE033eT2VwOKuIugzpC4oeRNt7IsXhDUsfZqkrq1cvvn/H7yCACncjMpKrby5aqXAQhscREDLv27M8uTGua2t00YOnQoUHI67uuvv67QnpSUxEsvvcS6desqtJWe9luyZAlxcXEEBAQ4PJUH4OfnVzY8P2XKlLJwZbVamTlzJhMnTsRiKcmt1RmhysnJYfDgwXh6evLRRx+dZ49FxJVYPKHtlVVbp+1VYPaonXqk7v1ny4d8smIin6yYyKmc38nJP1X2/X+2fOjs8qSGue0I1RNPPMGKFSvYuHEjw4YNw9/fn4iICGw2GykpKRw/fhyAQ4cOVVi3dGJ66am6F154AT8/v3M+1vPPP8/DDz9MXFwc3377LWFhYSQmJpKXl8c777zD2LFjMZlMFYJTaaA61whVfn4+t956K4cPH2bjxo20adOmysfB2UI792X8F/bz9rlQu0h9ddFlYM2F37ZXrm/4pbVfk9SdV8euc3YJUofcdoTK29ub1atXM3v2bK688kqKiorYs2cPx44dIyIigvHjx7Ny5Uratm1bYd3SQAXQtm1bxo4de97HGjt2LHFxcURFRXHixAnS09MZNGgQ27dv5/LLL6e4uJjIyMhyoSw1NZXjx48TEBDgcAJqYWEhQ4cOZdu2bXz//fd07tzZwNEQEWcwmSCqL3QeCL4tHfdpEgBdboaoPiX9RaR+Mtntdg0PuBibzcZdd93Fd999x/Lly7nuuuvqvIb6OCl9+nDq1aR0ryZwzT+cXU3da6j7b7fDqTTYuahkXpXZEy65A5qFKEjVV5qU7hz9xqFJ6VI5jzzyCP/+97959tln8fHx4eeffy5ra9euncPbKoiIazOZoEVoydyqYmvJv81DnV2ViNQUtz3lV599//33AEybNo2rrrqq3FfpPa1ERETEdWiEygUlJyc7uwQRERGpAo1QiYiIiBikQCUiIiJikAKViIiIiEEKVCIiIiIGKVCJiIiIGKRAJSIiImKQApWIiIiIQQpUIiIiIgYpUImIiIgYpEAlIiIiYpAClYiIiIhB+iw/ccjTDNOHO7uKqvE0O7sCERFpqBSoxCGTCbz07BAREakUnfITERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCCLswsQ12S3g7XY2VVUjacZTCZnVyEiIg2RApU4ZC2GCQucXUXVTB8OXnpGi4iIE+iUn4iIiIhBClQiIiIiBilQiYiIiBikQCUiIiJikAKViIiIiEEKVCIiIiIGKVCJiIiIGKRAJSIiImKQApWIiIiIQQpUIiIiIgYpUDmZ3W7Hz88Pk8lEVlaWs8sRERGRalCgcrKDBw+SnZ1NSEgIAQEBzi5HREREqkGBysl27doFQPfu3Z1biIiIiFSbApWT7dy5E4Bu3bo5t5BakpqwjtkjTWxfNuucfWaPNPHtrEF1WJWI1DW7HU6mwN4fYNdi2P0tJK6H3BPOrqz22Gw2Fm54nftndOTm2Mbc83IY7y15knxrrrNLk1pgcXYBDZ1GqETE3WUdhsR1kHu8YtuRreB/EXQcAD7N67qy2jVnyeMs/vFNekffztA+T/Lbsb0s/vFNDqbtYPqDq2jUSGMa7sTtf5pWq5W5c+fSv39/WrZsiZeXF+3bt+fZZ58lJyenrN/y5csxmUy0a9fuvNvr27cvJpOJuLi4csuTk5OZOXMmN910E+3atcPX1xcfHx+6devGtGnTsFqtDrfn7iNUItKwHU2AnYsch6lSJ47A1i8hJ7Pu6qptyRnxfLvpLa6OvoNJ9y7i5ivG8I/bXuMft77GzoNrWbfrX84uUWqYWweqpKQkevTowYMPPsj69esJCAggMjKSI0eOMH36dPr06UNeXh4AMTExQEkwys/Pd7i95cuXs379ejp27Mjo0aPLtU2ePJlnnnmGH3/8EbPZTJcuXQgMDGT37t3ExsZy9913V9jeyZMnSUlJwdfXl/bt29fw3ouIONfpo5DwH8B+4b6F+bBjERSdrfWy6sTanfOx2+3ccc1j5ZbffMUYGnv4sOqXL5xTmNQatw1UJ06cYODAgcTHx/PAAw+QlpbG/v372bt3LwkJCXTq1IlffvmF119/HYCwsDCaNWuGzWZj3759FbZns9mIjY0FYOrUqZjN5nLtN9xwA9u3byc7O5sDBw6wZcsWkpOT2bp1K61bt2bRokXs2bOn3Dqlo1MxMTFuP/RbZM0jPzvL4ZeIuKfkLWC3Vb7/2eySES13sD9lK41Mjbg4/PJyyz09GhMZ3J0DKVudVJnUFrd9Fx8/fjxJSUmMHz+euXPnEhgYWNYWFRXFW2+9BcDixYvLlkdHRwOQkFDxN3revHns3r2bXr16MWTIkArtw4cPp0ePHphMpnLLe/bsyYABAwCIj48v19aQ5k/9vPBF4sa2cvglIu6nIBuykqq+XurOkgns9d3xM+n4+QbgafGq0BbQLITTuVkUFjmeCiL1k1tOSo+Pj2fevHkEBQUxdepUh31KQ0xaWlrZspiYGDZt2lQhUFmtViZOnAjAjBkzHG7v7NmzfPfdd6xfv57Dhw+TnZ2NzWYrqwfA09Oz3DqO5k9t3LiRl156ifj4eE6cOEGrVq3o3bs3kyZNolOnTpU8Aq4nut+DRF0xzGHbN9MG1HE1IlLbThypXjDKPV4yUtXYr+ZrqktnrXl4OAhTAJ6WxiV9CvPwsHg67CP1j1sGqvnz52Oz2SguLi4bHfqr0knivr6+ZcvONUI1Z84ckpOTGTx4ML17966wrdWrVzNq1ChSUlLOW1dkZGS570sD1Z9HqE6ePElMTAwPPfQQgYGBpKamMnXqVK666ip+/fVXQkNDz/sY59KzZ08yMjIq3d/s4c3tLydW67EcaR4URXh0/xrbniMdoqIoLnQ8/82VvDZ6K/5N23D06FFCQy9zdjl1TvvfMPZ/QPfRjOj7UrXW7XvtAFKz9tZwRTXP0+JN3KOOXye9PH3Iz/ndYZu1qKCkj4dPrdXmzqI6RGEtqp3X+qCgILZt21atdd0yUK1ZswaAzMxMMjPPf9lIRERE2f9LJ6b/OVBlZ2czZcoUzGazw9GuzZs3c/PNN1NYWMjo0aMZMWIE0dHRtGjRAovFwr59++jUqRMWi6XcCFNhYSF79+6lUaNGdO3atWz5bbfdxm233VbuMS677DIuvvhiFi5cyPjx4yt/IP4kIyOj3GjchVi86t8vevrRdIrO5jm7jAsqLi4u+7cqPxN3of1vGPt/LKT6+3Yk5SAZJ1z/2DQ+TyBq6RfMb8cSsBadrXDaL+t0Gs18AzQ6VU1H09MpKHS913q3DFSpqalAyRV7F110UaXXKx2hOnjwIFarFU9PT2bNmkVmZiZjxoxxeMotNjYWq9XKtGnTmDBhQoX2ZcuWAdC5c2e8vP74pUpISMBqtdKhQwd8fM4fXlq2bAmAxVL9H1dQUFCV+ps9vKv9WM4S3Ca4XoxQlV7QYDabCQkJcXI1dU/73zD2/8TZI0DJ55X+dW7p+ZzKPYanr40Qb9c/Np6Wc79OXhx2GdsP/MD+37YQE3lN2XJrYQGH0ncSE3ltXZToltoEB9fqCFV1uWWgys0tuQttQUFBldbz9/cnODiY9PR09u/fT2BgIK+99ho+Pj5MmjSpQv/i4mI2bNgAwKhRoyq022w2vvzySwAuueSScm0XmpBeXFyMzWbjyJEjxMbGEhQUxJ133lml/fmzqg5hni2CCQuq/XBOcSAxEa968Ize+B6czYE2bdqUhf+GRPvfcPZ/6zw4nV75MAVwyfWtOfJicu0UVMOKrbD2TcdtfbsNZ/6aV1i08Y1ygWr55rkUFOZx3SUj6qhK95N4IBGzCw7uueVVfuHh4QCsWrWqyuv++bTf5MmTycnJ4bHHHiM4OLhC39zc3LLhe0fh7dVXX2XHjh1AxUB1oRt69unTB09PT6Kioti5cydr1qyhVStdESci9Uf4pVXr38gCIV0v3K8+aNsmhtt6PcKPvy5i0qd3sHzzB7y35EneW/IEXSP7cN0l9zi7RKlhbhmohg4dCpScjvv6668rtCclJfHSSy+xbt26Cm2lp/2WLFlCXFwcAQEBDk/lAfj5+ZUN2U+ZMqUsXFmtVmbOnMnEiRPLTtNVdYTqww8/5Oeff2b+/Pn4+flxww038Ntvv11gz0VEXEfri6sQqkwQfUv9v7rvz8be9gYPDprFkWPxvP3NI6zb+S+G9P4nL9+/1O3vPdgQmex2d7jjR3n5+fnceOONbNy4ESg5lRcREYHNZiMlJYXjx0s+A+HQoUO0bdu23Lqffvop9913X9n3b7zxxnkngs+ZM4eHH34YgNatWxMWFkZiYiJ5eXm88847jB07FpvNxqlTp/Dz++OVIiAggOPHj5OamnrBeRSnTp0iIiKCkSNH8vbbb1fpWFRXfTzlN3049eqUn1cTuOYfzq6m7mn/G9b+2+1w+OeSL3ux4z4e3tBlIAREOm53Vec75Se1p984XPKUXz14+6k6b29vVq9ezZw5c5g/fz4JCQns2bOHgICAsmAyaNCgCmEK/jjlB9C2bVvGjh173scaO3YsFouFmTNnkpycjNlsZtCgQUyYMKHs1g3t2rUrF6ZSU1M5fvw4AQEBlZqU2rx5c9q3b09SUjXukici4kQmE0ReBaHdIP1XyNgLOVmAHUyNoPNN0LpDyek+kfrMbZ/CHh4ejBs3jnHjxlVpvR49elDVQbsxY8YwZswYh22OthUaGlqlx/j999/Zv38/V1xxRZXqEhFxFZ4+EHF5yVfpKJ2nD7Tp7OzKRGqG2waq+mrkyJG0b9+e7t2707x5cxITE3n99dexWCw8/vjjzi5PREREHFCgcjFXXnkln332GbNnz6agoICwsDD69evHc889V6V7aomIiEjdUaByMY8++iiPPvqos8sQERGRKtB1myIiIiIGKVCJiIiIGKRAJSIiImKQApWIiIiIQQpUIiIiIgYpUImIiIgYpEAlIiIiYpAClYiIiIhBClQiIiIiBilQiYiIiBikQCUiIiJikD7LTxzyNMP04c6uomo8zc6uQEQakkYe0G+cs6toeBp5OLsCxxSoxCGTCbz07BAROSeTCcyezq5CXIVO+YmIiIgYpEAlIiIiYpAClYiIiIhBClQiIiIiBilQiYiIiBikQCUiIiJikAKViIiIiEEKVCIiIiIGKVCJiIiIGKRAJSIiImKQApWIiIiIQQpUIiIiIgYpUImIiIgYpEAlIiIiYpAClYiIiIhBClQiIiIiBilQiYiIiBhkcXYB4prsdrAVOruKqmnkASZTzW2vto6B3f7Hv8XWmt12TR6Dhr7/UDvHoKHvf+l2S/919WMgUlkmu730qS3yh2IrrH3T2VVUTb9xYPasue019GPQ0Pcf6t8xaOj7DzV/DEQqS6f8RERERAxSoBIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIN3YU2rViq2fMOurUTx158fceNl9FdozTiTz96ltGXDpvTxz1yd1Xl9N23VwHU+916/cssaevoS26kD/Hn9nSO9/Yja7969dQz8G2v+Gvf/ScOlZLVIL+nW/m8s73owdOyezM1i5/TPeW/IEv/2+l8eHxjm7vDrR0I+B9r9h7780PApUIrUgKqQH/S8dWfb9rb0eZvSMjny/5QNG3TSF5k1aObG6utHQj4H2v2HvvzQ8mkMlUge8PX3peNGV2O120o8fdHY5TtHQj4H2v2Hvv7g/BSqROnL0/95E/Hz8nVyJ8zT0Y6D9b9j7L+5Np/xEakFBYR6nc7Ow20vmjyz56T2S0nbQMexyQlt1cHZ5daKhHwPtf8Pef2l4FKhcSFZWFjNmzGDRokWkpqbSqlUr7rjjDl555RXGjRvHRx99xFtvvcWjjz7q7FLlAj774UU+++HFcsuujr6Df97+jpMqqnsN/Rho/xv2/kvDo0DlInbu3MnAgQPJyMjA19eXzp07k56ezptvvsnBgwc5ceIEAN27d3duobXEZDI5u4QadcsVD3Jt12EU2Qo5fHQPC9ZNJ+t0Kp4ejcv67Dm0kec+HFhh3aJiKzZbMStmFNdlyTWuoR8D7X/D3n9peBSoXEBWVha33norGRkZPPnkk7z44os0bdoUgBkzZjBhwgQsFgsmk4muXbs6udqq8fLwBuBsYZ7D9gJrbrl+7iIkIIoeHfoDcHnHgUS3vZrH372a2Qv/wfMj/wVATOQ1LJmSU269rNPpPPJmTwb3qv+jkA39GGj/G/b+S8OjSekuYNy4caSmpvLoo48ya9assjAF8Mwzz9CtWzeKioqIiIjAz8/PiZVWXZB/WwB++32vw/bS5aX93FWXiF707/F31u1aQHzyfx32sRad5aXP7iA64mruuf65Oq6w9jX0Y6D9b9j7L+5PgcrJ9u7dy4IFCwgICGDq1KkO+1x66aUAdOvWrS5LqxFRIT1o1TyMdTv/Rdbp9HJthUVWvt30NiaTias63+akCuvOiP4TadTIzKcr/p/D9tkL/4G1sICnh39St4XVoYZ+DLT/DXv/xb0pUDnZ/PnzsdlsjBgxgiZNmjjs4+1dcjqsPgYqs9nC+DvmkFtwmode68rcZRNY9nMcX6yczMNv9GD3ofXc1S+WsMCLnV1qrQsJaE+/bnexI2k1ew5tLNf2zY9vsnnvUl66bzGNPX2cVGHta+jHQPvfsPdf3JsClZOtWbMGgH79+p2zT2pqKlA/AxXAFZ1u4Y1HNtGtfT9WbvuUt755hK83vEqzJq14YeQC7h84xdkl1pm7r3+eRqZGfPrDH3+h70xaywfLJjDx7/8myD/CecXVkYZ+DLT/DXv/xX2Z7Ha73dlFNGRhYWGkpqayY8cOh1fwFRUV0aZNG7Kysjh48CCRkZHVepyePXuSkZFR6f6eFm/iHk2s1mM5y4NvR2Etyq+x7dXFMcg4kcyjb17GyAEvMqS38Um4NXkM6uo5UJPHoKE/Bxr6/kPNHwNpWIKCgti2bVu11tVVfk6Wm1tylVt+vuMXgAULFpCVlUXTpk1p27b6E7czMjJIS0urdP/GHvVvyP1oejoF57iasDpq+xgUWPN48ZMhXNX5thp5I4GaPQZ18Ryo6WPQ0J8DDX3/oeaPgUhlKVA5WVBQECdPnuSXX37hqquuKtd29OhRnn76aQC6du1q6F5NQUFBVervaal/tzFoExxc43+d16aNexZy6Ogu0rIOsG7XggrtHz6VQGCL8CptsyaPQV08B2r6GDT050BD33+o+WMgDUtV3yv/TKf8nGzcuHG89dZbhIWFsWrVKjp0KPlIhq1bt/L3v/+dQ4cOUVhYyCOPPMLbb79dZ3UVW2Htm3X2cDWi3zgwe9bc9hr6MWjo+w/17xg09P2Hmj8GIpWlSelO9swzz9CyZUtSUlLo0qULMTExREVFcfnllxMZGcl1110H1N8J6SIiIg2BApWThYaGsnHjRm655RYaN25McnIy/v7+vP/++yxbtowDBw4AClQiIiKuTHOoXECnTp1YunRpheU5OTkkJyfTqFEjoqOjnVCZiIiIVIZGqFxYfHw8drudqKgofHzq31V3IiIiDYUClQvbs2cPoNN9IiIirk6n/FyYOwWq1MxEZi64l9O5Wfg2bsbTwz8hIqiLs8uqUSNficDD4lV2qfnd18XSt/vwcn12JK3hw+XPkn82B5PJxBUdb2H0zdNo1Kjkb5t/rZ3Oym2fYjF74unRmEcGv0nH8MvrfF+q453F4/gp4TuOnTzCnMd20D6kO1C1n/3ho3t4e/E/OZlzDIBRN03hmpg76moXDLEWFjDly7s4ciwBLw9vmjcJZNwdcwgJaM+81a+wcvunpGUl8uL/LKJ39BCH28g/m8NLn/2NxNTtFNuKWDz5VJ3uQ035z9aPefWr+5l07zf0jh7CzAWjiE/ehJeHN409m/Dw4De4OOyyCutlnU5n1lejOHYyGQ+zFyEBUYz/23s0b9LKCXshUjUKVC7MnQLV7IUPcfMVD3LjZfexYffXzFxwH++M3+rssmrc8yMWlAUJR5p6t+D5Ef+iTctIrIUFPBPXn5XbP+PGy+4jKW0nS/77Lh88FY+3VxNWbf+Ctxc/ytvjttTdDhhwTdeh3Nn3GR5/9+pyyyv7sy+w5vH/PhnMhLs+I7rt1RTbisnOO1FX5deIm694kMs7DsRkMrF409u89u8HeHXsOnpE9adf97uY9dX9513fbPZgeL8JNPX256n3+tZN0TUs40Qy32+eS6fwK8uW9Y6+nSeGzsVstvBzwlImfz6ML55LrrCuuZGZkf0nEt225DkUt/Rp4pY+zTN3fVJH1YtUnwKVCyv9nD9XkpN/ijGvRnO2MJ9WzcIoLD5LxvFDXH/p33ly2AcO1zmZ8zsHUrcxbcwPAFwT8zfe/uZR0rKSCAloX6OP5erah1xS9n9Pj8a0C+7OsZPJAJhMJopshRRYc/H2akJOwSkCmoU6qdKq6xp5bYVlVfnZr9kxj07hV5a9mZobmevVyISnR2Ou6HRz2fedwq/k6/WzACo9yuhp8eKS9teRcSK5NkqsdTabjdf+/QCPDHmL95c8Wba8V5fbyv7f6aIryTqdRnFxEWZz+begFk1b06Jp67LvO4Zfwbeb6u7+eyJGKFBJlTTxbs513e/B26spIwdMZOv+Fcxf88p5A07mqRT8/dqUvXiaTCYCW4Tz+6nfzhuoqvNYzjbjX/+DHTsdwy5n9M3TzhsITpzJYOPur5l8f8kVnu2Cu/G3ax7n71Pb0tTHHw+zF689vKGuSq8VVfnZ/3YsAQ+LFy98NIjMU6lEtunKQ7e+Wq9C1Z998+Nsruoy2Nll1KmFG16jS0RvOoRees4+32yczeUdb64Qpv6q2FbMt5veplcDO4ZSf2lSulRZUvrOspGWxNTttA++5AJr1I/HMuq1sRuIe3I3cx77BT/fAGYsuPecfXMLzjDx41u5s+8zXBzWE4CjJw7z455FfDIhifkvpHLHtY/z8hfDz7kNd1NsK2JH4ioe+9v7vPf4DgKahfDmorHOLqta5q1+hfSsJEYPnOrsUurM4Yxf2bhnISP6v3DOPqu2f8H63V/x+NC4827Lbrfz1qKHaerdgtuvHl/TpYrUCgUqqbJDfw05IecPOa2ah3HizFGKi4uAkhfL30/+RmDzC39GV1Ufy5lKP3PMYvbgjmse49fDGx32yyvI5rkPbqJXl8EM7fNE2fIfdy+kbZsYApoFA3DjZSUTeQuLrLVffC2pys8+sHk43dr1I6BZCCaTiet7jGTvbz/XdcmG/XvdLH78dRGvPPA9jT0bzu1Ofj20kWMnk7lvehQjX4lg728/88bXD7Lkv3MAWLdzAZ+veonpY1aWO63nyDvfjuP30yk8P3JB2QUbIq5Oz1SpkqzTaWAyEdAsBIBDGbtpGxQDwPT5/8OPe76psE6LJoG0D+nBql++AEo+EDWgeWjZKZ9zrXe+x3I1+dZccvJPlX2/dsd8h6Np+WdziP3gJnpefFOFv+SDWkYSn7yJ/LM5AGxOWEpoqw54WOrvB5Nd6Gf/Z3263cn+1K3kFpwBYMu+5US2qV8XZHy9/jXW7pzP9DEraeLd3Nnl1Klbe41lwf87yhfPJfPFc8l0Cr+Sx4bGcWuvsazf9RUfr3iBGQ+uuuCHHb+zeBzpWUlMuvebev3cl4ZHc6ikSpLSdpQLCk0aN+e7n97lyWEfcCB1G0OuHudwvcf+9j4zF9zH/DWv4NPYj6fv/Lis7Vzrne+xXM2p7GO89NnfsNmKsWOnjX8kz9z1GQCv/vsBrup8G7263MaiH2ezP2ULBdZcftyzCIBruw1jxPXPc3X07RxI2cojs3viYfGisacvsffMc+ZuVckbXz/E5n3LOJGdQewHN+Lj1ZRPn00678/+z8cmsEU4d1/3HI+93QuTqREBzUJ47AKnhlxJ5qlU3l/6JG38I3nqvX5AySTzt8Zt5stVL7P05/c4nZPJaxm/8vbiR5nz2A6aN2nFJyv+Hy39grn1qn8A8OCrXTmdm0ne2TPc/XIo3dr149m7P3fmrhk2dd4I/JsG8f8+/mM+1MyHVuPn25IlP73H8TPp3Hfj//Lr4U0s3vQWYYEd+eebVwDQxr8tk+6r+AeXiKsx2e12u7OLENdT1U+ZP5WTydR59zD9wZVVepzqrudITX/KfFWPgSuoyWPQ0Pcf6t8xaOj7DzV/DEQqS6f8pEY0b9KqWqGouuuJiIi4EgUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgXeUnDtntYCt0dhVV08gDTKaa215DPwYNff+h/h2Dhr7/UPPHQKSyFKhEREREDNIpPxERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoxKE1a9ZgNptp3769s0sRERFxeQpUUkFGRgb33nsvN9xwg7NLERERqRcszi5AXIvNZmPkyJE88sgjFBQUkJiY6OySREREXJ5GqKScyZMnYzKZmDBhgrNLERERqTc0QiVl1q5dy3vvvceOHTswmUzOLkdERKTe0AiVAJCVlcXIkSP5+OOPCQoKcnY5IiIi9YrJbrfbnV2EON+6devo168fZrO5bJnNZsNut2M2m/nss8+45557nFihiIiI61KgEgByc3M5fPhwuWXvvvsuS5cuZfny5YSFhdGsWTMnVSciIuLaNIdKAPD19SU6OrrcssDAQDw9PSssFxERkfI0h0pERETEIJ3yExERETFII1RSZYdTjlJYWOTsMkRERFyG5lBJlWTn5PHRV8tp3NiLR/8+hGZ+TZxdkoiIiNNphMrFFBcX8/nnn3PDDTfQqlUrvLy8CA8P56abbuKDDz6guLjYqfWt37KLwqJiWvg1wa+pr1NrERERcRWaQ+VCzpw5w5AhQ1i7di0AwcHBhISEkJ6eTnp6Ona7nZMnT9K8eXOn1Jedk8eM9+dTWFTM/cMG0iEyzCl1iIiIuBqd8nMho0ePZu3atYSGhvLZZ5/Rr1+/srZjx47x4Ycf4uHh4bT6SkenwoMDiWob6rQ6REREXI1GqFzE9u3b6dmzJxaLhR07dtT4vZ/e+nQR2Tn51V7fbreTnZsHgI+3FxazsriIiLiXpk28+ee9d1RrXb0ruojFixcDcMstt9TKjTSzc/I5k5NbI9vKyz8LnK2RbYmIiLgDBSoXkZCQAMBVV11VK9tv2sS72utqdEpERBoCI++Vemd0EWfOnAGotc/Lq+4QJsDSNT/x49Y9hAcHMnbkYEwmUw1WJiIiUv8pULkIPz8/AE6fPl0r26/uHKo/j05lnTzN1Hfn1XRpIiIiLkFzqNxAly5dWLRoET/99FOtbL8m5lBp7pSIiIhjClQu4vbbb2fy5MksX76chIQEOnfuXKPbr855Yc2dEhGRhsTIHCrdNsGFDB8+nK+++orw8HA+++wz+vTpU9Z27NgxPvroI8aNG4evb93coVxzp0RERCpHgcqFnDlzhsGDB7Nu3ToAQkJCCA4O5ujRo6SlpdXpndJ1V3QREZHK02f5uRA/Pz9WrVrFhx9+SN++fcnLy2PXrl00atSIG2+8kQ8//JCmTZvWSS26K7qIiEjlaYRKHFq/eSdrf9rJPbddr9EpERGRC1CgknMqOGvFy9NDc6dEREQuQIFKRERExCDNoRIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCAFKhERERGDFKhEREREDFKgEhERETFIgUpERETEIAUqEREREYMUqEREREQMUqASERERMUiBSkRERMQgBSoRERERgxSoRERERAxSoBIRERExSIFKRERExCAFKhERERGD/j/3pH9usytJ/QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 748.215x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pe_circ.decompose(reps = 2).draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "643ee9bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 664.604x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pe_circ.measure(evr, cr)\n",
    "pe_circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ba5d2568",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.primitives import Sampler\n",
    "\n",
    "sampler = Sampler()\n",
    "results = sampler.run(pe_circ).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "152917af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    " \n",
    "plot_histogram(results.quasi_dists[0].binary_probabilities())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "57311de8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4375"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(\"\".join(reversed('1110')),2)/2**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c3fe0016",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.375"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(\"\".join(reversed('0110')),2)/2**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "138f5d75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                ┌───┐\n",
       "       phase_0: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_1: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_2: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_3: ┤ H ├\n",
       "                ├───┤\n",
       "  eigenstate_0: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_1: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_2: ─────\n",
       "                     \n",
       "  eigenstate_3: ─────\n",
       "                     \n",
       "  eigenstate_4: ─────\n",
       "                ┌───┐\n",
       "  eigenstate_5: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_6: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_7: ─────\n",
       "                ┌───┐\n",
       "   phase two_0: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_1: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_2: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_3: ┤ H ├\n",
       "                ├───┤\n",
       "eigstate two_0: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_1: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_2: ─────\n",
       "                     \n",
       "eigstate two_3: ─────\n",
       "                     \n",
       "eigstate two_4: ─────\n",
       "                ┌───┐\n",
       "eigstate two_5: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_6: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_7: ─────\n",
       "                     \n",
       "      output: 4/═════\n",
       "                     \n",
       "  output two: 4/═════\n",
       "                     </pre>"
      ],
      "text/plain": [
       "                ┌───┐\n",
       "       phase_0: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_1: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_2: ┤ H ├\n",
       "                ├───┤\n",
       "       phase_3: ┤ H ├\n",
       "                ├───┤\n",
       "  eigenstate_0: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_1: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_2: ─────\n",
       "                     \n",
       "  eigenstate_3: ─────\n",
       "                     \n",
       "  eigenstate_4: ─────\n",
       "                ┌───┐\n",
       "  eigenstate_5: ┤ X ├\n",
       "                ├───┤\n",
       "  eigenstate_6: ┤ X ├\n",
       "                └───┘\n",
       "  eigenstate_7: ─────\n",
       "                ┌───┐\n",
       "   phase two_0: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_1: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_2: ┤ H ├\n",
       "                ├───┤\n",
       "   phase two_3: ┤ H ├\n",
       "                ├───┤\n",
       "eigstate two_0: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_1: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_2: ─────\n",
       "                     \n",
       "eigstate two_3: ─────\n",
       "                     \n",
       "eigstate two_4: ─────\n",
       "                ┌───┐\n",
       "eigstate two_5: ┤ X ├\n",
       "                ├───┤\n",
       "eigstate two_6: ┤ X ├\n",
       "                └───┘\n",
       "eigstate two_7: ─────\n",
       "                     \n",
       "      output: 4/═════\n",
       "                     \n",
       "  output two: 4/═════\n",
       "                     "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Initialize the circuit\n",
    "\n",
    "n = 4 # for phase estimation\n",
    "m = 8 # for eigenstate\n",
    "\n",
    "qr = QuantumRegister(n, name = 'phase')\n",
    "qr2 = QuantumRegister(m, name = 'eigenstate')\n",
    "cr = ClassicalRegister(n, 'output')\n",
    "\n",
    "qrp = QuantumRegister(n, name = 'phase two')\n",
    "qr2p = QuantumRegister(m, name = 'eigstate two')\n",
    "crp = ClassicalRegister(n, 'output two')\n",
    "\n",
    "qc = QuantumCircuit(qr,qr2,cr,qrp,qr2p,crp)\n",
    "\n",
    "\n",
    "# Apply H-Gates to counting qubits:\n",
    "for qubit in range(2*n):\n",
    "    if qubit < n:\n",
    "        qc.h(qubit)\n",
    "    else:\n",
    "        qc.h(qubit + m)\n",
    "\n",
    "# Prepare our eigenstate |psi>: state 198\n",
    "eig = '11000110'\n",
    "\n",
    "eigstatelist = ['11000110', '01101100', '10001101',\n",
    "                '01110010', '11100001', '10110100']\n",
    "\n",
    "for ind, val in enumerate(eig):\n",
    "    if(int(val)):\n",
    "        qc.x(ind + n)\n",
    "        qc.x(ind + 2*n + m)\n",
    "\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "0395bf3f",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Operator' object has no attribute 'control'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[42], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m U \u001b[38;5;241m=\u001b[39m qi\u001b[38;5;241m.\u001b[39mOperator(U)\n\u001b[0;32m----> 3\u001b[0m qc\u001b[38;5;241m.\u001b[39mappend(\u001b[43mPhaseEstimation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mCU\u001b[49m\u001b[43m)\u001b[49m, \u001b[38;5;28mrange\u001b[39m(n \u001b[38;5;241m+\u001b[39m m))\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/qiskit/circuit/library/phase_estimation.py:94\u001b[0m, in \u001b[0;36mPhaseEstimation.__init__\u001b[0;34m(self, num_evaluation_qubits, unitary, iqft, name)\u001b[0m\n\u001b[1;32m     91\u001b[0m circuit\u001b[38;5;241m.\u001b[39mh(qr_eval)  \u001b[38;5;66;03m# hadamards on evaluation qubits\u001b[39;00m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_evaluation_qubits):  \u001b[38;5;66;03m# controlled powers\u001b[39;00m\n\u001b[0;32m---> 94\u001b[0m     circuit\u001b[38;5;241m.\u001b[39mcompose(\u001b[43munitary\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpower\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mj\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcontrol\u001b[49m(), qubits\u001b[38;5;241m=\u001b[39m[j] \u001b[38;5;241m+\u001b[39m qr_state[:], inplace\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[1;32m     96\u001b[0m circuit\u001b[38;5;241m.\u001b[39mcompose(iqft, qubits\u001b[38;5;241m=\u001b[39mqr_eval[:], inplace\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)  \u001b[38;5;66;03m# final QFT\u001b[39;00m\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;241m*\u001b[39mcircuit\u001b[38;5;241m.\u001b[39mqregs, name\u001b[38;5;241m=\u001b[39mcircuit\u001b[38;5;241m.\u001b[39mname)\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Operator' object has no attribute 'control'"
     ]
    }
   ],
   "source": [
    "U = qi.Operator(U)\n",
    "\n",
    "qc.append(PhaseEstimation(n, U), range(n + m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f04dc24f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operator([[ 0.30901699+0.95105652j,  0.        +0.j        ,\n",
      "            0.        +0.j        , ...,  0.        +0.j        ,\n",
      "            0.        +0.j        ,  0.        +0.j        ],\n",
      "          [ 0.        +0.j        ,  0.06279052+0.99802673j,\n",
      "            0.        +0.j        , ...,  0.        +0.j        ,\n",
      "            0.        +0.j        ,  0.        +0.j        ],\n",
      "          [ 0.        +0.j        ,  0.        +0.j        ,\n",
      "            0.18738131+0.98228725j, ...,  0.        +0.j        ,\n",
      "            0.        +0.j        ,  0.        +0.j        ],\n",
      "          ...,\n",
      "          [ 0.        +0.j        ,  0.        +0.j        ,\n",
      "            0.        +0.j        , ..., -0.80901699+0.58778525j,\n",
      "           -0.        +0.j        , -0.        +0.j        ],\n",
      "          [ 0.        +0.j        ,  0.        +0.j        ,\n",
      "            0.        +0.j        , ..., -0.        +0.j        ,\n",
      "           -0.72896863+0.68454711j, -0.        +0.j        ],\n",
      "          [ 0.        +0.j        ,  0.        +0.j        ,\n",
      "            0.        +0.j        , ..., -0.        +0.j        ,\n",
      "           -0.        +0.j        , -0.18738131+0.98228725j]],\n",
      "         input_dims=(2, 2, 2, 2, 2, 2, 2, 2), output_dims=(2, 2, 2, 2, 2, 2, 2, 2))\n"
     ]
    }
   ],
   "source": [
    "U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "5812a1dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Instruction(name='rz', num_qubits=1, num_clbits=0, params=[5.277875658030852])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RZGate(2*np.pi*2*0.42)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b267e48d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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