Variational_Classifier.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_quantum as tfq\n",
    "import os\n",
    "\n",
    "import cirq\n",
    "import sympy\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import collections\n",
    "import itertools as it\n",
    "import random\n",
    "import math\n",
    "import qutip\n",
    "import pydot\n",
    "import cmath\n",
    "import scipy.linalg as splin\n",
    "import warnings\n",
    "\n",
    "# visualization tools\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from cirq.contrib.svg import SVGCircuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Variational Classifier \n",
    "\n",
    "This program implements and tests the [Havlíček et al. (2018)](10.1038/s41586-019-0980-2) variational quantum classifier. The algorithm takes on the original supervised learning problem: we are given data from a training set $T$ and a test set $S$ of a subset $\\Omega \\subset {\\rm I\\!R}^d$. Both are assumed to be labeled by a map $m$: $T \\cup S \\longrightarrow \\{+1,-1\\}$ unknown to the algorithm. The goal is to approximate the map $\\tilde{m}: S \\rightarrow \\{+1,-1\\}$ such that is agrees with high probability with the true map $m(\\textbf{s}) = \\tilde{m}(\\textbf{s})$ on the test data $\\textbf{s} \\in S$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0. Helper Functions and Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 2 # num qubits\n",
    "qs = [cirq.GridQubit(i, 0) for i in range(n)]\n",
    "pauli_z = np.array([[1,0],[0,-1]] , dtype=float) # Pauli-Z\n",
    "pauli_y = np.array([[0,-1j],[1j,0]], dtype=complex) # Pauli-Y\n",
    "I = np.eye(n) # Identity\n",
    "H = cirq.H # Hadamard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Ry(theta):\n",
    "    return np.array([[cmath.cos(theta/2.), -1*cmath.sin(theta/2.)], \n",
    "                     [cmath.cos(theta/2.), cmath.sin(theta/2.)]])\n",
    "\n",
    "def Rz(theta):\n",
    "    return np.array([[cmath.exp(-1j*theta/2), 0],\n",
    "                     [0, cmath.exp(1j*theta/2)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from numpy source code: this is their unitary check\n",
    "def is_unitary(matrix: np.ndarray, *, rtol: float = 1e-5, atol: float = 1e-8) -> bool:\n",
    "    return (matrix.shape[0] == matrix.shape[1] and\n",
    "    np.allclose(matrix.dot(np.conj(matrix.T)),\n",
    "    np.eye(matrix.shape[0]),\n",
    "    rtol=rtol,\n",
    "    atol=atol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "flatten = lambda t: [item for sublist in t for item in sublist]\n",
    "expand = lambda a: np.array([list(a)]*10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# all sub-lists must be of equal length\n",
    "def lst_average(lst):\n",
    "    N = len(lst)\n",
    "    m = len(lst[0])\n",
    "    new = [0]*m\n",
    "    for i in range(N):\n",
    "        for j in range(m):\n",
    "            new[j] += lst[i][j]\n",
    "    return [x/N for x in new]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regex_complex(U):\n",
    "    str_U = str(U)\n",
    "    regex = re.compile(r'(\\d.\\s+(-|\\+)\\d.\\d?j|-?\\d.\\d*\\s?(-|\\+)\\d.\\d*j)')\n",
    "    nums = regex.findall(str_U)\n",
    "\n",
    "    complex_array = []\n",
    "    for i, n in enumerate(nums):\n",
    "        complex_array.append(complex(n[0].replace(' ', '')))\n",
    "    \n",
    "    complex_array = np.array(complex_array)\n",
    "    return complex_array.reshape((4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def powerset_help(S):\n",
    "    x = len(S)\n",
    "    masks = [1 << i for i in range(x)]\n",
    "    for i in range(1 << x):\n",
    "        yield [ss for mask, ss in zip(masks, S) if i & mask]\n",
    "        \n",
    "def powerset(S, mx):\n",
    "    return [l for l in list(powerset_help(S)) if len(l) <= mx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kron(*elts):\n",
    "    res = 1\n",
    "    for e in elts:\n",
    "        res = np.kron(res,e)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Construct non-trivial data encoding feature map with entanglement $\\left| \\Phi(x_i) \\right\\rangle \\left\\langle \\Phi(x_i) \\right|  $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The feature map is an injective encoding of the classical data $\\textbf{x} \\in {\\rm I\\!R}^d$ into a quantum state $\\left| \\Phi \\right\\rangle \\left\\langle \\Phi \\right|$. We use the following unitary feature map onto $n$-qubits, where $H$ denotes the conventional Hadamard gate:\n",
    "\n",
    "$$\\left|\\Phi(\\textbf{x})\\right\\rangle = \\mathcal{U}_{\\Phi(\\textbf{x})}\\left|0\\right\\rangle^{\\otimes n} = U_{\\Phi(\\textbf{x})}H^{\\otimes n} U_{\\Phi(\\textbf{x})}H^{\\otimes n} \\left|0\\right\\rangle^{\\otimes n}$$\n",
    "where,\n",
    "$$U_{\\Phi(\\textbf{x})} = \\exp\\bigg(i \\sum_{S \\subseteq [n]} \\phi_S(\\textbf{x}) \\prod_{i \\in S} Z_i \\bigg)$$\n",
    "where the $2^n$ coefficients $\\phi(\\textbf{x}) \\in {\\rm I\\!R}$ are now non-linear functions of the input data $\\textbf{x} \\in {\\rm I\\!R}^n$. In general, maps with low degree expansions $|S| \\leq d$ can be implemented efficiently. As in the original paper, we will use $n=d=2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns a matrix that applies the 1-qubit matrix U to the qubits indexed by ns (a list)\n",
    "# does nothing to the other qubits\n",
    "def U_apply(U, ns, n_qubits):\n",
    "    U_n = 1\n",
    "    for i in range(n_qubits-1, -1, -1): #n_qubits-1 -> 0, inclusive\n",
    "        U_n = np.kron(U_n, U if (i in ns) else I)\n",
    "    return U_n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considering only Ising type interactions ($d=2$), the unitaries are generated from one- and two- big gates of the form\n",
    "\n",
    "$$U_{\\phi_{\\{k\\}}(\\textbf{x})} = \\exp\\big(i\\phi_{\\{k\\}}(\\textbf{x})Z_k \\big)$$\n",
    "$$U_{\\phi_{\\{l,m\\}}(\\textbf{x})} = \\exp\\big(i\\phi_{\\{k,l\\}}(\\textbf{x})Z_kZ_l\\big)$$\n",
    "\n",
    "where we have followed Havlíček et al. and chosen $\\phi_{\\{ i \\}} = x_i$ and $\\phi_{\\{ 1,2 \\}} = (\\pi - x_1)(\\pi - x_2)$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# each term of phi_S in sum\n",
    "def phi(S,x):\n",
    "    if len(S) == 2:\n",
    "        return (np.pi - x[S[0]])*(np.pi-x[S[1]])\n",
    "    elif len(S) == 1:\n",
    "        return x[S[0]]\n",
    "    elif len(S) == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        assert False, \"expected |S|<=2\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2^n x 2^n Block diagonal unitary for x\n",
    "def u_phi(x, n, S_size):\n",
    "    ss = powerset(np.arange(n), S_size)\n",
    "    total = np.zeros((2**n,2**n))\n",
    "    for s in ss:\n",
    "        total += phi(s, x)*U_apply(pauli_z,s,n)\n",
    "    u = np.exp(1j*total)\n",
    "    u = np.diag(np.diag(u))\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_x_input(n):\n",
    "    return [random.random()*2*np.pi for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u_gate(x, n):\n",
    "    return u_phi(x, n, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# given matrix, create equivalent circuit using only operations from tfq.util.get_supported_gates()\n",
    "def synthesized_circuit(matrix):\n",
    "    synthesized_operations = cirq.two_qubit_matrix_to_operations(\n",
    "    cirq.GridQubit(0,0),\n",
    "    cirq.GridQubit(1,0),\n",
    "    matrix,\n",
    "    allow_partial_czs=False,\n",
    "    )\n",
    "    \n",
    "    synth_circuit = cirq.Circuit(synthesized_operations)\n",
    "    \n",
    "    synthesized_matrix = cirq.unitary(synth_circuit)\n",
    "\n",
    "    cirq.testing.assert_allclose_up_to_global_phase(\n",
    "        matrix,\n",
    "        synthesized_matrix,\n",
    "        atol=1e-2\n",
    "    )\n",
    "    \n",
    "    return synth_circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# two-qubit feature map with d=2\n",
    "def feature_map(x, n, d=2):\n",
    "    circuit = cirq.Circuit()\n",
    "    u_gate_matrix = u_gate(x, n)\n",
    "    synth_circuit = synthesized_circuit(u_gate_matrix)\n",
    "    for _ in range(d):\n",
    "        circuit.append([H(q) for q in qs], strategy=cirq.InsertStrategy.INLINE)\n",
    "        circuit.append(synth_circuit)\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"1283.715703125\" height=\"100.0\"><line x1=\"32.246796875\" x2=\"1253.715703125\" y1=\"25.0\" y2=\"25.0\" stroke=\"#1967d2\" stroke-width=\"1\" /><line x1=\"32.246796875\" x2=\"1253.715703125\" y1=\"75.0\" y2=\"75.0\" stroke=\"#1967d2\" stroke-width=\"1\" /><line x1=\"252.4556640625\" x2=\"252.4556640625\" y1=\"25.0\" y2=\"75.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"442.246953125\" x2=\"442.246953125\" y1=\"25.0\" y2=\"75.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"842.0667187500001\" x2=\"842.0667187500001\" y1=\"25.0\" y2=\"75.0\" stroke=\"black\" stroke-width=\"3\" /><line x1=\"1031.8580078125\" x2=\"1031.8580078125\" y1=\"25.0\" y2=\"75.0\" stroke=\"black\" stroke-width=\"3\" /><rect x=\"10.0\" y=\"5.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(0, 0): </text><rect x=\"10.0\" y=\"55.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(1, 0): </text><rect x=\"74.49359375\" y=\"5.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"94.49359375\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">H</text><rect x=\"74.49359375\" y=\"55.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"94.49359375\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">H</text><rect x=\"134.49359375\" y=\"5.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"173.47462890625002\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(1)^0.5</text><circle cx=\"252.4556640625\" cy=\"25.0\" r=\"10.0\" /><circle cx=\"252.4556640625\" cy=\"75.0\" r=\"10.0\" /><rect x=\"292.4556640625\" y=\"5.0\" width=\"109.79128906250003\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"347.35130859375\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(-0.5)^0.426</text><circle cx=\"442.246953125\" cy=\"25.0\" r=\"10.0\" /><circle cx=\"442.246953125\" cy=\"75.0\" r=\"10.0\" /><rect x=\"482.24695312499995\" y=\"5.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"521.22798828125\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(0)^0.5</text><rect x=\"482.24695312499995\" y=\"55.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"521.22798828125\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Z^-0.327</text><rect x=\"580.2090234375\" y=\"5.0\" width=\"63.895624999999995\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"612.1568359375001\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Z^-0.316</text><rect x=\"664.1046484375\" y=\"5.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"684.1046484375\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">H</text><rect x=\"664.1046484375\" y=\"55.0\" width=\"40\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"684.1046484375\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"18px\" font-family=\"Arial\">H</text><rect x=\"724.1046484375\" y=\"5.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"763.08568359375\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(1)^0.5</text><circle cx=\"842.0667187500001\" cy=\"25.0\" r=\"10.0\" /><circle cx=\"842.0667187500001\" cy=\"75.0\" r=\"10.0\" /><rect x=\"882.0667187500001\" y=\"5.0\" width=\"109.79128906250003\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"936.9623632812501\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(-0.5)^0.426</text><circle cx=\"1031.8580078125\" cy=\"25.0\" r=\"10.0\" /><circle cx=\"1031.8580078125\" cy=\"75.0\" r=\"10.0\" /><rect x=\"1071.8580078125\" y=\"5.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1110.8390429687502\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">PhX(0)^0.5</text><rect x=\"1071.8580078125\" y=\"55.0\" width=\"77.9620703125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1110.8390429687502\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Z^-0.327</text><rect x=\"1169.820078125\" y=\"5.0\" width=\"63.895624999999995\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"1201.767890625\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Z^-0.316</text></svg>"
      ],
      "text/plain": [
       "<cirq.contrib.svg.svg.SVGCircuit at 0x7fd1e93f3c70>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print out resulting feature map circuit for a random test input\n",
    "test_input = random_x_input(n)\n",
    "feature_map_circuit = cirq.Circuit()\n",
    "feature_map_circuit.append(feature_map(test_input, n))\n",
    "SVGCircuit(feature_map_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Construct short-depth discriminator circuit $W(\\theta)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general short-depth circuit to define a seperating hyperplane is comprised of the following sequence of single qubit and multi-qubit gates:\n",
    "\n",
    "$$ W(\\theta) = U_{loc}^{(l)}(\\theta_l)U_{ent}...U_{loc}^{(2)}(\\theta_2)U_{ent}U_{loc}^{(1)}(\\theta_1) $$\n",
    "\n",
    "\n",
    "We apply a circuit of $l$ repeated entanglers and interleave them with layers comprised of local single qubit rotations:\n",
    "\n",
    "$$ U_{loc}^{(t)}(\\theta_t) = \\otimes_{m=1}^n U(\\theta_{m,t}) \\quad \\text{and} \\quad U(\\theta_{m,t}) = \\exp\\bigg(i \\frac{1}{2}\\theta_{m,t}^z Z_m\\bigg) \\exp\\bigg(i \\frac{1}{2}\\theta_{m,t}^y Y_m\\bigg) $$\n",
    "\n",
    "parameterized by $\\theta_t \\in {\\rm I\\!R}^{2n}$ and $\\theta_{i,t} \\in {\\rm I\\!R}^{2}$. For the feature map that we consider, we use entangling unitaries comprised of products of controlled-Z phase gates $CZ(i,j)$ between qubits $i$ and $j$. The entangling interations follow the interaction graph that $G=(E,V)$ that we used to generate the feature map.\n",
    "\n",
    "$$ U_{ent} = \\prod_{(i,j) \\in E} CZ(i,j) $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# local single-qubit rotations\n",
    "def U_loc(theta, n, t, qs, layer):\n",
    "    #circuit = cirq.Circuit()\n",
    "    #y_angles = []\n",
    "    #z_angles = []\n",
    "    for m in range(n):\n",
    "        for i in range(t):\n",
    "            if (m % 2 == 0):\n",
    "                #y_angles.append(theta[4*layer+2*m+i])\n",
    "                yield cirq.ry(theta[4*layer+2*m+i]).on(qs[m])\n",
    "            else:\n",
    "                #z_angles.append(theta[4*layer+2*m+i])\n",
    "                yield cirq.rz(theta[4*layer+2*m+i]).on(qs[m])\n",
    "#     for m in range(n):\n",
    "#         matrix_RyRz = np.kron(Ry(y_angles[m]), Rz(z_angles[m]))\n",
    "#         print(matrix_RyRz)\n",
    "#         matrix_RyRz_new = regex_complex(matrix_RyRz)\n",
    "#         synth = synthesized_circuit(np.round(matrix_RyRz_new, 3))\n",
    "#         circuit.append(synth)\n",
    "#     return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# entangling interactions\n",
    "def U_ent(qs):\n",
    "    for m in range(len(qs)-1):\n",
    "        yield cirq.CZ(qs[m],qs[m+1])\n",
    "    #yield cirq.CZ(qs[-1], qs[0]) # comment out for n <= 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def W_help(theta, n, t, qs, layer, l):\n",
    "    #theta = flatten([[theta[0]]*2, [theta[1]]*2]*2) # uncomment to reduc num params to two\n",
    "    W = cirq.Circuit()\n",
    "    U_local = U_loc(theta, n, t, qs, layer)\n",
    "    W.append(U_local)\n",
    "    if (layer != l-1): # repeated entanglers\n",
    "        W.append(U_ent(qs))\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"562.580625\" height=\"100.0\"><line x1=\"32.246796875\" x2=\"532.580625\" y1=\"25.0\" y2=\"25.0\" stroke=\"#1967d2\" stroke-width=\"1\" /><line x1=\"32.246796875\" x2=\"532.580625\" y1=\"75.0\" y2=\"75.0\" stroke=\"#1967d2\" stroke-width=\"1\" /><line x1=\"293.537109375\" x2=\"293.537109375\" y1=\"25.0\" y2=\"75.0\" stroke=\"black\" stroke-width=\"3\" /><rect x=\"10.0\" y=\"5.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(0, 0): </text><rect x=\"10.0\" y=\"55.0\" width=\"44.49359375\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"0\" /><text x=\"32.246796875\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">(1, 0): </text><rect x=\"74.49359375\" y=\"5.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.212π)</text><rect x=\"74.49359375\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"114.25447265625\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Rz(0.156π)</text><rect x=\"174.01535156249997\" y=\"5.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"213.77623046875\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.082π)</text><rect x=\"174.01535156249997\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"213.77623046875\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Rz(0.21π)</text><circle cx=\"293.537109375\" cy=\"25.0\" r=\"10.0\" /><circle cx=\"293.537109375\" cy=\"75.0\" r=\"10.0\" /><rect x=\"333.537109375\" y=\"5.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"373.29798828125\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.109π)</text><rect x=\"333.537109375\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"373.29798828125\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Rz(0.121π)</text><rect x=\"433.0588671875\" y=\"5.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"472.81974609375004\" y=\"25.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Ry(0.135π)</text><rect x=\"433.0588671875\" y=\"55.0\" width=\"79.5217578125\" height=\"40\" stroke=\"black\" fill=\"white\" stroke-width=\"1\" /><text x=\"472.81974609375004\" y=\"75.0\" dominant-baseline=\"middle\" text-anchor=\"middle\" font-size=\"14px\" font-family=\"Arial\">Rz(0.098π)</text></svg>"
      ],
      "text/plain": [
       "<cirq.contrib.svg.svg.SVGCircuit at 0x7fd1e944ddc0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# short-depth discriminator circuit \n",
    "def W_circuit(theta, n=2, t=2, l=2):\n",
    "    qs = [cirq.GridQubit(i,0) for i in range(n)]\n",
    "    W_circuit = cirq.Circuit()\n",
    "    for layer in range(l):\n",
    "        W_circuit.append(W_help(theta, n, t, qs, layer, l))\n",
    "    return W_circuit\n",
    "\n",
    "# theta = np.random.rand(l,n,t)\n",
    "theta = np.random.rand(8)\n",
    "SVGCircuit(W_circuit(theta, 2, 2, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Binary label classification in the X-Z plane of the Bloch Sphere"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will apply now test our two-qubit variational circuit for a binary classification task. In this task, two random vectors in the X-Z plane of the Bloch sphere are chosen. Around these two vectors, we randomly sample two sets of quantum data points; the task is to learn to distinguish the two sets. \n",
    "\n",
    "An arbitrary single qubit state can be written:\n",
    "\n",
    "$$ \\left| \\psi \\right\\rangle = e^{i \\gamma} \\big(\\cos \\frac{\\theta}{2}\\left|0\\right\\rangle + e^{i \\phi} \\sin \\frac{\\theta}{2}\\left|1\\right\\rangle \\big) $$ \n",
    "\n",
    "where $\\theta$, $\\phi$ and $\\gamma$ are real numbers. The numbers $0 \\leq \\theta \\leq \\pi$ and $0 \\leq \\phi \\leq 2\\pi$ define a point on the Bloch sphere. For testing purposes, we also generate data-sets for binary classification on a number-line, and on the unit-circle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a.  Generate dataset and apply feature map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def number_line_data(num_samples):\n",
    "    q_data = []\n",
    "    labels = []\n",
    "    for _ in range(num_samples):\n",
    "        coin = random.random()\n",
    "        q_data.append(coin)\n",
    "        if coin > 0.5:\n",
    "            labels.append(1)\n",
    "        else:\n",
    "            labels.append(0)\n",
    "    return np.array(q_data), np.array(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thetas(n, t0=0):\n",
    "    dtheta = 2 * np.pi / n\n",
    "    return t0 + np.array([i*dtheta for i in range(n)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unit_circle_data(t, n, t0=0):      \n",
    "    T = (np.tile([0]*n, (t,1)) + \n",
    "    np.array([np.array([np.cos(theta), np.sin(theta)]) for theta in thetas(t, t0)]))\n",
    "    ys = np.array([[1,0]]*int(np.floor(t/2)) + [[0,1]]*int(np.ceil(t/2)))\n",
    "        \n",
    "    return T, ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unit_sphere_data(theta_a, theta_b, num_samples):\n",
    "    q_data = []\n",
    "    bloch = {\"a\": [[], [], []], \"b\": [[], [], []]}\n",
    "    labels = []\n",
    "    blob_size = abs(theta_a - theta_b) / 5\n",
    "    for _ in range(num_samples):\n",
    "        coin = random.random()\n",
    "        spread_x = np.random.uniform(-blob_size, blob_size)\n",
    "        spread_y = np.random.uniform(-blob_size, blob_size)\n",
    "        if coin < 0.5:\n",
    "            label = [1,0]\n",
    "            angle = theta_a + spread_y\n",
    "            source = \"a\"\n",
    "        else:\n",
    "            label = [0,1]\n",
    "            angle = theta_b + spread_y\n",
    "            source = \"b\"\n",
    "        labels.append(label)\n",
    "        q_data.append([angle, spread_x])\n",
    "        bloch[source][0].append(np.cos(angle))\n",
    "        bloch[source][1].append(np.sin(angle)*np.sin(spread_x))\n",
    "        bloch[source][2].append(np.sin(angle)*np.cos(spread_x))\n",
    "    return np.array(q_data), np.array(labels), bloch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector label to scalar label \n",
    "def get_label(v):\n",
    "    if (v[0] == 1):\n",
    "        return 1\n",
    "    elif (v[0] == 0):\n",
    "        return -1\n",
    "    else:\n",
    "        return \"error\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert classical data to quantum data using feature map circuit\n",
    "def convert_to_circuit(x, n=2):\n",
    "    qs = [cirq.GridQubit(i,0) for i in range(n)]\n",
    "    circuit = cirq.Circuit()\n",
    "    circuit.append(feature_map(x, 2))\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def map_plus_tf(c_data):  \n",
    "    x_circ = []\n",
    "    for j in range(len(c_data)):\n",
    "        circuit_rep = convert_to_circuit(c_data[j])\n",
    "        x_circ.append(circuit_rep)\n",
    "        \n",
    "    x_tfcirc = tfq.convert_to_tensor(x_circ)\n",
    "   \n",
    "    return x_tfcirc "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b.  Training phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns a bit string {0,1}^n corrensponding to the result of a measurement in the Z-basis\n",
    "# x = training samples, theta = values of the variational parameters\n",
    "def measure(x, R, theta, n=2):\n",
    "    circuit = cirq.Circuit()\n",
    "    qs = [cirq.GridQubit(i, 0) for i in range(n)]\n",
    "    circuit.append(feature_map(x, n))\n",
    "    W_circuit = cirq.Circuit()\n",
    "    for layer in range(2):\n",
    "        W_circuit.append(W_help(theta, n, 2, qs, layer, 2))\n",
    "    circuit.append(W_circuit)\n",
    "    \n",
    "    sampler = cirq.Simulator()\n",
    "    run_circuit = cirq.Circuit(circuit, cirq.measure(qs[0], qs[1], key='out'))\n",
    "    measurement = sampler.run(run_circuit, repetitions=R)\n",
    "    return measurement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function $f : \\{0,1\\}^n \\rightarrow C$ is fixed and chosen by the programmer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns 1 (0) if z is even (odd)\n",
    "def f(z):\n",
    "    if z==2:\n",
    "        return 1\n",
    "    return 0 # represents -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# returns measurement probility distribution pd = (py(-1), py(+1)) for\n",
    "# data vector x and parameters theta\n",
    "def prob_dist(x, R, theta, C=[-1,+1]):\n",
    "    \n",
    "    res = measure(x, R, theta)\n",
    "    probs = np.zeros(len(C))\n",
    "    \n",
    "    hist = res.histogram(key=\"out\")\n",
    "    for k in hist.keys():\n",
    "        classification = f(k) # classification function f defined by programmer\n",
    "        probs[classification] += hist[k]\n",
    "    \n",
    "    p0 = probs[0] / R    # probability of -1 measurement\n",
    "    p1 = probs[1] / R    # probability of +1 measurement\n",
    "    \n",
    "    return (p0, p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability that the label $m(\\textbf{x}) = y$ is assigned incorrectly is approximated by\n",
    "\n",
    "$$ \\text{Pr}(\\tilde{m}(\\textbf{x}) \\neq m(\\textbf{x})) \\approx \\text{sig}\\bigg( \\frac{\\sqrt{R}\\big( \\frac{1}{2} - \\big( \\hat{p}_y(\\textbf{x})+ \\frac{yb}{2} \\big) \\big)}{\\sqrt{2(1-\\hat{p}_y(\\textbf{x}))\\hat{p}_y(\\textbf{x})}} \\bigg) $$ \n",
    "\n",
    "where $\\text{sig}(x) = (1+ e^{-x})^{-1}$ is the sigmoid function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sig(x): \n",
    "    return (1/(1+np.exp(-x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# error probablility\n",
    "def prob_incorrect(R, pd, y, b=0):\n",
    "    if y == -1:\n",
    "        py = pd[0]\n",
    "    elif y == 1:\n",
    "        py = pd[1]\n",
    "    else: \n",
    "        assert False, \"expected y in {-1,+1}\"\n",
    "    n = np.sqrt(R)*(1/2.-(py+y*b/2.))\n",
    "    d = np.sqrt(2*(1-py)*py)\n",
    "    if d == 0:\n",
    "        return 0\n",
    "    return sig(n/d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the empirical risk $R_{\\text{emp}}(\\theta)$ in terms of the error probability $\\text{Pr}(\\tilde{m}(\\textbf{x} \\neq m(\\textbf{x}))$ of assigning the incorrect label, based on the decision rule $\\tilde{m}(\\textbf{s}) = \\text{argmax}_y\\{ \\hat{p}_y(\\textbf{s}) \\}$ after R shots, averaged over the samples in the training set $T$. In the binary case this decision rule simplifies to $\\tilde{m}(\\textbf{x}) = y$ whenever $\\hat{p}_y(\\textbf{x}) > \\hat{p}_{-y}(\\textbf{x}) - yb$.\n",
    "\n",
    "$$ R_{\\text{emp}}(\\theta) = \\frac{1}{|T|} \\sum_{\\textbf{x} \\in T} \\text{Pr}(\\tilde{m}(\\textbf{x}) \\neq m(\\textbf{x})).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Remp(x, y, R, T, theta):\n",
    "    risk = 0.0\n",
    "    for i in range(T):\n",
    "        try:\n",
    "            pd = prob_dist(x[i], R, theta)\n",
    "        except ValueError:\n",
    "            return -1\n",
    "        pi = prob_incorrect(R, pd, get_label(y[i]))\n",
    "        risk += pi\n",
    "    return risk/T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SPSA (simultaneous perturbation stochastic approximation) to optimize theta\n",
    "def SPSA(N, R, a, A, c, alpha, gamma, theta):\n",
    "    p = len(theta) # dimension for random perturbation vector\n",
    "    risk = []\n",
    "    for k in range(1,N):\n",
    "        if (100*k/N)%20 == 0:\n",
    "            print(str(100*k/N)+\"%...\")\n",
    "        ak = a/((A+k)**alpha)\n",
    "        ck = c/(k**gamma)\n",
    "        delta = 0.2*np.around(np.random.rand(1,p),2)-1\n",
    "        thetaplus = theta+(ck*delta)\n",
    "        thetaminus = theta-(ck*delta)\n",
    "        yplus = Remp(q_data, labels, R, num_samples, thetaplus[0])\n",
    "        yminus = Remp(q_data, labels, R, num_samples, thetaminus[0])\n",
    "        if yplus - yminus == 0:\n",
    "            pass\n",
    "        elif (yplus == -1 or yminus == -1):\n",
    "            pass\n",
    "        else:\n",
    "            for i,x in enumerate(delta[0]):\n",
    "                if x == 0:\n",
    "                    print(\"got here oops\")\n",
    "                    delta[0][i] = 1e-2\n",
    "            ghat = (yplus - yminus)/(2*ck*delta)\n",
    "            theta = theta-ak*ghat\n",
    "            risk.append(yplus)\n",
    "    print(\"Done\")\n",
    "    return theta, risk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adjust_param(R, delta, i, theta):\n",
    "    thetaplus = theta.copy()\n",
    "    thetaminus = theta.copy()\n",
    "    thetaplus[i*2] += delta\n",
    "    thetaplus[i*2+1] += delta\n",
    "    thetaminus[i*2] -= delta\n",
    "    thetaminus[i*2+1] -= delta    \n",
    "    y = Remp(q_data, labels, R, num_samples, theta)\n",
    "    yplus = Remp(q_data, labels, R, num_samples, thetaplus)\n",
    "    yminus = Remp(q_data, labels, R, num_samples, thetaminus)\n",
    "    if (yplus < y and yplus < yminus and yplus != -1):\n",
    "        #print(\"i = \" + str(i) + \" returning yplus, theta = \" + str(thetaplus))\n",
    "        return thetaplus, yplus\n",
    "    elif (yminus < y and yminus < yplus and yminus != -1):\n",
    "        #print(\"i = \" + str(i) + \" returning yminus, theta = \" + str(thetaminus))\n",
    "        return thetaminus, yminus\n",
    "    else:\n",
    "        #print(\"i = \" + str(i) + \" returning original, theta = \" + str(theta))\n",
    "        return theta, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize_theta(N, R, delta, i, theta, risk):\n",
    "    if N == 0:\n",
    "        return theta, risk\n",
    "    else:\n",
    "        theta_new, risk_new = adjust_param(R, delta, i, theta)\n",
    "        if i == (len(theta)/2)-1:\n",
    "            #print(\"N = \" +  str(N-1))\n",
    "            #print(\"theta = \" + str(theta))\n",
    "            risk_copy = risk.copy()\n",
    "            risk_copy.append(risk_new)\n",
    "            return optimize_theta(N-1, R, delta, 0, theta_new, risk_copy)\n",
    "        else:\n",
    "            return optimize_theta(N, R, delta, i+1, theta_new, risk)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize needed variables and coefficients\n",
    "qubit = cirq.GridQubit(0,0)\n",
    "\n",
    "theta0 = np.random.rand(8) # initialize parameters to be trained\n",
    "N = 100 # number of iterations\n",
    "R = 10 # number of measurement shots\n",
    "num_samples = 20\n",
    "n = 2\n",
    "a = 1e-9 \n",
    "A = 10\n",
    "c = 1e-6\n",
    "alpha = 0.1\n",
    "gamma = 10\n",
    "\n",
    "delta = 0.01\n",
    "\n",
    "# shuffler = np.random.permutation(len(q_data))\n",
    "# q_data = q_data[shuffler]\n",
    "# labels = labels[shuffler]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#theta_prime, risk = optimize_theta(N, R, delta, 0, theta0, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#theta_prime, risk = SPSA(N, R, a, A, c, alpha, gamma, theta0) # new optimized thetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_model(i):\n",
    "    \n",
    "    a,b,c,d,e,f,g,h = sympy.symbols('a b c d e f g h')\n",
    "    theta0 = sympy.Matrix([a,b,c,d,e,f,g,h])\n",
    "    q_model = cirq.Circuit()\n",
    "    q_model.append(W_circuit(theta0))\n",
    "    q_data_input = tf.keras.Input(shape=(), dtype=tf.dtypes.string)\n",
    "    measure_z = tfq.layers.PQC(q_model, cirq.Z(qubit))\n",
    "    measure_zout = measure_z(q_data_input)\n",
    "    \n",
    "    weights = \"cp\"+str(i)+\".cpkt\"\n",
    "    checkpoint_path = \"training/\"+weights\n",
    "    checkpoint_dir = os.path.dirname(checkpoint_path)\n",
    "\n",
    "    classifier = tf.keras.layers.Dense(2, activation=tf.keras.activations.sigmoid)\n",
    "    classifier_output = classifier(measure_zout)\n",
    "    model = tf.keras.Model(inputs=q_data_input, outputs=classifier_output)\n",
    "    model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.1),\n",
    "        loss=tf.keras.losses.BinaryCrossentropy(),metrics=['accuracy'])\n",
    "    \n",
    "    return model, checkpoint_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_help(train_data, train_labels, epochs, i, N):\n",
    "    \n",
    "    x_train_tfcirc = map_plus_tf(expand(train_data))\n",
    "    model, checkpoint_path = build_model(i)\n",
    "    cp_callback = tf.keras.callbacks.ModelCheckpoint(filepath=checkpoint_path,save_weights_only=True,verbose=0)\n",
    "    history = model.fit(x=x_train_tfcirc, y=expand(train_labels), epochs=epochs, verbose=0, callbacks=[cp_callback])\n",
    "    \n",
    "    progress = 100*(i+1)/N\n",
    "    if (progress%10 == 0):\n",
    "        print(str(progress)+\"%...\")\n",
    "    \n",
    "    return checkpoint_path, history.history['loss']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(train_data, train_labels, epochs):\n",
    "    N = len(train_data)\n",
    "    assert(N == len(train_labels))\n",
    "    hst = []\n",
    "    print(\"progress: \")\n",
    "    for i in range(N):\n",
    "        checkpoint_path, history = train_help(train_data[i], train_labels[i], epochs, i, N)\n",
    "        hst.append((checkpoint_path, history))\n",
    "    return hst"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c. Classification phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(x, y, R, theta_prime):\n",
    "    count_correct = 0\n",
    "    for i in range(len(x)):\n",
    "        pd = prob_dist(x[i], R, theta_prime)\n",
    "        label = np.argmax(pd)\n",
    "        if label == y[i][0]:\n",
    "            count_correct +=1\n",
    "    return count_correct/(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(test_data, test_labels, hst):\n",
    "    N = len(test_data)\n",
    "    assert(N == len(test_labels))\n",
    "    accuracy = []\n",
    "    error = []\n",
    "    for i in range(N):\n",
    "        path = hst[i][0]\n",
    "        x_test_tfcirc = map_plus_tf(expand(test_data[i]))\n",
    "        model, _ = build_model(i)\n",
    "        model.load_weights(path)\n",
    "        result = model.evaluate(x_test_tfcirc, expand(test_labels[i]), verbose=0)\n",
    "        accuracy.append(result[1])\n",
    "        error.append(hst[i][1])\n",
    "    return sum(accuracy)/N, lst_average(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid search for optimal parameters\n",
    "params = [0.0001, 0.1, 10]\n",
    "best = 0.0\n",
    "second_best = 0.0\n",
    "optimal_params = [0,0,0,0,0]\n",
    "second_params = [0,0,0,0,0]\n",
    "progress = 0\n",
    "for a in [1e-9, 1e-6, 1e-3]:\n",
    "    for A in [10, 100]:\n",
    "        for c in [1e-9, 1e-6, 1e-3]:\n",
    "            for alpha in [0.001, 0.1, 1]:\n",
    "                for gamma in [0.0001, 0.1, 10]:\n",
    "                    theta_prime = SPSA(N, R, a, A, c, alpha, gamma, theta0)[0]\n",
    "                    accuracy = classify(q_data, labels, 10, theta_prime)\n",
    "                    if accuracy > best:\n",
    "                        best = accuracy\n",
    "                        optimal_params = [a, A, c, alpha, gamma]\n",
    "                    elif accuracy > second_best:\n",
    "                        second_best = accuracy\n",
    "                        second_params = [a, A, c, alpha, gamma]\n",
    "                    #progress += 1\n",
    "                    #if progress%27 == 0:\n",
    "                        #print(str(100*progress/162)+\"%...\")\n",
    "# print(\"best=\"+str(best))\n",
    "# print(optimal_params)\n",
    "# print(\"second best=\"+str(second_best))\n",
    "# print(second_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test on unit-circle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "circle_data, circle_labels = unit_circle_data(t=30,n=2,t0=-np.pi/2+0.04)\n",
    "\n",
    "x_blue = []\n",
    "y_blue = []\n",
    "x_red = []\n",
    "y_red = []\n",
    "for i in range(len(circle_data)):\n",
    "    if circle_labels[i][0] == 0:\n",
    "        x_red.append(circle_data[i][0])\n",
    "        y_red.append(circle_data[i][1])\n",
    "    else:\n",
    "        x_blue.append(circle_data[i][0])\n",
    "        y_blue.append(circle_data[i][1])\n",
    "\n",
    "plt.plot(x_red, y_red,'o', color=\"red\")\n",
    "plt.plot(x_blue, y_blue,'o')\n",
    "plt.grid()\n",
    "plt.savefig('unit_circle')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "progress: \n",
      "10.0%...\n",
      "20.0%...\n",
      "30.0%...\n",
      "40.0%...\n",
      "50.0%...\n",
      "60.0%...\n",
      "70.0%...\n",
      "80.0%...\n",
      "90.0%...\n",
      "100.0%...\n"
     ]
    }
   ],
   "source": [
    "history = train(circle_data, circle_labels, epochs=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy = 1.0\n"
     ]
    }
   ],
   "source": [
    "accuracy, error = test(circle_data, circle_labels, history)\n",
    "print(\"accuracy = \"+str(accuracy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(error)\n",
    "plt.title(\"Unit-Circle Binary Classification\")\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.savefig('Unit_Circle_Classification')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test on unit-sphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_a = 1\n",
    "theta_b = 4\n",
    "num_samples = 50\n",
    "bloch_data, bloch_labels, bloch_p = unit_sphere_data(theta_a, theta_b, num_samples)\n",
    "bloch_data_test, bloch_labels_test, _, = unit_sphere_data(theta_a, theta_b, num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# View the dataset on the Bloch sphere using qutip\n",
    "bloch = qutip.Bloch()\n",
    "bloch.sphere_alpha = 0.0\n",
    "bloch.frame_alpha = 0.05\n",
    "bloch.vector_color[0] = bloch.point_color[0] = \"#a4c2f4ff\"\n",
    "bloch.vector_color[1] = bloch.point_color[1] = \"#ffab40ff\"\n",
    "bloch.add_points(bloch_p[\"a\"])\n",
    "bloch.add_points(bloch_p[\"b\"])\n",
    "vec = [[np.cos(theta_a),0,np.sin(theta_a)]]\n",
    "bloch.add_vectors(vec)\n",
    "vec = [[np.cos(theta_b),0,np.sin(theta_b)]]\n",
    "bloch.add_vectors(vec)\n",
    "bloch.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "progress: \n",
      "10.0%...\n",
      "20.0%...\n",
      "30.0%...\n",
      "40.0%...\n",
      "50.0%...\n",
      "60.0%...\n",
      "70.0%...\n",
      "80.0%...\n",
      "90.0%...\n",
      "100.0%...\n"
     ]
    }
   ],
   "source": [
    "history = train(bloch_data, bloch_labels, epochs=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy = 0.98\n"
     ]
    }
   ],
   "source": [
    "accuracy, error = test(bloch_data, bloch_labels, history)\n",
    "print(\"accuracy = \"+str(accuracy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(error)\n",
    "plt.title(\"Unit-Sphere Binary Classification\")\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.savefig('Unit_Sphere_Classification')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Binary label classification for two numbers from the MNIST dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Future work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the MNIST dataset\n",
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
    "\n",
    "# Rescale the images from [0,255] to the [0.0,1.0] range.\n",
    "x_train, x_test = x_train[..., np.newaxis]/255.0, x_test[..., np.newaxis]/255.0\n",
    "\n",
    "print(\"Number of original training examples:\", len(x_train))\n",
    "print(\"Number of original test examples:\", len(x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# With one readout bit we cannot label ten digits so instead we pick two digits, say 3 and 6. So filter dataset \n",
    "# to keep just 3s and 6s and convert label (y) to boolean: 3=True, 6=False\n",
    "def filter_36(x, y):\n",
    "    keep = (y == 3) | (y == 6)\n",
    "    x, y = x[keep], y[keep]\n",
    "    y = y == 3\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, y_train = filter_36(x_train, y_train)\n",
    "x_test, y_test = filter_36(x_test, y_test)\n",
    "\n",
    "print(\"Number of filtered training examples:\", len(x_train))\n",
    "print(\"Number of filtered test examples:\", len(x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show first example\n",
    "print(y_train[0])\n",
    "\n",
    "plt.imshow(x_train[0, :, :, 0])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Can only easily handle say 16 bit data using a classical simulator of a 17 qubit quantum computer with one \n",
    "# readout bit, so resize images from 28x28 to 4x4\n",
    "x_train_small = tf.image.resize(x_train, (4,4)).numpy()\n",
    "x_test_small = tf.image.resize(x_test, (4,4)).numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show first example after resize\n",
    "print(y_train[0])\n",
    "\n",
    "plt.imshow(x_train_small[0,:,:,0], vmin=0, vmax=1)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filter the dataset to remove images that are labeled as belonging to both classes, as suggested in Farhi et al. \n",
    "# Section 3.3 Learning to Distinguish Digits. Note: this filtering will not totally prevent the model from \n",
    "# receiving contradictory training examples.\n",
    "def remove_contradicting(xs, ys):\n",
    "    mapping = collections.defaultdict(set)\n",
    "    # Determine the set of labels for each unique image:\n",
    "    for x,y in zip(xs,ys):\n",
    "        mapping[tuple(x.flatten())].add(y)\n",
    "\n",
    "    new_x = []\n",
    "    new_y = []\n",
    "    for x,y in zip(xs, ys):\n",
    "        labels = mapping[tuple(x.flatten())]\n",
    "        if len(labels) == 1:\n",
    "            new_x.append(x)\n",
    "            new_y.append(labels.pop())\n",
    "        else:\n",
    "            # Throw out images that match more than one label.\n",
    "            pass\n",
    "\n",
    "    num_3 = sum(1 for value in mapping.values() if True in value)\n",
    "    num_6 = sum(1 for value in mapping.values() if False in value)\n",
    "    num_both = sum(1 for value in mapping.values() if len(value) == 2)\n",
    "\n",
    "    print(\"Number of unique images:\", len(mapping.values()))\n",
    "    print(\"Number of 3s: \", num_3)\n",
    "    print(\"Number of 6s: \", num_6)\n",
    "    print(\"Number of contradictory images: \", num_both)\n",
    "    print()\n",
    "    print(\"Initial number of examples: \", len(xs))\n",
    "    print(\"Remaining non-contradictory examples: \", len(new_x))\n",
    "\n",
    "    return np.array(new_x), np.array(new_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_nocon, y_train_nocon = remove_contradicting(x_train_small, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To process images using a quantum computer, represent each pixel with a qubit, with the state depending on\n",
    "# the value of the pixel. First, convert to a binary encoding.\n",
    "THRESHOLD = 0.5\n",
    "\n",
    "x_train_bin = np.array(x_train_nocon > THRESHOLD, dtype=np.float32)\n",
    "x_test_bin = np.array(x_test_small > THRESHOLD, dtype=np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# def convert_to_circuit(image, n=4):\n",
    "#     x = image.flatten()\n",
    "#     qs = [cirq.GridQubit(i, 0) for i in range(n)]\n",
    "#     circuit = cirq.Circuit()\n",
    "#     circuit.append(feature_map(x, 4))\n",
    "#     circuit.append(W_circuit)\n",
    "#     return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_circ = [convert_to_circuit(x) for x in x_train_bin]\n",
    "x_test_circ = [convert_to_circuit(x) for x in x_test_bin]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "SVGCircuit(x_train_circ[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# x_train_tfcirc = tfq.convert_to_tensor(x_train_circ)\n",
    "# x_test_tfcirc = tfq.convert_to_tensor(x_test_circ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tfq.util.get_supported_gates()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}