{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learn to optimize Mølmer–Sørensen gates for trapped ions\n",
    "**Creating optimal operations with the trapped ions module**\n",
    "\n",
    "In this tutorial you will create a gate to efficiently prepare quantum states of trapped ion qubits using Mølmer–Sørensen-type interactions.\n",
    "\n",
    "This tutorial will introduce you to the [Boulder Opal trapped ions functionality](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/ions) to perform calculations and the [Q-CTRL Visualizer package](https://docs.q-ctrl.com/references/qctrl-visualizer/) to visualize their results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizing a Mølmer–Sørensen gate\n",
    "\n",
    "Your task will be to generate an entangling Mølmer–Sørensen gate for two trapped Ytterbium ions.\n",
    "\n",
    "Mølmer–Sørensen-type operations entangle multiple ions using laser drives tuned close to the frequency of an ion chain oscillation mode.\n",
    "Particular drives give rise to [relative phases and phase space displacements](https://doi.org/10.1002/qute.202000044) during an operation.\n",
    "The [operational infidelity](https://doi.org/10.1002/qute.202000044) of the gate is determined by the relative phases and displacements at the final time of the drives.\n",
    "In a successful Mølmer–Sørensen operation in an ion chain, the phase-space trajectories for all modes return to zero (that is, avoiding residual internal-motional entanglement), and set the phase acquired between the internal states of each pair of ions to a target value.\n",
    "\n",
    "The interaction Hamiltonian for Mølmer–Sørensen-type operations in a chain with $N$ ions takes the form ($\\hbar=1$ as per Boulder Opal convention)\n",
    "$$\n",
    "H(t) = \\frac{i}{2} \\sum_{j=1}^N\n",
    "    \\sigma_{x, j} \\sum_{p=1}^{3N} \\eta_{pj} \\left( \n",
    "        \\gamma_j(t) e^{i \\delta_p t} a_{p}^\\dagger - \\gamma_j^\\ast(t) e^{-i \\delta_p t} a_p\n",
    "    \\right) ,\n",
    "$$\n",
    "where the axis dimension and collective mode dimension are combined into a single index $p$ for simplicity,\n",
    "$\\sigma_{x,j}$ is the Pauli $X$ operator for ion $j$,\n",
    "$\\eta_{pj}$ is the Lamb–Dicke parameter of mode $p$ for ion $j$,\n",
    "$\\gamma_j(t)$ is the drive addressing ion $j$,\n",
    "$a_p$ is the annihilation operator for mode $p$,\n",
    "and\n",
    "$\\delta_p=\\nu_p-\\delta$ is the relative detuning of the laser frequency from the motional frequency of mode $p$.\n",
    "\n",
    "The trapped ions module is capable of finding optimal drives $\\gamma_j(t)$ which create the target entangling phases in the system.\n",
    "With $\\psi_{jk}$ indicating the phase between each pair of ions ($j, k$) (indexing from 0), the operation acting on the internal degrees of freedom of the ions can be described as:\n",
    "$$ U = \\exp\\left(i \\sum_{j=1}^{N-1} \\sum_{k=0}^{j-1} \\psi_{jk} \\sigma_{x,j} \\sigma_{x,k} \\right) . $$\n",
    "By [imposing a combination of symmetry to the ions drives](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.13.024022) and [penalizing the displacement of each mode's center of mass trajectory](https://doi.org/10.1002/qute.202000044), the module can also generate error-robust gates resilient against common noise sources (for example, laser-detuning noise).\n",
    "\n",
    "Although the trapped ions module can deal with larger ion chains, in this tutorial you will work with a pair of ions and create an entangling gate with a global beam addressing both ions.\n",
    "With a target phase of $\\psi_{10} = \\pi/4$, the corresponding entangling operation is then\n",
    "$$ U = \\exp\\left(i \\frac{\\pi}{4} \\sigma_{x,0} \\sigma_{x,1} \\right) =\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0 \\\\\n",
    "0 & \\tfrac{1+i}{2} & \\tfrac{-1+i}{2} & 0 \\\\\n",
    "0 & \\tfrac{-1+i}{2} & \\tfrac{1+i}{2} & 0 \\\\\n",
    "0 & 0 & 0 & 1 \\\\\n",
    "\\end{pmatrix} .\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Import libraries\n",
    "\n",
    "Before doing any calculation with Boulder Opal, you always need to import the necessary libraries.\n",
    "\n",
    "In this case, import the `numpy`, `matplotlib.pyplot`, `qctrlvisualizer`, and `boulderopal` packages.\n",
    "To learn more about installing Boulder Opal, see the [Get started](https://docs.q-ctrl.com/boulder-opal/toolkit/get-started-with-boulder-opal-toolkit) guide."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T02:38:22.969026Z",
     "start_time": "2021-07-08T02:38:18.293647Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import packages.\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import qctrlvisualizer\n",
    "import boulderopal as bo\n",
    "\n",
    "# Apply Q-CTRL style to plots created in pyplot.\n",
    "plt.style.use(qctrlvisualizer.get_qctrl_style())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Obtain ion chain properties\n",
    "\n",
    "Start by specifying the physical parameters for the laser drive and ion trap, and calculating the ion chain properties with the `boulderopal.ions.obtain_ion_chain_properties` function.\n",
    "The function returns a dictionary containing the Lamb–Dicke parameters and relative detunings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828681\") is queued.\n",
      "Your task (action_id=\"1828681\") has started.\n",
      "Your task (action_id=\"1828681\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Number of ions in the system.\n",
    "ion_count = 2\n",
    "\n",
    "# Calculate Lamb–Dicke parameters and relative detunings.\n",
    "ion_chain_properties = bo.ions.obtain_ion_chain_properties(\n",
    "    atomic_mass=171,  # Yb ions\n",
    "    ion_count=ion_count,\n",
    "    center_of_mass_frequencies=[1.6e6, 1.5e6, 0.3e6],  # Hz\n",
    "    wavevector=[(2 * np.pi) / 355e-9, (2 * np.pi) / 355e-9, 0.0],  # rad/m\n",
    "    laser_detuning=1.6e6 + 4.7e3,  # Hz\n",
    ")\n",
    "lamb_dicke_parameters = ion_chain_properties[\"lamb_dicke_parameters\"]\n",
    "relative_detunings = ion_chain_properties[\"relative_detunings\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Define optimizable drives\n",
    "\n",
    "Define the optimizable drives according to the degrees of freedom in the hardware.\n",
    "In this case, define a single optimizable piecewise-constant complex drive $\\gamma(t)$ by creating a `boulderopal.ions.ComplexOptimizableDrive` object.\n",
    "Pass to it its maximum Rabi rate (modulus) and the ions it addresses in the system (both of them), as well as the number of optimizable piecewise-constant segments it should have."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optimizable drive characteristics.\n",
    "maximum_rabi_rate = 2 * np.pi * 100e3  # rad/s\n",
    "segment_count = 64\n",
    "\n",
    "drive = bo.ions.ComplexOptimizableDrive(\n",
    "    count=segment_count, maximum_rabi_rate=maximum_rabi_rate, addressing=(0, 1)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Define optimization target\n",
    "\n",
    "Define the duration of the gate to be implemented, as well as the target phases for all the ions.\n",
    "The target phases must be a strictly lower triangular matrix, that is, $\\psi_{kl}$ indicates the total relative phase target for ions $k$ and $l$, with $k > l$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gate duration.\n",
    "duration = 2e-4  # s\n",
    "\n",
    "# Target phases.\n",
    "target_phase = np.pi / 4\n",
    "target_phases = np.array([[0, 0], [target_phase, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Execute optimization\n",
    "\n",
    "You now have everything necessary to carry out the optimization.\n",
    "Use the `boulderopal.ions.ms_optimize` function to obtain the optimized pulse that implements the target Mølmer–Sørensen gate.\n",
    "Pass to it the system parameters, the optimizable drives, as well as the gate duration and the target phases matrix.\n",
    "You can also use the `cost_history_scope` parameter to request the evolution of the cost value during the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828688\") is queued.\n",
      "Your task (action_id=\"1828688\") has started.\n",
      "Your task (action_id=\"1828688\") has completed.\n"
     ]
    }
   ],
   "source": [
    "result = bo.ions.ms_optimize(\n",
    "    drives=[drive],\n",
    "    lamb_dicke_parameters=lamb_dicke_parameters,\n",
    "    relative_detunings=relative_detunings,\n",
    "    duration=duration,\n",
    "    target_phases=target_phases,\n",
    "    cost_history_scope=\"ITERATION_VALUES\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Extract the optimization outputs\n",
    "\n",
    "After the calculation is complete, the results are stored in the output of the [returned dictionary](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/ions/ms_optimize), `result`.\n",
    "It contains the optimized values for each optimizable drive, as well as the optimized system dynamics (the `\"phases\"`, `\"displacements\"`, and `\"infidelities\"`) and the `\"sample_times\"` at which they're sampled.\n",
    "\n",
    "#### Extract the final gate infidelity\n",
    "\n",
    "A low infidelity at the end of the operation ensures us that the ion pairs have acquired the right phases, without generating any entanglement without the internal and external degrees of freedom of the ions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Infidelity reached: 6.446e-12\n"
     ]
    }
   ],
   "source": [
    "print(f\"Infidelity reached: {result['output']['infidelities']['value'][-1]:.3e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualize the cost history\n",
    "\n",
    "You can retrieve the evolution of the cost during the different optimizations from the optimized values dictionary, and plot them with the `plot_cost_histories` function from the [Q-CTRL Visualizer](https://docs.q-ctrl.com/references/qctrl-visualizer/) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qctrlvisualizer.plot_cost_histories(\n",
    "    result[\"cost_history\"][\"iteration_values\"], y_axis_log=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualize the optimized pulse\n",
    "\n",
    "You can retrieve the values of the optimized drive from the optimized values dictionary, and plot them with the [Q-CTRL Visualizer](https://docs.q-ctrl.com/references/qctrl-visualizer/)'s `plot_controls`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qctrlvisualizer.plot_controls({r\"$\\gamma$\": result[\"output\"][\"drive\"]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualize the phase dynamics\n",
    "\n",
    "You can easily visualize the dynamics of the relative phase between the two ions over the duration of the gate, by extracting the phases from the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_times = result[\"output\"][\"sample_times\"][\"value\"] * 1e3\n",
    "plt.plot(sample_times, result[\"output\"][\"phases\"][\"value\"][:, 1, 0])\n",
    "plt.plot([0, sample_times[-1]], [target_phase, target_phase], \"k--\")\n",
    "plt.yticks([0, target_phase], [\"0\", r\"$\\frac{\\pi}{4}$\"])\n",
    "plt.xlabel(\"Time (ms)\")\n",
    "plt.ylabel(\"Relative phase\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For high-fidelity operations, the relative phase obtained at the end of the operation should match the target phase for the ion pair (marked by a horizontal dashed black line)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualize phase space trajectories\n",
    "\n",
    "\n",
    "You can visualize the trajectory of the center of a coherent state in (rotating) optical phase space for each mode.\n",
    "The closure of these trajectories is a necessary condition for an effective operation.\n",
    "You can obtain the overall displacement for each mode by summing the displacements [over the ion dimension](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/ions/ms_optimize)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_displacement = np.sum(result[\"output\"][\"displacements\"][\"value\"], axis=-1)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2)\n",
    "plot_range = 1.05 * np.max(np.abs(total_displacement))\n",
    "fig.suptitle(\"Phase space trajectories\")\n",
    "\n",
    "for k in range(2):\n",
    "    for mode in range(ion_count):\n",
    "        axs[k].plot(\n",
    "            np.real(total_displacement[:, k, mode]),\n",
    "            np.imag(total_displacement[:, k, mode]),\n",
    "            label=f\"mode {mode % ion_count}\",\n",
    "        )\n",
    "        axs[k].plot(\n",
    "            np.real(total_displacement[-1, k, mode]),\n",
    "            np.imag(total_displacement[-1, k, mode]),\n",
    "            \"k*\",\n",
    "            markersize=10,\n",
    "        )\n",
    "\n",
    "    axs[k].set_xlim(-plot_range, plot_range)\n",
    "    axs[k].set_ylim(-plot_range, plot_range)\n",
    "    axs[k].set_aspect(\"equal\")\n",
    "    axs[k].set_xlabel(\"q\")\n",
    "\n",
    "axs[0].set_title(\"$x$-axis\")\n",
    "axs[0].set_ylabel(\"p\")\n",
    "axs[1].set_title(\"$y$-axis\")\n",
    "axs[1].yaxis.set_ticklabels([])\n",
    "\n",
    "hs, ls = axs[0].get_legend_handles_labels()\n",
    "axs[1].legend(handles=hs, labels=ls, loc=\"upper left\", bbox_to_anchor=(1, 1))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, $q \\equiv q_m = (a_m^\\dagger + a_m)/\\sqrt{2}$ and $p \\equiv p_m = i (a_m^\\dagger - a_m)/\\sqrt{2}$ are the dimensionless quadratures for each mode $m$.\n",
    "The black star marks the final displacement for each mode, which overlap at zero; this indicates that the operation has not caused any residual state-motional entanglement or motional heating.\n",
    "The z-axis modes are not addressed, and thus have no excursions in phase space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You've reached the end of the tutorial.\n",
    "Congratulations on obtaining your first Mølmer–Sørensen gate.\n",
    "\n",
    "You can easily extend the calculations you have done here by having longer ion chains, adding drives that address different ions, trying a robust optimization, etc.\n",
    "The different classes and functions in the trapped ions module are described in [their reference page](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/ions).\n",
    "\n",
    "You can perform more flexible optimizations and simulations of Mølmer–Sørensen-type interactions by using [the graph framework in Boulder Opal](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/get-an-introduction-to-graphs-in-boulder-opal).\n",
    "You can find more information in the [How to optimize error-robust Mølmer–Sørensen gates for trapped ions](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/trapped-ion-quantum-computing/how-to-optimize-error-robust-molmer-sorensen-gates-for-trapped-ions) and [How to calculate system dynamics for arbitrary Mølmer–Sørensen gates](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/trapped-ion-quantum-computing/how-to-calculate-system-dynamics-for-arbitrary-molmer-sorensen-gates) user guides\n",
    "\n",
    "You can also visit our [topics page](https://docs.q-ctrl.com/boulder-opal) to learn more about Boulder Opal and its capabilities."
   ]
  }
 ],
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