other/StatePreparationTutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# State preparation algorithm tutorial\n",
    "\n",
    "This tutorial shows:\n",
    "- How to define a quantum gate not included in Tequila's gate set\n",
    "- How to construct a parametrized quantum circuit\n",
    "- How to compute the fidelity between two states\n",
    "- How to train a parametrized quantum circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import everthing you need\n",
    "import tequila as tq\n",
    "import numpy as np\n",
    "import random\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum gate construction\n",
    "\n",
    "Sometimes, one may need to use a particular quantum gate that is not included in the basic gate set. If we know the decomposition of this gate in terms of Tequila's gates, we can define a function that runs a small quantum circuit that constructs this particular gate.  \n",
    "  \n",
    "As an example, let's define the general one-qubit unitary gate  \n",
    "$$ U(\\theta,\\phi,\\lambda) = \\left( \\begin{array}{cc}\n",
    " e^{-\\frac{1}{2} i (\\lambda +\\phi )} \\cos \\left(\\frac{\\theta }{2}\\right) & -e^{\\frac{1}{2} i (\\lambda -\\phi )} \\sin \\left(\\frac{\\theta }{2}\\right) \\\\\n",
    " e^{-\\frac{1}{2} i (\\lambda -\\phi )} \\sin \\left(\\frac{\\theta }{2}\\right) & e^{\\frac{1}{2} i (\\lambda +\\phi )} \\cos \\left(\\frac{\\theta }{2}\\right) \\end{array} \\right) = R_{z}\\left(\\phi\\right) R_{y}\\left(\\theta\\right) R_{z}\\left(\\lambda\\right) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ───Rz(0.25π)───Ry(π)───Rz(0.5π)───\n"
     ]
    }
   ],
   "source": [
    "# q0 = target qubit\n",
    "def U(th,phi,lam,q0):\n",
    "    ugate = tq.gates.Rz(target=q0,angle=phi) + tq.gates.Ry(target=q0,angle=th) + tq.gates.Rz(target=q0,angle=lam)\n",
    "    return ugate\n",
    "# draw the circuit for some (th,phi,lam) for qubit \"0\"\n",
    "tq.draw(U(np.pi, np.pi/4.0, np.pi/2.0, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can construct a multi-qubit gate. For instance, the controlled-phase gate:  \n",
    "$$ CPh\\left(\\varphi \\right) = \\left(\n",
    "\\begin{array}{cccc}\n",
    " 1 & 0 & 0 & 0 \\\\\n",
    " 0 & 1 & 0 & 0 \\\\\n",
    " 0 & 0 & 1 & 0 \\\\\n",
    " 0 & 0 & 0 & e^{i \\varphi } \\\\\n",
    "\\end{array}\n",
    "\\right)  = e^{i\\phi/4} \\left(R_{z}\\left(\\varphi/2\\right)\\otimes\\mathbb{I}\\right)CR_{z}\\left(\\phi/2\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ───Rz(0.25π)───@───────────\n",
      "                  │\n",
      "1: ───────────────Rz(0.25π)───\n"
     ]
    }
   ],
   "source": [
    "# q0 = control qubit\n",
    "# q1 = target qubit\n",
    "def CPh(phi,q0,q1):\n",
    "    cph = tq.gates.Rz(target=q0, angle=phi/2) + tq.gates.CRz(control=q0, target=q1, angle=phi/2)\n",
    "    return cph\n",
    "# draw the circuit for some varphi for qubits \"0\" and \"1\"\n",
    "tq.draw(CPh(np.pi/2,0,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gate defined is equal to $CPh(\\varphi)$ gate up to a global phase."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the fidelity\n",
    "\n",
    "Let's compute the fidelity between two states, one constructed from a string (target state $|\\tilde{\\psi}\\rangle$) and other obtained from a given quantum circuit, $|\\psi\\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target state:  +0.7071|00> +0.7071|11> \n"
     ]
    }
   ],
   "source": [
    "# Target state example: Bell state\n",
    "wfn_targ = tq.QubitWaveFunction.from_string(string=\"1.0*|00> + 1.0*|11>\")\n",
    "wfn_targ = wfn_targ.normalize() # Remember to normalize the state!!! \n",
    "print(\"target state: \", wfn_targ) # Print the wavefunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "circuit state:  +0.9641e^(-0.3614πi)|00> +0.0247e^(+0.8932πi)|10> +0.2462e^(-0.3614πi)|01> +0.0967e^(-0.1068πi)|11> \n",
      "circuit diagram: \n",
      "0: ───Rz(0.5π)───Ry(0.064π)───Rz(0.159π)───@───Rz(0.064π)───@─────────────────────────\n",
      "                                           │                │\n",
      "1: ────────────────────────────────────────X────────────────Rz(0.064π)───Ry(0.159π)───\n"
     ]
    }
   ],
   "source": [
    "# Quantum circuit\n",
    "q0 = 0\n",
    "q1 = 1\n",
    "qc = U(0.2, np.pi/2.0, 0.5, q0) + tq.gates.CNOT(target=q1,control=q0) + CPh(0.4,q0,q1) + tq.gates.Ry(target=q1,angle=0.5)\n",
    "wfn_qc = tq.simulate(qc) # Simulate the wavefunction \n",
    "print(\"circuit state: \", wfn_qc) \n",
    "print(\"circuit diagram: \")\n",
    "tq.draw(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two ways to compute the fidelity of these two states. The natural way to do it, in case we have both wavefunctions, is just by computing the inner product of these two states:\n",
    "$$ F\\left(|\\psi\\rangle, |\\tilde{\\psi}\\rangle\\right) = |\\langle \\psi | \\tilde{\\psi} \\rangle|^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fidelity =  0.5343666886804502\n"
     ]
    }
   ],
   "source": [
    "fidelity = abs(wfn_targ.inner(wfn_qc))**2\n",
    "print('fidelity = ', fidelity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second method consists on computing the expected value of the target state density matrix operator $\\rho = |\\tilde{\\psi}\\rangle\\langle\\tilde{\\psi}|$, i.e. \n",
    "$$ F\\left(|\\psi\\rangle, |\\tilde{\\psi}\\rangle\\right) = \\langle \\psi | \\rho |\\psi\\rangle = \\langle \\psi |\\tilde{\\psi}\\rangle \\langle \\tilde{\\psi} |\\psi\\rangle = |\\langle \\psi | \\tilde{\\psi} \\rangle|^2$$\n",
    "\n",
    "To do so, we need to write the density operator in terms of pauli matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+0.2500+0.2500Z(0)Z(1)+0.2500X(0)X(1)-0.2500Y(0)Y(1)\n"
     ]
    }
   ],
   "source": [
    "# construct the density operator of target state\n",
    "rho_targ =  tq.paulis.Projector(wfn=wfn_targ)\n",
    "print(rho_targ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we trait this operator as a Hamiltonian and compute the objective expectation value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fidelity =  0.5343666886804503\n"
     ]
    }
   ],
   "source": [
    "O = tq.Objective.ExpectationValue(U=qc, H=rho_targ)\n",
    "fidelity= tq.simulate(O)\n",
    "print('fidelity = ', fidelity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct a parametrized quantum circuit \n",
    "\n",
    "Parametrized quantum circuits (PQC) are usually defined with a small gate set. Same gates are used along the circuit with different parameters, which makes more natural to define them as vectors. In the following example, we construct a parametrized quantum circuit of two qubits using the $U(\\theta,\\phi,\\lambda)$ (defined above) and a CNOT gate. Parameters are identified with the vectors $\\vec{\\theta}$, $\\vec{\\phi}$ and $\\vec{\\lambda}$. The circuit ansatz consist on applying general unitary gates on both qubits, then entangle them with the CNOT gate, and finally apply another unitary gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#qubits\n",
    "q0=0\n",
    "q1=1\n",
    "\n",
    "#define variables\n",
    "th = [tq.Variable(name='theta_{}'.format(i)) for i in range(0,4)]\n",
    "phi = [tq.Variable(name='phi_{}'.format(i)) for i in range(0,4)]\n",
    "lam = [tq.Variable(name='lam_{}'.format(i)) for i in range(0,4)]\n",
    "\n",
    "# PQC\n",
    "pqc  = U(th[0],phi[0],lam[0],q0) + U(th[1],phi[1],lam[1],q1) \n",
    "pqc += tq.gates.CNOT(control = q0, target = q1)\n",
    "pqc += U(th[2],phi[2],lam[2],q0) + U(th[3],phi[3],lam[3],q1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ───Rz(0.318309886183791*pi*f((phi_0,))_0)───Ry(0.318309886183791*pi*f((theta_0,))_1)───Rz(0.318309886183791*pi*f((lam_0,))_2)───@───Rz(0.318309886183791*pi*f((phi_2,))_6)───Ry(0.318309886183791*pi*f((theta_2,))_7)────Rz(0.318309886183791*pi*f((lam_2,))_8)────\n",
      "                                                                                                                                   │\n",
      "1: ───Rz(0.318309886183791*pi*f((phi_1,))_3)───Ry(0.318309886183791*pi*f((theta_1,))_4)───Rz(0.318309886183791*pi*f((lam_1,))_5)───X───Rz(0.318309886183791*pi*f((phi_3,))_9)───Ry(0.318309886183791*pi*f((theta_3,))_10)───Rz(0.318309886183791*pi*f((lam_3,))_11)───\n"
     ]
    }
   ],
   "source": [
    "# Draw the circuit \n",
    "n_th = len(th)\n",
    "n_phi = len(phi)\n",
    "n_lam = len(lam)\n",
    "\n",
    "tq.draw(pqc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize random values for the variables\n",
    "th0 ={key : random.uniform(0, np.pi) for key in th}\n",
    "phi0 = {key: random.uniform(0, np.pi) for key in phi}\n",
    "lam0 = {key: random.uniform(0, np.pi) for key in lam}\n",
    "all_values = {**th0, **phi0, **lam0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{theta_0: 1.9400742456012434,\n",
       " theta_1: 0.18708644852210973,\n",
       " theta_2: 1.6718785378724963,\n",
       " theta_3: 2.9210555160438036}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "th0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ───Rz(0.318309886183791*pi*f((phi_0,))_0)───Ry(0.318309886183791*pi*f((theta_0,))_1)───Rz(0.318309886183791*pi*f((lam_0,))_2)───@───Rz(0.318309886183791*pi*f((phi_2,))_6)───Ry(0.318309886183791*pi*f((theta_2,))_7)────Rz(0.318309886183791*pi*f((lam_2,))_8)────\n",
      "                                                                                                                                   │\n",
      "1: ───Rz(0.318309886183791*pi*f((phi_1,))_3)───Ry(0.318309886183791*pi*f((theta_1,))_4)───Rz(0.318309886183791*pi*f((lam_1,))_5)───X───Rz(0.318309886183791*pi*f((phi_3,))_9)───Ry(0.318309886183791*pi*f((theta_3,))_10)───Rz(0.318309886183791*pi*f((lam_3,))_11)───\n"
     ]
    }
   ],
   "source": [
    "# in case you want to look at the circuit with specific values\n",
    "tq.draw(pqc, variables=all_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now compute the fidelity of the output state of this PQC with some two-qubit random state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "random state:  +0.5890e^(-0.1420πi)|00> +0.4439e^(-0.2940πi)|01> +0.5727e^(-0.7747πi)|10> +0.3577e^(-0.4773πi)|11> \n"
     ]
    }
   ],
   "source": [
    "# 2-qubit random state wavefunction from array\n",
    "rand_array = np.asarray([random.uniform(-1, 1)+1j*random.uniform(-1, 1) for x in range(1,5)])\n",
    "wfn_rand = tq.QubitWaveFunction.from_array(rand_array)\n",
    "wfn_rand = wfn_rand.normalize()\n",
    "print(\"random state: \", wfn_rand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can compute the fidelity of these two states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fidelity =  0.18646916747892608\n",
      "fidelity =  0.18646916747892608\n"
     ]
    }
   ],
   "source": [
    "# Fidelity method 1: using inner product\n",
    "wfn_pqc = tq.simulate(pqc, variables=all_values) # compute the PQC wavefunction\n",
    "fid_rand = abs(wfn_rand.inner(wfn_pqc))**2\n",
    "print(\"fidelity = \", fid_rand)\n",
    "\n",
    "# Fidelity method 2: using the the density matrix as objective\n",
    "rho_rand = tq.paulis.Projector(wfn=wfn_rand) # density operator target state\n",
    "fid_pqc = tq.Objective.ExpectationValue(U=pqc, H=rho_rand)\n",
    "print(\"fidelity = \", tq.simulate(fid_pqc, variables = all_values))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State preparation algorithm\n",
    "\n",
    "This algorithm minimizes the fidelity between a PQC and a the target state. Since the optimizer only minimizes, we will minimize the infidelity, i.e. $ 1 - F(|\\tilde{\\psi}\\rangle,|\\psi\\rangle)$.\n",
    "\n",
    "We can use any of the two methods to compute the infidelity, but it will be more convenient to use the second one.\n",
    "\n",
    "The goal of this example is to obtain a quantum circuit that generates the Bell state\n",
    "$$ |\\tilde{\\psi}\\rangle = \\frac{1}{\\sqrt{2}}\\left(|00\\rangle + |11\\rangle\\right) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bell state:  +0.7071|00> +0.7071|11> \n"
     ]
    }
   ],
   "source": [
    "# Bell state wavefunction from array\n",
    "bell_array = np.asarray([1,0,0,1])\n",
    "wfn_bell = tq.QubitWaveFunction.from_array(bell_array)\n",
    "wfn_bell = wfn_targ.normalize()\n",
    "print(\"Bell state: \", wfn_bell)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
      "backend         : qulacs\n",
      "samples         : None\n",
      "save_history    : True\n",
      "noise           : None\n",
      "\n",
      "Method          : TNC\n",
      "Objective       : 1 expectationvalues\n",
      "bounds          : {theta_0: [0, 6.283185307179586], theta_1: [0, 6.283185307179586], theta_2: [0, 6.283185307179586], theta_3: [0, 6.283185307179586], phi_0: [0, 6.283185307179586], phi_1: [0, 6.283185307179586], phi_2: [0, 6.283185307179586], phi_3: [0, 6.283185307179586], lam_0: [0, 6.283185307179586], lam_1: [0, 6.283185307179586], lam_2: [0, 6.283185307179586], lam_3: [0, 6.283185307179586]}\n",
      "gradient        : 36 expectationvalues\n",
      "\n",
      "active variables : 12\n",
      "\n",
      "E=+0.97978838  angles= {theta_1: 0.18708644852210973, phi_2: 0.814058741440068, theta_2: 1.6718785378724963, phi_0: 0.2345203432452239, lam_2: 1.4159205992271224, lam_3: 0.13148303719773408, lam_1: 2.2681484065626556, lam_0: 2.3054575437873366, theta_0: 1.9400742456012434, phi_3: 1.535128381817424, theta_3: 2.9210555160438036, phi_1: 0.3289124675729237}  samples= None\n",
      "E=+0.97978833  angles= {theta_1: 0.18708646000189555, phi_2: 0.814058833791607, theta_2: 1.6718785383234156, phi_0: 0.23452034324522408, lam_2: 1.415920500429734, lam_3: 0.13148293840034553, lam_1: 2.2681483849790918, lam_0: 2.305457636138876, theta_0: 1.9400743288187945, phi_3: 1.5351284785470272, theta_3: 2.92105543325136, phi_1: 0.3289124675729238}  samples= None\n",
      "E=+0.85149465  angles= {theta_1: 0.2023641517385193, phi_2: 0.9369634159388589, theta_2: 1.6724786370702835, phi_0: 0.23452034324522408, lam_2: 1.2844375620293884, lam_3: 0.0, lam_1: 2.2394242408406675, lam_0: 2.4283622182861277, theta_0: 2.0508230875941647, phi_3: 1.6638595378398793, theta_3: 2.8108724224129618, phi_1: 0.3289124675729238}  samples= None\n",
      "E=+0.85149431  angles= {theta_1: 0.2023642802237453, phi_2: 0.9369636874231029, theta_2: 1.6724786704097288, phi_0: 0.23452034324522408, lam_2: 1.2844372717859731, lam_3: 0.0, lam_1: 2.2394241923699836, lam_0: 2.4283624897703713, theta_0: 2.050823147531501, phi_3: 1.6638598242833953, theta_3: 2.8108721796234564, phi_1: 0.3289124675729238}  samples= None\n",
      "E=+0.81863091  angles= {theta_1: 0.770960170998253, phi_2: 2.138384505960894, theta_2: 1.82001836892913, phi_0: 0.23452034324522408, lam_2: 0.0, lam_3: 0.0, lam_1: 2.0249230194821095, lam_0: 3.6297833083081628, theta_0: 2.3160686088759577, phi_3: 2.931481100380665, theta_3: 1.736436469372996, phi_1: 0.32891246757292425}  samples= None\n",
      "E=+0.16575584  angles= {theta_1: 0.48666216136838614, phi_2: 1.5376739609498764, theta_2: 1.7462485029997068, phi_0: 0.23452034324522408, lam_2: 0.642218781014694, lam_3: 0.0, lam_1: 2.1321736301613887, lam_0: 3.0290727632971453, theta_0: 2.183445848235061, phi_3: 2.297670319110272, theta_3: 2.273654445892979, phi_1: 0.32891246757292425}  samples= None\n",
      "E=+0.16575572  angles= {theta_1: 0.48666227262304407, phi_2: 1.5376739611263435, theta_2: 1.7462486073305992, phi_0: 0.23452034324522408, lam_2: 0.6422185127771218, lam_3: 0.0, lam_1: 2.132173524155168, lam_0: 3.029072763473612, theta_0: 2.1834456081792064, phi_3: 2.2976704050408365, theta_3: 2.273654352135036, phi_1: 0.32891246757292425}  samples= None\n",
      "E=+0.16575582  angles= {theta_1: 0.4866621494975738, phi_2: 1.5376739299684588, theta_2: 1.7462484283132789, phi_0: 0.23452034324522453, lam_2: 0.6422187020957812, lam_3: 0.0, lam_1: 2.132173575551841, lam_0: 3.0290727323157274, theta_0: 2.1834458264374574, phi_3: 2.29767031979944, theta_3: 2.2736544354244668, phi_1: 0.32891246757292425}  samples= None\n",
      "E=+0.16575574  angles= {theta_1: 0.48666227988751487, phi_2: 1.5376737685485447, theta_2: 1.7462481752768262, phi_0: 0.23452034324522408, lam_2: 0.6422185089202155, lam_3: 0.0, lam_1: 2.1321733759939048, lam_0: 3.0290725708958157, theta_0: 2.1834457798304143, phi_3: 2.2976701916997615, theta_3: 2.273654181670317, phi_1: 0.32891246757292425}  samples= None\n",
      "E=+0.08113876  angles= {theta_1: 0.5427053432896312, phi_2: 1.3917605441194907, theta_2: 1.499116903717589, phi_0: 0.2345203442100483, lam_2: 0.0, lam_3: 0.0, lam_1: 1.767930638584934, lam_0: 2.8831593468762438, theta_0: 1.8389547309123337, phi_3: 2.387441218774743, theta_3: 2.129888432702298, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.08726450  angles= {theta_1: 0.5146837523290086, phi_2: 1.4647172525346837, theta_2: 1.622682703358648, phi_0: 0.23452034372763642, lam_2: 0.32110939050734677, lam_3: 0.0, lam_1: 1.9500521343731614, lam_0: 2.9561160550866945, theta_0: 2.011200289573697, phi_3: 2.342555768942508, theta_3: 2.2017714392976386, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.07436449  angles= {theta_1: 0.5286945478093199, phi_2: 1.4282388983270873, theta_2: 1.5608998035381185, phi_0: 0.23452034396884214, lam_2: 0.1605546952536736, lam_3: 0.0, lam_1: 1.8589913864790477, lam_0: 2.919637700981469, theta_0: 1.9250775102430155, phi_3: 2.3649984938586255, theta_3: 2.165829935999968, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.07436447  angles= {theta_1: 0.5286945539738492, phi_2: 1.4282388811537676, theta_2: 1.5608997893806995, phi_0: 0.23452034396884214, lam_2: 0.16055465306835526, lam_3: 1.3108153540386525e-07, lam_1: 1.8589913525322808, lam_0: 2.91963768380815, theta_0: 1.9250774762797043, phi_3: 2.3649984869514364, theta_3: 2.165829920201008, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.07436448  angles= {theta_1: 0.5286945569985897, phi_2: 1.4282388919853437, theta_2: 1.5608998117277175, phi_0: 0.2345203439688408, lam_2: 0.1605546850756836, lam_3: 0.0, lam_1: 1.8589913740684647, lam_0: 2.9196376946397256, theta_0: 1.9250774978573206, phi_3: 2.364998484604847, theta_3: 2.1658299247020203, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.07436449  angles= {theta_1: 0.5286945452911498, phi_2: 1.428238899428805, theta_2: 1.5608998006492636, phi_0: 0.23452034396883725, lam_2: 0.16055469563179736, lam_3: 0.0, lam_1: 1.858991377976206, lam_0: 2.9196377020831874, theta_0: 1.9250775002608946, phi_3: 2.36499848958337, theta_3: 2.165829937176665, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.07436449  angles= {theta_1: 0.5286945451915859, phi_2: 1.428238905615189, theta_2: 1.5608998115570107, phi_0: 0.23452034396881904, lam_2: 0.16055470981843056, lam_3: 0.0, lam_1: 1.8589913754294178, lam_0: 2.9196377082695713, theta_0: 1.9250775033341594, phi_3: 2.3649984844601795, theta_3: 2.1658299404436274, phi_1: 0.3289124675729247}  samples= None\n",
      "E=+0.00709803  angles= {theta_1: 0.5606696392198067, phi_2: 1.3640003738170998, theta_2: 1.529935097807913, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.2190515959374082, lam_1: 1.5777560538300686, lam_0: 2.855399178375335, theta_0: 1.6224789494137757, phi_3: 2.2321879608371633, theta_3: 2.0777091495701763, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00709803  angles= {theta_1: 0.5606696392039807, phi_2: 1.364000371409756, theta_2: 1.5299350986021882, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.2190516011976067, lam_1: 1.577756054985087, lam_0: 2.855399175967991, theta_0: 1.6224789474072632, phi_3: 2.232187956728475, theta_3: 2.077709148018407, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00709803  angles= {theta_1: 0.5606696404457652, phi_2: 1.3640003758712678, theta_2: 1.5299351003827062, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.21905159868476298, lam_1: 1.5777560471059562, lam_0: 2.855399180429503, theta_0: 1.6224789469409322, phi_3: 2.232187960753988, theta_3: 2.077709146686549, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00004723  angles= {theta_1: 0.5682047456782451, phi_2: 1.3432743639677562, theta_2: 1.557352684944983, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.310121390877224, lam_1: 1.5513916250917585, lam_0: 2.8346731681628277, theta_0: 1.5787249237101468, phi_3: 2.1741055936153617, theta_3: 2.037726258960663, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00004723  angles= {theta_1: 0.5682047032403403, phi_2: 1.3432744140182464, theta_2: 1.5573526406157854, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.3101213945509178, lam_1: 1.5513917157632686, lam_0: 2.834673218213318, theta_0: 1.5787247953018517, phi_3: 2.1741056465643167, theta_3: 2.037726285914776, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00004723  angles= {theta_1: 0.5682047586305501, phi_2: 1.3432743399327565, theta_2: 1.5573527054670637, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.31012139399891403, lam_1: 1.551391739330553, lam_0: 2.834673144127828, theta_0: 1.5787248270916314, phi_3: 2.174105566104301, theta_3: 2.037726246757807, phi_1: 0.3289124675729256}  samples= None\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E=+0.00004723  angles= {theta_1: 0.5682047495405631, phi_2: 1.3432743674824092, theta_2: 1.5573526873581178, phi_0: 0.2345202638142112, lam_2: 0.0, lam_3: 0.3101213860430594, lam_1: 1.551391698079409, lam_0: 2.8346731716774802, theta_0: 1.5787249436490394, phi_3: 2.174105598157262, theta_3: 2.0377262555491673, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00004723  angles= {theta_1: 0.5682047276855315, phi_2: 1.3432743522593686, theta_2: 1.5573526673001021, phi_0: 0.23452026381420987, lam_2: 0.0, lam_3: 0.31012140049050085, lam_1: 1.5513916613688044, lam_0: 2.834673156454439, theta_0: 1.5787249381088497, phi_3: 2.1741055840078936, theta_3: 2.0377262793832838, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00000001  angles= {theta_1: 0.5670536193843128, phi_2: 1.344372507559821, theta_2: 1.5563466101327212, phi_0: 0.23452026373299661, lam_2: 0.0, lam_3: 0.3100936072527172, lam_1: 1.57078726889731, lam_0: 2.8357713116589265, theta_0: 1.5707849336977442, phi_3: 2.1753215680989224, theta_3: 2.038346318435992, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00000001  angles= {theta_1: 0.5670536068271934, phi_2: 1.3443725425168338, theta_2: 1.5563466667480204, phi_0: 0.23452026373299661, lam_2: 1.2136837801435263e-07, lam_3: 0.3100937286210952, lam_1: 1.5707872705321904, lam_0: 2.8357713466159393, theta_0: 1.5707849408264822, phi_3: 2.175321526205309, theta_3: 2.038346254387977, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00000001  angles= {theta_1: 0.5670536225433711, phi_2: 1.3443725161628017, theta_2: 1.5563466125885126, phi_0: 0.23452026373299617, lam_2: 0.0, lam_3: 0.3100936053340444, lam_1: 1.570787270325883, lam_0: 2.8357713202619075, theta_0: 1.5707849375850738, phi_3: 2.175321575631915, theta_3: 2.038346313459311, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00000000  angles= {theta_1: 0.5670461281848205, phi_2: 1.3444030838073346, theta_2: 1.5563897167244758, phi_0: 0.23452026373288248, lam_2: 8.839510847957754e-05, lam_3: 0.3101820023612252, lam_1: 1.5707892723719388, lam_0: 2.835801887906597, theta_0: 1.5707923609973422, phi_3: 2.175294895597056, theta_3: 2.0382963240591634, phi_1: 0.3289124675729256}  samples= None\n",
      "E=+0.00000000  angles= {theta_1: 0.5670461281848205, phi_2: 1.3444030838073346, theta_2: 1.5563897167244758, phi_0: 0.23452026373288248, lam_2: 8.839510847957754e-05, lam_3: 0.3101820023612252, lam_1: 1.5707892723719388, lam_0: 2.835801887906597, theta_0: 1.5707923609973422, phi_3: 2.175294895597056, theta_3: 2.0382963240591634, phi_1: 0.3289124675729256}  samples= None\n",
      "Infidelity =  7.946199254149633e-12\n",
      "Fidelity =  0.9999999999920538\n",
      "Execution time:  7.999989986419678  sec\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "rho_bell = tq.paulis.Projector(wfn=wfn_bell) # density operator\n",
    "\n",
    "# we take as initial values ther random values generated above\n",
    "initial_values = all_values\n",
    "# Infidelity = 1 - Fidelity\n",
    "inf =  1.0 - tq.Objective.ExpectationValue(U=pqc, H=rho_bell)\n",
    "\n",
    "# we can define the bounds on the parameters\n",
    "# Caution! Not all minimizers accept bounds! In this example, we use 'TNC' minimizer.\n",
    "# bounds should be defined in a dictionary form, as initial_values\n",
    "max_angles = 2*np.pi\n",
    "min_angles = 0\n",
    "bnds_list = [[min_angles,max_angles]]\n",
    "for i in range(0, len(all_values)):\n",
    "    bnds_list.append([min_angles,max_angles])\n",
    "bnds = dict(zip([str(th[i]) for i in range(0,n_th)],bnds_list))\n",
    "bnds = {**bnds, **dict(zip([str(phi[i]) for i in range(0,n_phi)],bnds_list))}\n",
    "bnds = {**bnds, **dict(zip([str(lam[i]) for i in range(0,n_lam)],bnds_list))}\n",
    "\n",
    "# set \"silent = True\" to avoid printing all the minimization process\n",
    "t0 = time.time()\n",
    "infid = tq.optimizer_scipy.minimize(objective=inf, initial_values=initial_values, method = 'TNC', method_bounds = bnds, silent=True)\n",
    "t1 = time.time()\n",
    "\n",
    "print(\"Infidelity = \", infid.energy)\n",
    "print(\"Fidelity = \", 1.0-infid.energy)\n",
    "print(\"Execution time: \", t1-t0, \" sec\" )\n",
    "\n",
    "print(infid.history.plot('energies', label='fidelity'))\n",
    "print(infid.history.plot('angles', label=\"\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "# some example on how to use the convenience plotter\n",
    "infid.history.plot([\"angles\", \"gradients\"], key=[\"lam_1\", \"lam_2\"], labels=[\"\", \"grad\"], title=\"Some Data\", ylim=(-1.0, 3.0), xlim=(-3, 5), loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# in case you want to extract the history data\n",
    "history_phi_0 = infid.history.extract_angles(\"phi_0\")\n",
    "history_energies = infid.history.extract_energies()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that the final state solution is the Bell state up to a global phase:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final state solution: \n",
      "+0.7071e^(+0.6603πi)|00> +0.0000i|10> -0.0000|01> +0.7071e^(+0.6603πi)|11> \n"
     ]
    }
   ],
   "source": [
    "wfn_sol = tq.simulate(pqc, variables=infid.angles)\n",
    "print('final state solution: ')\n",
    "print(wfn_sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain the angles of the PQC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "theta_1 : 0.5670461281848205\n",
       "phi_2 : 1.3444030838073346\n",
       "theta_2 : 1.5563897167244758\n",
       "phi_0 : 0.23452026373288248\n",
       "lam_2 : 8.839510847957754e-05\n",
       "lam_3 : 0.3101820023612252\n",
       "lam_1 : 1.5707892723719388\n",
       "lam_0 : 2.835801887906597\n",
       "theta_0 : 1.5707923609973422\n",
       "phi_3 : 2.175294895597056\n",
       "theta_3 : 2.0382963240591634\n",
       "phi_1 : 0.3289124675729256"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
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