{
 "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": [
      "matplotlib.pylab 1.16.4\n",
      "numpy            1.16.4\n",
      "weylchamber      0.3.1\n",
      "scipy            1.2.1\n",
      "krotov           0.3.0+dev\n",
      "matplotlib       3.1.0\n",
      "qutip            4.3.1\n",
      "CPython 3.7.3\n",
      "IPython 7.5.0\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"
   ]
  },
  {
   "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",
    "$$\n",
    "\\begin{split}\n",
    "  \\epsilon^{(i+1)}(t)\n",
    "  & =\n",
    "  \\epsilon^{ref}(t) + \\frac{S(t)}{\\lambda_a} \\Im \\left\\{\n",
    "    \\sum_{k=1}^{N}\n",
    "    \\Bigg\\langle\n",
    "      \\chi_k^{(i)}(t)\n",
    "    \\Bigg\\vert\n",
    "    \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t) \\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "    \\Bigg\\vert\n",
    "    \\phi_k^{(i+1)}(t)\n",
    "    \\Bigg\\rangle\n",
    "    \\\\\n",
    "    +\n",
    "    \\frac{1}{2} \\sigma(t)\n",
    "    \\Bigg\\langle\n",
    "      \\Delta\\phi_k(t)\n",
    "      \\Bigg\\vert\n",
    "              \\left.\\frac{\\partial \\Op{H}}{\\partial \\epsilon}\\right\\vert_{{\\scriptsize \\begin{matrix}\\phi^{(i+1)}(t)\\\\\\epsilon^{(i+1)}(t)\\end{matrix}}}\n",
    "      \\Bigg\\vert\n",
    "      \\phi_k^{(i+1)}(t)\n",
    "     \\Bigg\\rangle\n",
    "  \\right\\}\\,,\n",
    "\\end{split}\n",
    "$$\n",
    "\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"
   ]
  },
  {
   "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",
      "    S(t) (ranges): [0.000000, 1.000000]\n",
      "    duration: 1.3 secs (started at 2019-06-28 14:36:42)\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: 4.5 secs (started at 2019-06-28 14:36:43)\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: 4.9 secs (started at 2019-06-28 14:36:47)\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: 4.3 secs (started at 2019-06-28 14:36:52)\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: 4.1 secs (started at 2019-06-28 14:36:57)\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: 4.3 secs (started at 2019-06-28 14:37:01)\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: 4.2 secs (started at 2019-06-28 14:37:05)\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: 4.4 secs (started at 2019-06-28 14:37:09)\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: 4.4 secs (started at 2019-06-28 14:37:14)\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: 4.9 secs (started at 2019-06-28 14:37:18)\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": [
    "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, 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 2019-06-28 14:36:42\n",
       "- Number of objectives: 4\n",
       "- Number of iterations: 9\n",
       "- Reason for termination: Reached convergence: achieved perfect entangler\n",
       "- Ended at 2019-06-28 14:37:23"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oct_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 = [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": [
    "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(oct_result.optimized_controls[0], tlist)"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": ""
  },
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}