{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization towards a Perfect Entangler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scipy            1.2.1\n",
      "krotov           0.3.0\n",
      "matplotlib       3.0.3\n",
      "qutip            4.3.1\n",
      "numpy            1.15.4\n",
      "matplotlib.pylab 1.15.4\n",
      "weylchamber      0.3.1\n",
      "CPython 3.6.8\n",
      "IPython 7.3.0\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "%load_ext watermark\n",
    "import qutip\n",
    "import numpy as np\n",
    "import scipy\n",
    "import matplotlib\n",
    "import matplotlib.pylab as plt\n",
    "import krotov\n",
    "import weylchamber as wc\n",
    "from weylchamber.visualize import WeylChamber\n",
    "from weylchamber.coordinates import from_magic\n",
    "\n",
    "%watermark -v --iversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{tr}[0]{\\operatorname{tr}}\n",
    "\\newcommand{diag}[0]{\\operatorname{diag}}\n",
    "\\newcommand{abs}[0]{\\operatorname{abs}}\n",
    "\\newcommand{pop}[0]{\\operatorname{pop}}\n",
    "\\newcommand{aux}[0]{\\text{aux}}\n",
    "\\newcommand{opt}[0]{\\text{opt}}\n",
    "\\newcommand{tgt}[0]{\\text{tgt}}\n",
    "\\newcommand{init}[0]{\\text{init}}\n",
    "\\newcommand{lab}[0]{\\text{lab}}\n",
    "\\newcommand{rwa}[0]{\\text{rwa}}\n",
    "\\newcommand{bra}[1]{\\langle#1\\vert}\n",
    "\\newcommand{ket}[1]{\\vert#1\\rangle}\n",
    "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n",
    "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n",
    "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2} \\mid\n",
    "#2\\vphantom{#1}\\right\\rangle}\n",
    "\\newcommand{op}[1]{\\hat{#1}}\n",
    "\\newcommand{Op}[1]{\\hat{#1}}\n",
    "\\newcommand{dd}[0]{\\,\\text{d}}\n",
    "\\newcommand{Liouville}[0]{\\mathcal{L}}\n",
    "\\newcommand{DynMap}[0]{\\mathcal{E}}\n",
    "\\newcommand{identity}[0]{\\mathbf{1}}\n",
    "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n",
    "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n",
    "\\newcommand{avg}[1]{\\langle#1\\rangle}\n",
    "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n",
    "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n",
    "\\newcommand{Re}[0]{\\operatorname{Re}}\n",
    "\\newcommand{Im}[0]{\\operatorname{Im}}$\n",
    "\n",
    "In this example, an optimization with an \"unconventional\" optimization target is demonstrated. Instead of a set of initial and target states or a certain target gate that should be implemented at final time, we rather just optimize for the closest perfectly entangling gate. See the following to references for details.\n",
    "\n",
    "* P. Watts, et al., Phys. Rev. A 91, 062306 (2015)\n",
    "\n",
    "* M. H. Goerz, et al., Phys. Rev. A 91, 062307 (2015)\n",
    "\n",
    "## Define parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "w1 = 1.1  # qubit 1 level splitting\n",
    "w2 = 2.1  # qubit 2 level splitting\n",
    "J = 0.2  # effective qubit coupling\n",
    "u0 = 0.3  # initial driving strength\n",
    "la = 1.1  # relative pulse coupling strength of second qubit\n",
    "T = 25.0  # final time\n",
    "nt = 250  # number of time steps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the Hamiltonian\n",
    "\n",
    "The system is a two-qubit system described by the effective Hamiltonian\n",
    "\n",
    "\\begin{equation}\n",
    "  \\op{H}(t) = - \\frac{\\omega_1}{2} \\op{\\sigma}_{z}^{(1)} - \\frac{\\omega_2}{2} \\op{\\sigma}_{z}^{(2)} + 2 J \\left(\\op{\\sigma}_{x}^{(1)} \\op{\\sigma}_{x}^{(2)} + \\op{\\sigma}_{y}^{(1)} \\op{\\sigma}_{y}^{(2)}\\right) + u(t) \\left(\\op{\\sigma}_{x}^{(1)} + \\lambda \\op{\\sigma}_{x}^{(2)}\\right),\n",
    "\\end{equation}\n",
    "where $\\omega_1$ and $\\omega_2$ are the energy level splitting of both qubits, respectively, $J$ is the effective coupling strength and $u(t)$ is the control field. $\\lambda$ defines the relative pulse coupling between both qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ham_and_states(w1=w1, w2=w2, J=J, la=la, u0=u0):\n",
    "    \"\"\"Two qubit Hamiltonian\n",
    "\n",
    "    Args:\n",
    "        w1 (float): energy separation of the first qubit levels\n",
    "        w2 (float): energy separation of the second qubit levels\n",
    "        J (float): effective coupling between both qubits\n",
    "        la (float): factor that pulse coupling strength differs for second qubit\n",
    "        u0 (float): constant amplitude of the driving field\n",
    "    \"\"\"\n",
    "    # local qubit Hamiltonians\n",
    "    Hq1 = 0.5 * w1 * np.diag([-1, 1])\n",
    "    Hq2 = 0.5 * w2 * np.diag([-1, 1])\n",
    "\n",
    "    # lift Hamiltonians to joint system operators\n",
    "    H0 = np.kron(Hq1, np.identity(2)) + np.kron(np.identity(2), Hq2)\n",
    "\n",
    "    # define the interaction Hamiltonian\n",
    "    sig_x = np.array([[0, 1], [1, 0]])\n",
    "    sig_y = np.array([[0, -1j], [1j, 0]])\n",
    "    Hint = 2 * J * (np.kron(sig_x, sig_x) + np.kron(sig_y, sig_y))\n",
    "    H0 = H0 + Hint\n",
    "\n",
    "    # define the drive Hamiltonian\n",
    "    H1 = np.kron(np.array([[0, 1], [1, 0]]), np.identity(2)) + la * np.kron(\n",
    "        np.identity(2), np.array([[0, 1], [1, 0]])\n",
    "    )\n",
    "\n",
    "    # convert Hamiltonians to QuTiP objects\n",
    "    H0 = qutip.Qobj(H0)\n",
    "    H1 = qutip.Qobj(H1)\n",
    "\n",
    "    # canonical basis\n",
    "    psi_00 = qutip.Qobj(np.kron(np.array([1, 0]), np.array([1, 0])))\n",
    "    psi_01 = qutip.Qobj(np.kron(np.array([1, 0]), np.array([0, 1])))\n",
    "    psi_10 = qutip.Qobj(np.kron(np.array([0, 1]), np.array([1, 0])))\n",
    "    psi_11 = qutip.Qobj(np.kron(np.array([0, 1]), np.array([0, 1])))\n",
    "\n",
    "    # define guess field\n",
    "    eps0 = lambda t, args: u0\n",
    "    return ([H0, [H1, eps0]], psi_00, psi_01, psi_10, psi_11)\n",
    "\n",
    "\n",
    "H, psi_00, psi_01, psi_10, psi_11 = ham_and_states(\n",
    "    w1=w1, w2=w2, J=J, la=la, u0=u0\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [],
   "source": [
    "proj_00 = psi_00 * psi_00.dag()\n",
    "proj_01 = psi_01 * psi_01.dag()\n",
    "proj_10 = psi_10 * psi_10.dag()\n",
    "proj_11 = psi_11 * psi_11.dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the optimization target\n",
    "\n",
    "The time grid is given by `nt` equidistant\n",
    "time steps between $t=0$ and $t=T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    }
   },
   "outputs": [],
   "source": [
    "tlist = np.linspace(0, T, nt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to specify the closest perfectly entangling gate as optimization target, we pass the canonical basis and specify `\"PE\"` as target gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [],
   "source": [
    "objectives = krotov.gate_objectives(\n",
    "    basis_states=[psi_00, psi_01, psi_10, psi_11], gate=\"PE\", H=H\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore, we define the shape function $S(t)$, which we use in order to\n",
    "ensure a smooth switch on and off in the beginning and end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    }
   },
   "outputs": [],
   "source": [
    "def S(t):\n",
    "    \"\"\"Shape function for the field update\"\"\"\n",
    "    return krotov.shapes.flattop(\n",
    "        t, t_start=0, t_stop=T, t_rise=T / 20, t_fall=T / 20, func='sinsq'\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the update-shape function $S(t)$ does not as such have any connection to the shape of the guess field, for convenience we also adopt it here as a pulse shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [],
   "source": [
    "def shape_field(eps0):\n",
    "    \"\"\"Applies the shape function S(t) to the guess field\"\"\"\n",
    "    eps0_shaped = lambda t, args: eps0(t, args) * S(t)\n",
    "    return eps0_shaped\n",
    "\n",
    "\n",
    "H[1][1] = shape_field(H[1][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before performing the optimization, we still have to choose `lambda_a`, which defines the control update magnitude in each iteration, and assign $S(t)$ to be used as shape function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "pulse_options = {H[1][1]: dict(lambda_a=1.0e2, shape=S)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the guess field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    }
   },
   "outputs": [],
   "source": [
    "def plot_pulse(pulse, tlist):\n",
    "    fig, ax = plt.subplots()\n",
    "    if callable(pulse):\n",
    "        pulse = np.array([pulse(t, args=None) for t in tlist])\n",
    "    ax.plot(tlist, pulse)\n",
    "    ax.set_xlabel('time')\n",
    "    ax.set_ylabel('pulse amplitude')\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows the guess field $u_{0}(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "11"
    }
   },
   "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": [
    "plot_pulse(H[1][1], tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "## Optimize\n",
    "\n",
    "Our optimization target is the closest perfectly entangling gate, quantified by the perfect-entangler functional\n",
    "\n",
    "\\begin{equation}\n",
    "  F_{PE} = g_3 \\sqrt{g_1^2 + g_2^2} - g_1,\n",
    "\\end{equation}\n",
    "\n",
    "where $g_1, g_2, g_3$ are the local invariants of the implemented gate, which uniquely identify its non-local content. As an alternative, one can also use the Weyl coordinates $c_1, c_2, c_3$ to plot the gate in the Weyl chamber. The perfectly entangling gates lie within a polyhedron within the general Weyl chamber and $F_{PE}$ becomes zero exactly at its boundaries.\n",
    "\n",
    "In order to get feedback from the optimization, we define `print_fidelity`, which is called after each OCT step and which calculates $F_{PE}$ and the gate concurrence (as an alternative measure for the entangling power of quantum gates).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "def print_fidelity(**args):\n",
    "    basis = [objectives[i].initial_state for i in [0, 1, 2, 3]]\n",
    "    states = [args['fw_states_T'][i] for i in [0, 1, 2, 3]]\n",
    "    U = wc.gates.gate(basis, states)\n",
    "    c1, c2, c3 = wc.coordinates.c1c2c3(from_magic(U))\n",
    "    g1, g2, g3 = wc.local_invariants.g1g2g3_from_c1c2c3(c1, c2, c3)\n",
    "    conc = wc.perfect_entanglers.concurrence(c1, c2, c3)\n",
    "    F_PE = wc.perfect_entanglers.F_PE(g1, g2, g3)\n",
    "    print(\n",
    "        \"    F_PE: %f\\n    gate conc.: %f\"\n",
    "        % (F_PE, conc)\n",
    "    )\n",
    "    return F_PE, [c1, c2, c3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since Krotov's method needs to know how to calculate the so-called co-states, we must provide a callable function called `chi_constructor` to the optimization function `optimize_pulses`. This function returns\n",
    "\n",
    "\\begin{equation}\n",
    "  \\ket{\\chi_{i}} = \\frac{\\partial F_{PE}}{\\partial \\bra{\\phi_i}} \\Bigg|_{\\ket{\\phi_{i}(T)}}\n",
    "\\end{equation}\n",
    "\n",
    "for all $i$ and with $\\ket{\\phi_i(T)}$ a set of forward propagated Bell basis states. The required function is implemented in the package `weylchamber`, and is taken from there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_constructor = wc.perfect_entanglers.make_PE_krotov_chi_constructor(\n",
    "    [psi_00, psi_01, psi_10, psi_11]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the perfect-entangler functional $F_{PE}$ depends strongly non-linearly on the states, Krotov's method formally requires the second-order contribution in order to guarantee monotonic convergence (see D. M. Reich, et al., J. Chem. Phys. 136, 104103 (2012) for details). In this case, the update formula can be extended and reads\n",
    "\n",
    "\\begin{split}\n",
    "  \\epsilon^{(i+1)}(t)\n",
    "  & =\n",
    "  \\epsilon^{ref}(t) + \\frac{S(t)}{\\lambda_a} \\Im \\left\\{\n",
    "    \\sum_{k=1}^{N}\n",
    "    \\Bigg\\langle\n",
    "      \\chi_k^{(i)}(t)\n",
    "    \\Bigg\\vert\n",
    "    \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t) \\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "    \\Bigg\\vert\n",
    "    \\phi_k^{(i+1)}(t)\n",
    "    \\Bigg\\rangle\n",
    "    \\\\\n",
    "    +\n",
    "    \\frac{1}{2} \\sigma(t)\n",
    "    \\Bigg\\langle\n",
    "      \\Delta\\phi_k(t)\n",
    "      \\Bigg\\vert\n",
    "              \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t)\\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "      \\Bigg\\vert\n",
    "      \\phi_k^{(i+1)}(t)\n",
    "     \\Bigg\\rangle\n",
    "  \\right\\}\\,,\n",
    "\\end{split}\n",
    "\n",
    "where the latter term defines the second-order contribution. In order to evaluate the second-order term, we need to pass the scalar function $\\sigma(t)$ to the optimizer `optimize_pulses`. We take\n",
    "\n",
    "\\begin{equation}\n",
    "   \\sigma(t) = -\\max\\left(\\varepsilon_A,2A+\\varepsilon_A\\right)\n",
    "\\end{equation}\n",
    "\n",
    "with $\\varepsilon_A$ a small non-negative number, and $A$ a parameter that can be recalculated numerically after each iteration (see D. M. Reich, et al., J. Chem. Phys. 136, 104103 (2012) for details). The sigma function is expressed by subclassing `krotov.second_order.Sigma`, allowing us to connect the evaluation of the function $\\sigma(t)$ and the recalculation of $A$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "class sigma(krotov.second_order.Sigma):\n",
    "    def __init__(self, A, epsA=0):\n",
    "        self.A = A\n",
    "        self.epsA = epsA\n",
    "\n",
    "    def __call__(self, t):\n",
    "        ϵ, A = self.epsA, self.A\n",
    "        return -max(ϵ, 2 * A + ϵ)\n",
    "\n",
    "    def refresh(\n",
    "        self,\n",
    "        forward_states,\n",
    "        forward_states0,\n",
    "        chi_states,\n",
    "        chi_norms,\n",
    "        optimized_pulses,\n",
    "        guess_pulses,\n",
    "        objectives,\n",
    "        result,\n",
    "    ):\n",
    "        try:\n",
    "            Delta_J_T = result.info_vals[-1][0] - result.info_vals[-2][0]\n",
    "        except IndexError:  # first iteration\n",
    "            Delta_J_T = 0\n",
    "        self.A = krotov.second_order.numerical_estimate_A(\n",
    "            forward_states, forward_states0, chi_states, chi_norms, Delta_J_T\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following, we carry out the optimization and save the Weyl coordinates $c_1, c_2, c_3$ from each iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "    objectives:\n",
      "        1:|(4)⟩ - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        2:|(4)⟩ - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        3:|(4)⟩ - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        4:|(4)⟩ - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "    adjoint objectives:\n",
      "        1:⟨(4)| - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        2:⟨(4)| - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        3:⟨(4)| - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "        4:⟨(4)| - {[Herm[4,4], [Herm[4,4], u1(t)]]} - 'PE'\n",
      "    S(t) (ranges): [0.000000, 1.000000]\n",
      "    duration: 1.3 secs (started at 2019-03-01 01:49:03)\n",
      "    optimized pulses (ranges): [0.00, 0.30]\n",
      "    ∫gₐ(t)dt: 0.00e+00\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): None, [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 1.447666\n",
      "    gate conc.: 0.479571\n",
      "Iteration 1\n",
      "    duration: 4.7 secs (started at 2019-03-01 01:49:05)\n",
      "    optimized pulses (ranges): [0.00, 0.32]\n",
      "    ∫gₐ(t)dt: 2.56e-03\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 1.000458\n",
      "    gate conc.: 0.645400\n",
      "Iteration 2\n",
      "    duration: 4.7 secs (started at 2019-03-01 01:49:09)\n",
      "    optimized pulses (ranges): [0.00, 0.34]\n",
      "    ∫gₐ(t)dt: 2.18e-03\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.587432\n",
      "    gate conc.: 0.782093\n",
      "Iteration 3\n",
      "    duration: 4.6 secs (started at 2019-03-01 01:49:14)\n",
      "    optimized pulses (ranges): [0.00, 0.36]\n",
      "    ∫gₐ(t)dt: 1.44e-03\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.309838\n",
      "    gate conc.: 0.889907\n",
      "Iteration 4\n",
      "    duration: 4.6 secs (started at 2019-03-01 01:49:19)\n",
      "    optimized pulses (ranges): [0.00, 0.37]\n",
      "    ∫gₐ(t)dt: 7.71e-04\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.158278\n",
      "    gate conc.: 0.949411\n",
      "Iteration 5\n",
      "    duration: 4.6 secs (started at 2019-03-01 01:49:23)\n",
      "    optimized pulses (ranges): [0.00, 0.38]\n",
      "    ∫gₐ(t)dt: 3.92e-04\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.079730\n",
      "    gate conc.: 0.979050\n",
      "Iteration 6\n",
      "    duration: 4.5 secs (started at 2019-03-01 01:49:28)\n",
      "    optimized pulses (ranges): [0.00, 0.38]\n",
      "    ∫gₐ(t)dt: 2.07e-04\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.037817\n",
      "    gate conc.: 0.992901\n",
      "Iteration 7\n",
      "    duration: 4.5 secs (started at 2019-03-01 01:49:32)\n",
      "    optimized pulses (ranges): [0.00, 0.39]\n",
      "    ∫gₐ(t)dt: 1.16e-04\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.014284\n",
      "    gate conc.: 0.998580\n",
      "Iteration 8\n",
      "    duration: 4.6 secs (started at 2019-03-01 01:49:37)\n",
      "    optimized pulses (ranges): [0.00, 0.39]\n",
      "    ∫gₐ(t)dt: 6.83e-05\n",
      "    λₐ: 1.00e+02\n",
      "    storage (bw, fw, fw0): [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB), [4 * ndarray(250)] (0.5 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n",
      "    F_PE: 0.000359\n",
      "    gate conc.: 0.999999\n"
     ]
    }
   ],
   "source": [
    "oct_result = krotov.optimize_pulses(\n",
    "    objectives,\n",
    "    pulse_options=pulse_options,\n",
    "    tlist=tlist,\n",
    "    propagator=krotov.propagators.expm,\n",
    "    chi_constructor=chi_constructor,\n",
    "    info_hook=krotov.info_hooks.chain(\n",
    "        krotov.info_hooks.print_debug_information,\n",
    "        print_fidelity,\n",
    "    ),\n",
    "    check_convergence=None,\n",
    "    sigma=sigma(A=0.0),\n",
    "    iter_stop=8,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots the path of the quantum gate within the Weyl chamber as a function of the iterations. As can be seen, the optimization drives the implemented gate towards the closest boundary of the polyhedron of perfect entanglers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1003.94x708.661 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = WeylChamber()\n",
    "c1c2c3 = [oct_result.info_vals[i][1] for i in range(len(oct_result.iters))]\n",
    "for i in range(len(oct_result.iters)):\n",
    "    w.add_point(c1c2c3[i][0], c1c2c3[i][1], c1c2c3[i][2])\n",
    "w.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the optimized field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "17"
    }
   },
   "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": [
    "plot_pulse(oct_result.optimized_controls[0], tlist)"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "text_representation": {
    "extension": ".md",
    "format_name": "markdown",
    "format_version": "1.0",
    "jupytext_version": "0.8.6"
   }
  },
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}