{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization towards a Perfect Entangler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    },
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:39.704713Z",
     "iopub.status.busy": "2021-11-07T04:56:39.704280Z",
     "iopub.status.idle": "2021-11-07T04:56:40.675745Z",
     "shell.execute_reply": "2021-11-07T04:56:40.676045Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.8.1\n",
      "IPython version      : 7.24.1\n",
      "\n",
      "scipy      : 1.6.3\n",
      "qutip      : 4.6.1\n",
      "weylchamber: 0.3.2\n",
      "matplotlib : 3.4.2\n",
      "krotov     : 1.2.1+dev\n",
      "numpy      : 1.20.3\n",
      "\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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.678940Z",
     "iopub.status.busy": "2021-11-07T04:56:40.678588Z",
     "iopub.status.idle": "2021-11-07T04:56:40.680083Z",
     "shell.execute_reply": "2021-11-07T04:56:40.680338Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.682795Z",
     "iopub.status.busy": "2021-11-07T04:56:40.682428Z",
     "iopub.status.idle": "2021-11-07T04:56:40.684240Z",
     "shell.execute_reply": "2021-11-07T04:56:40.683936Z"
    }
   },
   "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"
    },
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.686912Z",
     "iopub.status.busy": "2021-11-07T04:56:40.686568Z",
     "iopub.status.idle": "2021-11-07T04:56:40.688359Z",
     "shell.execute_reply": "2021-11-07T04:56:40.688055Z"
    },
    "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.702584Z",
     "iopub.status.busy": "2021-11-07T04:56:40.697922Z",
     "iopub.status.idle": "2021-11-07T04:56:40.802048Z",
     "shell.execute_reply": "2021-11-07T04:56:40.802289Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.807799Z",
     "iopub.status.busy": "2021-11-07T04:56:40.807488Z",
     "iopub.status.idle": "2021-11-07T04:56:40.808723Z",
     "shell.execute_reply": "2021-11-07T04:56:40.808971Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.813058Z",
     "iopub.status.busy": "2021-11-07T04:56:40.812756Z",
     "iopub.status.idle": "2021-11-07T04:56:40.814423Z",
     "shell.execute_reply": "2021-11-07T04:56:40.814119Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.817253Z",
     "iopub.status.busy": "2021-11-07T04:56:40.816953Z",
     "iopub.status.idle": "2021-11-07T04:56:40.818653Z",
     "shell.execute_reply": "2021-11-07T04:56:40.818344Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.821806Z",
     "iopub.status.busy": "2021-11-07T04:56:40.821502Z",
     "iopub.status.idle": "2021-11-07T04:56:40.823038Z",
     "shell.execute_reply": "2021-11-07T04:56:40.822688Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.825630Z",
     "iopub.status.busy": "2021-11-07T04:56:40.825332Z",
     "iopub.status.idle": "2021-11-07T04:56:40.827047Z",
     "shell.execute_reply": "2021-11-07T04:56:40.827282Z"
    }
   },
   "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": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.829742Z",
     "iopub.status.busy": "2021-11-07T04:56:40.829442Z",
     "iopub.status.idle": "2021-11-07T04:56:40.834118Z",
     "shell.execute_reply": "2021-11-07T04:56:40.834354Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.836638Z",
     "iopub.status.busy": "2021-11-07T04:56:40.836341Z",
     "iopub.status.idle": "2021-11-07T04:56:40.838225Z",
     "shell.execute_reply": "2021-11-07T04:56:40.837924Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.843719Z",
     "iopub.status.busy": "2021-11-07T04:56:40.843426Z",
     "iopub.status.idle": "2021-11-07T04:56:40.845072Z",
     "shell.execute_reply": "2021-11-07T04:56:40.844773Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.848624Z",
     "iopub.status.busy": "2021-11-07T04:56:40.848323Z",
     "iopub.status.idle": "2021-11-07T04:56:40.849953Z",
     "shell.execute_reply": "2021-11-07T04:56:40.849655Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.852534Z",
     "iopub.status.busy": "2021-11-07T04:56:40.852234Z",
     "iopub.status.idle": "2021-11-07T04:56:40.854028Z",
     "shell.execute_reply": "2021-11-07T04:56:40.853731Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.857233Z",
     "iopub.status.busy": "2021-11-07T04:56:40.856939Z",
     "iopub.status.idle": "2021-11-07T04:56:40.858563Z",
     "shell.execute_reply": "2021-11-07T04:56:40.858265Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.860725Z",
     "iopub.status.busy": "2021-11-07T04:56:40.860435Z",
     "iopub.status.idle": "2021-11-07T04:56:40.862084Z",
     "shell.execute_reply": "2021-11-07T04:56:40.861787Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:56:40.866429Z",
     "iopub.status.busy": "2021-11-07T04:56:40.866135Z",
     "iopub.status.idle": "2021-11-07T04:57:11.803119Z",
     "shell.execute_reply": "2021-11-07T04:57:11.802855Z"
    }
   },
   "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: 1.5 secs (started at 2021-11-07 05:56:40)\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: 1.447335\n",
      "    gate conc.: 0.479492\n",
      "Iteration 1\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:56:42)\n",
      "    optimized pulses (ranges): [0.00, 0.32]\n",
      "    ∫gₐ(t)dt: 2.58e-01\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: 0.998102\n",
      "    gate conc.: 0.645579\n",
      "Iteration 2\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:56:46)\n",
      "    optimized pulses (ranges): [0.00, 0.34]\n",
      "    ∫gₐ(t)dt: 2.20e-01\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: 0.582566\n",
      "    gate conc.: 0.784635\n",
      "Iteration 3\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:56:49)\n",
      "    optimized pulses (ranges): [0.00, 0.35]\n",
      "    ∫gₐ(t)dt: 1.46e-01\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: 0.304191\n",
      "    gate conc.: 0.892999\n",
      "Iteration 4\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:56:53)\n",
      "    optimized pulses (ranges): [0.00, 0.37]\n",
      "    ∫gₐ(t)dt: 7.72e-02\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: 0.153498\n",
      "    gate conc.: 0.951891\n",
      "Iteration 5\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:56:57)\n",
      "    optimized pulses (ranges): [0.00, 0.37]\n",
      "    ∫gₐ(t)dt: 3.88e-02\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: 0.076100\n",
      "    gate conc.: 0.980700\n",
      "Iteration 6\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:57:00)\n",
      "    optimized pulses (ranges): [0.00, 0.38]\n",
      "    ∫gₐ(t)dt: 2.03e-02\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: 0.035062\n",
      "    gate conc.: 0.993840\n",
      "Iteration 7\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:57:04)\n",
      "    optimized pulses (ranges): [0.00, 0.39]\n",
      "    ∫gₐ(t)dt: 1.13e-02\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: 0.012118\n",
      "    gate conc.: 0.998971\n",
      "Iteration 8\n",
      "    duration: 3.7 secs (started at 2021-11-07 05:57:08)\n",
      "    optimized pulses (ranges): [0.00, 0.39]\n",
      "    ∫gₐ(t)dt: 6.68e-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: -0.001422\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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:57:11.805984Z",
     "iopub.status.busy": "2021-11-07T04:57:11.805585Z",
     "iopub.status.idle": "2021-11-07T04:57:11.807918Z",
     "shell.execute_reply": "2021-11-07T04:57:11.807614Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2021-11-07 05:56:40\n",
       "- Number of objectives: 4\n",
       "- Number of iterations: 8\n",
       "- Reason for termination: Reached convergence: achieved perfect entangler\n",
       "- Ended at 2021-11-07 05:57:11 (0:00:31)"
      ]
     },
     "execution_count": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-11-07T04:57:11.818160Z",
     "iopub.status.busy": "2021-11-07T04:57:11.817703Z",
     "iopub.status.idle": "2021-11-07T04:57:12.431339Z",
     "shell.execute_reply": "2021-11-07T04:57:12.431589Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mgoerz/Documents/krotov/.tox/py38/lib/python3.8/site-packages/weylchamber/visualize.py:318: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_yticklabels(['0', '', '', '', '', r'$\\pi/2$'])\n",
      "/home/mgoerz/Documents/krotov/.tox/py38/lib/python3.8/site-packages/weylchamber/visualize.py:319: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_zticklabels(['0', '', '', '', '', r'$\\pi/2$'])\n"
     ]
    },
    {
     "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"
    },
    "execution": {
     "iopub.execute_input": "2021-11-07T04:57:12.457156Z",
     "iopub.status.busy": "2021-11-07T04:57:12.443818Z",
     "iopub.status.idle": "2021-11-07T04:57:12.512146Z",
     "shell.execute_reply": "2021-11-07T04:57:12.511842Z"
    }
   },
   "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"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "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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 "nbformat": 4,
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}