{
 "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": [
      "weylchamber      0.3.2\n",
      "matplotlib       3.2.1\n",
      "krotov           1.0.0+dev\n",
      "qutip            4.4.1\n",
      "numpy            1.17.2\n",
      "scipy            1.3.1\n",
      "matplotlib.pylab 1.17.2\n",
      "CPython 3.7.6\n",
      "IPython 7.13.0\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",
    "from IPython.display import display\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",
    "This example demonstrates the optimization with an \"unconventional\"\n",
    "optimization target. Instead of a state-to-state transition, or the realization\n",
    "of a specific quantum gate, we optimize for an arbitrary perfectly entangling\n",
    "gate. See\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",
    "for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a generic two-qubit Hamiltonian (motivated from the example of two\n",
    "superconducting transmon qubits, truncated to the logical subspace),\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "  \\op{H}(t)\n",
    "    = - \\frac{\\omega_1}{2} \\op{\\sigma}_{z}^{(1)}\n",
    "      - \\frac{\\omega_2}{2} \\op{\\sigma}_{z}^{(2)}\n",
    "      + 2 J \\left(\n",
    "            \\op{\\sigma}_{x}^{(1)} \\op{\\sigma}_{x}^{(2)}\n",
    "            + \\op{\\sigma}_{y}^{(1)} \\op{\\sigma}_{y}^{(2)}\n",
    "        \\right)\n",
    "      + u(t) \\left(\n",
    "            \\op{\\sigma}_{x}^{(1)} + \\lambda \\op{\\sigma}_{x}^{(2)}\n",
    "        \\right),\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where $\\omega_1$ and $\\omega_2$ are the energy level splitting of the\n",
    "respective qubit, $J$ is the effective coupling strength and $u(t)$ is the\n",
    "control field. $\\lambda$ defines the strength of the qubit-control coupling for\n",
    "qubit 2, relative to qubit 1.\n",
    "\n",
    "We use the following 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\n",
    "\n",
    "tlist = np.linspace(0, T, nt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are for illustrative purposes only, and do not correspond to any\n",
    "particular physical system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "The initial guess is defined as\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eps0(t, args):\n",
    "    return u0 * krotov.shapes.flattop(\n",
    "        t, t_start=0, t_stop=T, t_rise=(T / 20), t_fall=(T / 20), func='sinsq'\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    },
    "lines_to_next_cell": 2
   },
   "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": "code",
   "execution_count": 5,
   "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": [
    "plot_pulse(eps0, tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We instantiate the Hamiltonian with this guess pulse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hamiltonian(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",
    "    return [H0, [H1, eps0]]\n",
    "\n",
    "\n",
    "H = hamiltonian(w1=w1, w2=w2, J=J, la=la, u0=u0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As well as the canonical two-qubit logical basis,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "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])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with the corresponding projectors to calculate population dynamics below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "proj_00 = qutip.ket2dm(psi_00)\n",
    "proj_01 = qutip.ket2dm(psi_01)\n",
    "proj_10 = qutip.ket2dm(psi_10)\n",
    "proj_11 = qutip.ket2dm(psi_11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives for a perfect entangler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our optimization target is the closest perfectly entangling gate, quantified by\n",
    "the perfect-entangler functional\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "  F_{PE} = g_3 \\sqrt{g_1^2 + g_2^2} - g_1,\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where $g_1, g_2, g_3$ are the local invariants of the implemented gate that\n",
    "uniquely identify its non-local content. The local invariants are closely\n",
    "related to the Weyl coordinates $c_1, c_2, c_3$, which provide a useful\n",
    "geometric visualization in the Weyl chamber. The perfectly entangling gates lie\n",
    "within a polyhedron in the Weyl chamber and $F_{PE}$ becomes zero at its\n",
    "boundaries. We define $F_{PE} \\equiv 0$ for *all* perfect entanglers (inside\n",
    "the polyhedron)\n",
    "\n",
    "A list of four objectives that encode the minimization of $F_{PE}$ are\n",
    "generated by calling the `gate_objectives` function with the canonical basis,\n",
    "and `\"PE\"` as target \"gate\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "objectives = krotov.gate_objectives(\n",
    "    basis_states=[psi_00, psi_01, psi_10, psi_11], gate=\"PE\", H=H\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Objective[|Ψ₀(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]],\n",
       " Objective[|Ψ₁(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]],\n",
       " Objective[|Ψ₂(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]],\n",
       " Objective[|Ψ₃(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]]]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial states in these objectives are not the canonical basis states, but a Bell\n",
    "basis,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.707\\\\0.0\\\\0.0\\\\0.707\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.70710678]\n",
       " [0.        ]\n",
       " [0.        ]\n",
       " [0.70710678]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.707j\\\\0.707j\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.+0.j        ]\n",
       " [0.+0.70710678j]\n",
       " [0.+0.70710678j]\n",
       " [0.+0.j        ]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.707\\\\-0.707\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[ 0.        ]\n",
       " [ 0.70710678]\n",
       " [-0.70710678]\n",
       " [ 0.        ]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.707j\\\\0.0\\\\0.0\\\\-0.707j\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.+0.70710678j]\n",
       " [0.+0.j        ]\n",
       " [0.+0.j        ]\n",
       " [0.-0.70710678j]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "for obj in objectives:\n",
    "    display(obj.initial_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we don't know *which* perfect entangler the optimization result will\n",
    "implement, we cannot associate any \"target state\" with each objective, and the\n",
    "`target` attribute is set to the string 'PE'."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can treat the above objectives as a \"black box\"; the only important\n",
    "consideration is that the `chi_constructor` that we will pass to\n",
    "`optimize_pulses` to calculating the boundary condition for the backwards\n",
    "propagation,\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "  \\ket{\\chi_{k}} = \\frac{\\partial F_{PE}}{\\partial \\bra{\\phi_k}} \\Bigg|_{\\ket{\\phi_{k}(T)}}\\,,\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "must be consistent with how the `objectives` are set up. For the perfect\n",
    "entanglers functional, the calculation of the $\\ket{\\chi_{k}}$ is relatively\n",
    "complicated. The `weylchamber` package\n",
    "(https://github.com/qucontrol/weylchamber) contains a suitable routine that\n",
    "works on the `objectives` exactly as defined above (specifically, under the\n",
    "assumption that the $\\ket{\\phi_k}$ are the appropriate Bell states):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function make_PE_krotov_chi_constructor in module weylchamber.perfect_entanglers:\n",
      "\n",
      "make_PE_krotov_chi_constructor(canonical_basis, unitarity_weight=0)\n",
      "    Return a constructor for the χ's in a PE optimization.\n",
      "    \n",
      "    Return a `chi_constructor` that determines the boundary condition of the\n",
      "    backwards propagation in an optimization towards a perfect entangler in\n",
      "    Krotov's method, based on the foward-propagtion of the Bell states. In\n",
      "    detail, the function returns a callable function that calculates\n",
      "    \n",
      "    .. math::\n",
      "    \n",
      "        \\ket{\\chi_{i}}\n",
      "        =\n",
      "        \\frac{\\partial F_{PE}}{\\partial \\bra{\\phi_i}}\n",
      "        \\Bigg|_{\\ket{\\phi_{i}(T)}}\n",
      "    \n",
      "    for all $i$ with $\\ket{\\phi_{0}(T)}, ..., \\ket{\\phi_{3}(T)}$ the forward\n",
      "    propagated Bell states at final time $T$, cf. Eq. (33b) in Ref. [1].\n",
      "    $F_{PE}$ is the perfect-entangler functional\n",
      "    :func:`~weylchamber.perfect_entanglers.F_PE`. For the details of the\n",
      "    derivative see Appendix G in Ref. [2].\n",
      "    \n",
      "    References:\n",
      "    \n",
      "    [1] `M. H. Goerz, et al., Phys. Rev. A 91, 062307 (2015)\n",
      "    <https://doi.org/10.1103/PhysRevA.91.062307>`_\n",
      "    \n",
      "    [2] `M. H. Goerz, Optimizing Robust Quantum Gates in Open Quantum Systems.\n",
      "    PhD thesis, University of Kassel, 2015\n",
      "    <https://michaelgoerz.net/research/diss_goerz.pdf>`_\n",
      "    \n",
      "    Args:\n",
      "        canonical_basis (list[qutip.Qobj]): A list of four basis states that\n",
      "            define the canonical basis $\\ket{00}$, $\\ket{01}$, $\\ket{10}$, and\n",
      "            $\\ket{11}$ of the logical subspace.\n",
      "        unitarity_weight (float): A weight in [0, 1] that determines how much\n",
      "            emphasis is placed on  maintaining population in the logical\n",
      "            subspace.\n",
      "    \n",
      "    Returns:\n",
      "        callable: a function ``chi_constructor(fw_states_T, **kwargs)`` that\n",
      "        receives the result of a foward propagation of the Bell states\n",
      "        (obtained from `canonical_basis` via\n",
      "        :func:`weylchamber.gates.bell_basis`), and returns a list of statex\n",
      "        $\\ket{\\chi_{i}}$ that are the boundary condition for the backward\n",
      "        propagation in Krotov's method. Positional arguments beyond\n",
      "        `fw_states_T` are ignored.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(wc.perfect_entanglers.make_PE_krotov_chi_constructor)"
   ]
  },
  {
   "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": [
    "Again, the key point to take from this is that when defining a new or unusual\n",
    "functional, **the `chi_constructor` must be congruent with the way the\n",
    "objectives are defined**. As a user, you can choose whatever definition of\n",
    "objectives and implementation of `chi_constructor` is most suitable, as long\n",
    "they are compatible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second Order Update Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the perfect-entangler functional $F_{PE}$ is non-linear in\n",
    "the states, Krotov's method requires the second-order contribution in\n",
    "order to guarantee monotonic convergence (see D. M. Reich, et al., J. Chem.\n",
    "Phys. 136, 104103 (2012) for details). The second order update equation\n",
    "reads\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "  \\epsilon^{(i+1)}(t)\n",
    "  & =\n",
    "  \\epsilon^{ref}(t) + \\frac{S(t)}{\\lambda_a} \\Im \\Bigg\\{\n",
    "    \\sum_{k=1}^{N}\n",
    "    \\Bigg\\langle\n",
    "      \\chi_k^{(i)}(t)\n",
    "    \\Bigg\\vert\n",
    "    \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t) \\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "    \\Bigg\\vert\n",
    "    \\phi_k^{(i+1)}(t)\n",
    "    \\Bigg\\rangle\n",
    "    \\\\\n",
    "    & \\qquad +\n",
    "    \\frac{1}{2} \\sigma(t)\n",
    "    \\Bigg\\langle\n",
    "      \\Delta\\phi_k(t)\n",
    "      \\Bigg\\vert\n",
    "              \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t)\\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "      \\Bigg\\vert\n",
    "      \\phi_k^{(i+1)}(t)\n",
    "     \\Bigg\\rangle\n",
    "  \\Bigg\\}\\,,\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where the term proportional to $\\sigma(t)$ defines the second-order\n",
    "contribution. In order to use the second-order term, we need to pass\n",
    "a function to evaluate this $\\sigma(t)$ as `sigma` to `optimize_pulses`. We use\n",
    "the equation\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "   \\sigma(t) = -\\max\\left(\\varepsilon_A,2A+\\varepsilon_A\\right)\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "with $\\varepsilon_A$ a small non-negative number, and $A$ a parameter that can\n",
    "be recalculated numerically after each iteration (see D. M. Reich, et al., J.\n",
    "Chem. Phys. 136, 104103 (2012) for details).\n",
    "\n",
    "Generally, $\\sigma(t)$ has parametric dependencies like $A$ in this example,\n",
    "which should be refreshed for each iteration. Thus, since `sigma` holds\n",
    "internal state, it must be implemented as an object subclassing from\n",
    "`krotov.second_order.Sigma`:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "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": [
    "This combines the evaluation of the function, `sigma(t)`, with the recalculation of\n",
    "$A$ (or whatever parametrizations another $\\sigma(t)$ function might contain)\n",
    "in `sigma.refresh`, which `optimize_pulses` invokes automatically at the\n",
    "end of each iteration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "Before running the optimization, we define the shape function $S(t)$ to\n",
    "maintain the smooth switch-on and switch-off, and the $\\lambda_a$ parameter\n",
    "that determines the overall magnitude of the pulse update in each iteration:\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "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",
    "    )\n",
    "\n",
    "pulse_options = {H[1][1]: dict(lambda_a=1.0e2, update_shape=S)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In previous examples, we have used `info_hook` routines that display and store\n",
    "the value of the functional $J_T$. Here, we will also want to analyze the\n",
    "optimization in terms of the Weyl chamber coordinates $(c_1, c_2, c_3)$. We\n",
    "therefore write a custom `print_fidelity` routine that prints $F_{PE}$ as well\n",
    "as the gate concurrence (as an alternative measure for the entangling power of\n",
    "quantum gates), and results in the storage of a nested tuple `(F_PE, (c1, c2,\n",
    "c3))` for each iteration, in `Result.info_vals`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "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(\"    F_PE: %f\\n    gate conc.: %f\" % (F_PE, conc))\n",
    "    return F_PE, [c1, c2, c3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This structure must be taken into account in a `check_convergence` routine. This would\n",
    "affect routines like `krotov.convergence.value_below` that assume that\n",
    "`Result.info_vals` contains the values of $J_T$ only. Here, we define a check\n",
    "that stops the optimization as soon as we reach a perfect entangler:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_PE(result):\n",
    "    # extract F_PE from (F_PE, [c1, c2, c3])\n",
    "    F_PE = result.info_vals[-1][0]\n",
    "    if F_PE <= 0:\n",
    "        return \"achieved perfect entangler\"\n",
    "    else:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "    objectives:\n",
      "        1:|Ψ₀(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]\n",
      "        2:|Ψ₁(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]\n",
      "        3:|Ψ₂(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]\n",
      "        4:|Ψ₃(4)⟩ to PE via [H₀[4,4], [H₁[4,4], u₁(t)]]\n",
      "    adjoint objectives:\n",
      "        1:⟨Ψ₀(4)| to PE via [H₂[4,4], [H₃[4,4], u₁(t)]]\n",
      "        2:⟨Ψ₁(4)| to PE via [H₄[4,4], [H₅[4,4], u₁(t)]]\n",
      "        3:⟨Ψ₂(4)| to PE via [H₆[4,4], [H₇[4,4], u₁(t)]]\n",
      "        4:⟨Ψ₃(4)| to PE via [H₈[4,4], [H₉[4,4], u₁(t)]]\n",
      "    propagator: expm\n",
      "    chi_constructor: chi_constructor\n",
      "    mu: derivative_wrt_pulse\n",
      "    sigma: sigma\n",
      "    S(t) (ranges): [0.000000, 1.000000]\n",
      "    iter_start: 0\n",
      "    iter_stop: 20\n",
      "    duration: 2.1 secs (started at 2020-03-22 17:00:54)\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: 7.2 secs (started at 2020-03-22 17:00:57)\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: 6.2 secs (started at 2020-03-22 17:01:04)\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: 6.2 secs (started at 2020-03-22 17:01:10)\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: 6.7 secs (started at 2020-03-22 17:01:16)\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: 5.7 secs (started at 2020-03-22 17:01:23)\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: 6.3 secs (started at 2020-03-22 17:01:29)\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: 5.8 secs (started at 2020-03-22 17:01:35)\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: 5.5 secs (started at 2020-03-22 17:01:41)\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",
      "Iteration 9\n",
      "    duration: 5.5 secs (started at 2020-03-22 17:01:46)\n",
      "    optimized pulses (ranges): [0.00, 0.39]\n",
      "    ∫gₐ(t)dt: 4.26e-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: -0.008316\n",
      "    gate conc.: 1.000000\n"
     ]
    }
   ],
   "source": [
    "opt_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, print_fidelity\n",
    "    ),\n",
    "    check_convergence=check_PE,\n",
    "    sigma=sigma(A=0.0),\n",
    "    iter_stop=20,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2020-03-22 17:00:54\n",
       "- Number of objectives: 4\n",
       "- Number of iterations: 9\n",
       "- Reason for termination: Reached convergence: achieved perfect entangler\n",
       "- Ended at 2020-03-22 17:01:52 (0:00:58)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize how each iteration of the optimization brings the dynamics\n",
    "closer to the polyhedron of perfect entanglers (using the Weyl chamber\n",
    "coordinates that we calculated in the `info_hook` routine `print_fidelity`, and\n",
    "that were stored in `Result.info_vals`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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 = [opt_result.info_vals[i][1] for i in range(len(opt_result.iters))]\n",
    "for i in range(len(opt_result.iters)):\n",
    "    w.add_point(c1c2c3[i][0], c1c2c3[i][1], c1c2c3[i][2])\n",
    "w.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final optimized control field looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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(opt_result.optimized_controls[0], tlist)"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "jupytext": {
   "formats": ""
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
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  "toc": {
   "base_numbering": 1,
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   "number_sections": true,
   "sideBar": true,
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
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  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   "types_to_exclude": [
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