{
 "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": "2024-06-03T14:32:25.187140Z",
     "iopub.status.busy": "2024-06-03T14:32:25.186638Z",
     "iopub.status.idle": "2024-06-03T14:32:25.737586Z",
     "shell.execute_reply": "2024-06-03T14:32:25.737321Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.12.0\n",
      "IPython version      : 8.25.0\n",
      "\n",
      "scipy      : 1.12.0\n",
      "qutip      : 4.7.6\n",
      "krotov     : 1.3.0+dev\n",
      "weylchamber: 0.4.0\n",
      "matplotlib : 3.7.5\n",
      "numpy      : 1.26.4\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": "2024-06-03T14:32:25.759869Z",
     "iopub.status.busy": "2024-06-03T14:32:25.759602Z",
     "iopub.status.idle": "2024-06-03T14:32:25.761728Z",
     "shell.execute_reply": "2024-06-03T14:32:25.761475Z"
    }
   },
   "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": "2024-06-03T14:32:25.763170Z",
     "iopub.status.busy": "2024-06-03T14:32:25.763069Z",
     "iopub.status.idle": "2024-06-03T14:32:25.764762Z",
     "shell.execute_reply": "2024-06-03T14:32:25.764550Z"
    }
   },
   "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": "2024-06-03T14:32:25.766044Z",
     "iopub.status.busy": "2024-06-03T14:32:25.765962Z",
     "iopub.status.idle": "2024-06-03T14:32:25.767977Z",
     "shell.execute_reply": "2024-06-03T14:32:25.767752Z"
    },
    "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": "2024-06-03T14:32:25.769336Z",
     "iopub.status.busy": "2024-06-03T14:32:25.769220Z",
     "iopub.status.idle": "2024-06-03T14:32:25.846777Z",
     "shell.execute_reply": "2024-06-03T14:32:25.845740Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-06-03T14:32:25.856159Z",
     "iopub.status.busy": "2024-06-03T14:32:25.855355Z",
     "iopub.status.idle": "2024-06-03T14:32:25.870140Z",
     "shell.execute_reply": "2024-06-03T14:32:25.869001Z"
    }
   },
   "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": "2024-06-03T14:32:25.880759Z",
     "iopub.status.busy": "2024-06-03T14:32:25.880069Z",
     "iopub.status.idle": "2024-06-03T14:32:25.888306Z",
     "shell.execute_reply": "2024-06-03T14:32:25.887598Z"
    }
   },
   "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": "2024-06-03T14:32:25.895949Z",
     "iopub.status.busy": "2024-06-03T14:32:25.895424Z",
     "iopub.status.idle": "2024-06-03T14:32:25.902649Z",
     "shell.execute_reply": "2024-06-03T14:32:25.901109Z"
    }
   },
   "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": "2024-06-03T14:32:25.911504Z",
     "iopub.status.busy": "2024-06-03T14:32:25.911124Z",
     "iopub.status.idle": "2024-06-03T14:32:25.927263Z",
     "shell.execute_reply": "2024-06-03T14:32:25.920852Z"
    }
   },
   "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": "2024-06-03T14:32:25.936431Z",
     "iopub.status.busy": "2024-06-03T14:32:25.934388Z",
     "iopub.status.idle": "2024-06-03T14:32:25.949888Z",
     "shell.execute_reply": "2024-06-03T14:32:25.949033Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:32:25.957180Z",
     "iopub.status.busy": "2024-06-03T14:32:25.956511Z",
     "iopub.status.idle": "2024-06-03T14:32:25.984752Z",
     "shell.execute_reply": "2024-06-03T14:32:25.983508Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket $ \\\\ \\left(\\begin{matrix}0.707\\\\0.0\\\\0.0\\\\0.707\\\\\\end{matrix}\\right)$"
      ],
      "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 $ \\\\ \\left(\\begin{matrix}0.0\\\\0.707j\\\\0.707j\\\\0.0\\\\\\end{matrix}\\right)$"
      ],
      "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 $ \\\\ \\left(\\begin{matrix}0.0\\\\0.707\\\\-0.707\\\\0.0\\\\\\end{matrix}\\right)$"
      ],
      "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 $ \\\\ \\left(\\begin{matrix}0.707j\\\\0.0\\\\0.0\\\\-0.707j\\\\\\end{matrix}\\right)$"
      ],
      "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": "2024-06-03T14:32:25.994382Z",
     "iopub.status.busy": "2024-06-03T14:32:25.993854Z",
     "iopub.status.idle": "2024-06-03T14:32:25.999948Z",
     "shell.execute_reply": "2024-06-03T14:32:25.999317Z"
    }
   },
   "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": "2024-06-03T14:32:26.004313Z",
     "iopub.status.busy": "2024-06-03T14:32:26.004148Z",
     "iopub.status.idle": "2024-06-03T14:32:26.014026Z",
     "shell.execute_reply": "2024-06-03T14:32:26.013137Z"
    }
   },
   "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": "2024-06-03T14:32:26.018838Z",
     "iopub.status.busy": "2024-06-03T14:32:26.018718Z",
     "iopub.status.idle": "2024-06-03T14:32:26.025022Z",
     "shell.execute_reply": "2024-06-03T14:32:26.024128Z"
    }
   },
   "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": "2024-06-03T14:32:26.028478Z",
     "iopub.status.busy": "2024-06-03T14:32:26.028369Z",
     "iopub.status.idle": "2024-06-03T14:32:26.032169Z",
     "shell.execute_reply": "2024-06-03T14:32:26.030853Z"
    }
   },
   "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": "2024-06-03T14:32:26.036940Z",
     "iopub.status.busy": "2024-06-03T14:32:26.036397Z",
     "iopub.status.idle": "2024-06-03T14:32:26.041896Z",
     "shell.execute_reply": "2024-06-03T14:32:26.040303Z"
    }
   },
   "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": "2024-06-03T14:32:26.046945Z",
     "iopub.status.busy": "2024-06-03T14:32:26.046817Z",
     "iopub.status.idle": "2024-06-03T14:32:26.051515Z",
     "shell.execute_reply": "2024-06-03T14:32:26.050551Z"
    }
   },
   "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": "2024-06-03T14:32:26.053193Z",
     "iopub.status.busy": "2024-06-03T14:32:26.053110Z",
     "iopub.status.idle": "2024-06-03T14:32:52.474389Z",
     "shell.execute_reply": "2024-06-03T14:32:52.474076Z"
    }
   },
   "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: 1.4 secs (started at 2024-06-03 10:32:26)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 1.447335\n",
      "    gate conc.: 0.479492\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:27)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.998102\n",
      "    gate conc.: 0.645579\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 2\n",
      "    duration: 3.2 secs (started at 2024-06-03 10:32:30)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.582566\n",
      "    gate conc.: 0.784635\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 3\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:33)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.304191\n",
      "    gate conc.: 0.892999\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 4\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:36)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.153498\n",
      "    gate conc.: 0.951891\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 5\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:39)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.076100\n",
      "    gate conc.: 0.980700\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 6\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:43)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.035062\n",
      "    gate conc.: 0.993840\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 7\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:46)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    F_PE: 0.012118\n",
      "    gate conc.: 0.998971\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 8\n",
      "    duration: 3.1 secs (started at 2024-06-03 10:32:49)\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)] (0.4 MB), [4 * ndarray(250)] (0.4 MB), [4 * ndarray(250)] (0.4 MB)\n",
      "    fw_states_T norm: 1.000000, 1.000000, 1.000000, 1.000000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    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": "2024-06-03T14:32:52.475866Z",
     "iopub.status.busy": "2024-06-03T14:32:52.475776Z",
     "iopub.status.idle": "2024-06-03T14:32:52.478006Z",
     "shell.execute_reply": "2024-06-03T14:32:52.477763Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2024-06-03 10:32:26\n",
       "- Number of objectives: 4\n",
       "- Number of iterations: 8\n",
       "- Reason for termination: Reached convergence: achieved perfect entangler\n",
       "- Ended at 2024-06-03 10:32:52 (0:00:26)"
      ]
     },
     "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": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:32:52.479449Z",
     "iopub.status.busy": "2024-06-03T14:32:52.479366Z",
     "iopub.status.idle": "2024-06-03T14:32:52.652610Z",
     "shell.execute_reply": "2024-06-03T14:32:52.652339Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1003.94x708.661 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-06-03T14:32:52.654203Z",
     "iopub.status.busy": "2024-06-03T14:32:52.654108Z",
     "iopub.status.idle": "2024-06-03T14:32:52.716145Z",
     "shell.execute_reply": "2024-06-03T14:32:52.715845Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pulse(opt_result.optimized_controls[0], tlist)"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "jupytext": {
   "formats": ""
  },
  "kernelspec": {
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