{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to optimize Mølmer–Sørensen gates for a multitone global beam\n",
    "**Creating efficient gates for trapped ions without individually addressing the ions**\n",
    "\n",
    "Boulder Opal equips you to efficiently optimize trapped-ion gates that use Mølmer–Sørensen interactions.\n",
    "These gates use the vibrational modes of the ion chain to mediate the interaction between the ions, leaving the qubits in an entangled state and restoring the motional state after the operation.\n",
    "\n",
    "Mølmer–Sørensen-type operations can be performed using either individual addressing of each ion, or a global beam that interacts with all the ions in the chain.\n",
    "The current user guide shows how to perform the optimization in the case of a global beam with multiple tones.\n",
    "In other words, the control problem we consider here is one where the interaction Hamiltonian is of the form:\n",
    "\n",
    "$$\n",
    "H(t) = i\\frac{\\hbar}{2} \\sum_{j=1}^N \\sigma_{x, j} \\sum_{p=1}^{3N} \\sum_{k=1}^M \\eta_{kpj} \\left\\{ \\gamma^{(k)}(t) e^{i \\delta_{kp} t} a_{p}^\\dagger - \\left[ \\gamma^{(k)} (t) \\right]^* e^{-i \\delta_{kp} t} a_p \\right\\},\n",
    "$$\n",
    "\n",
    "where $N$ is the number of ions, $M$ is the number of tones in the global beam, and $a_p$ is the annihilation operator for the p-th mode of oscillation of the chain.\n",
    "The parameters $\\delta_{kp}$ indicate the relative detuning between the k-th tone of the global beam and the p-th mode of oscillation, and the $\\eta_{kpj}$ are the Lamb–Dicke parameters for the k-th tone, p-th mode of oscillation, and j-th ion.\n",
    "These two set of parameters are provided by you as input for the optimization, in order to obtain the controls $\\gamma^{(k)}(t)$ for the k-th tone of the global beam.\n",
    "\n",
    "For more information about the theory behind Mølmer-Sørensen gates, see the user guide [How to optimize error-robust Mølmer–Sørensen gates for trapped ions](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/trapped-ion-quantum-computing/learn-to-optimize-molmer-sorensen-gates-for-trapped-ions).\n",
    "There you find an introduction to the Mølmer–Sørensen gates and information about how to optimize them both for the case of a global single-tone beam, and for the more flexible case with individual ion addressing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Define and calculate ion trap properties\n",
    "\n",
    "Pass the parameters of the ion chain to `boulderopal.ions.obtain_ion_chain_properties` and obtain the Lamb–Dicke parameters and relative detunings associated with each of the vibrational modes.\n",
    "Note that the Lamb–Dicke parameters and frequencies might be different for each of the tones of the global beam; these should be calculated using a separate function evaluation for each tone with a distinct wave number.\n",
    "\n",
    "### 2. Optimize drives\n",
    "\n",
    "Inside a graph, define individual optimizable drives for each of the tones of the system.\n",
    "Use the tones to calculate the relative phases obtained between each ion, and the displacements of each motional mode due to the drives.\n",
    "The node `graph.ions.ms_phases_multitone`, which returns the relative phases, accepts Lamb-Dicke parameters and relative detunings for all the tones of the beam. In contrast, the node `graph.ions.ms_displacements` calculates the displacements for one tone at a time.\n",
    "After all the displacements have been calculated, you can add them together to obtain the total mode displacements due to all the tones.\n",
    "\n",
    "The performance or fidelity of the gate is determined by the final relative phases and mode displacements; the result of the phase and displacement calculations is thus passed to `graph.ions.ms_infidelity`, in order to obtain the cost function for optimal controls.\n",
    "(You can add the contribution from `graph.ions.ms_dephasing_robust_cost` if you want to build error-robust gates, as shown in the user guide [How to optimize error-robust Mølmer–Sørensen gates for trapped ions](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/trapped-ion-quantum-computing/learn-to-optimize-molmer-sorensen-gates-for-trapped-ions).)\n",
    "\n",
    "Run this optimization with `boulderopal.run_optimization` to obtain the optimal drives."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Optimal controls to perform a Mølmer–Sørensen gate with a two-tone global beam.\n",
    "\n",
    "The following example creates optimal two-tone global drives to maximally entangle a two-ion chain.\n",
    "At the end, the drives obtained are plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-22T03:12:45.565297Z",
     "start_time": "2022-04-22T03:12:45.098303Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-25T21:09:20.419143Z",
     "start_time": "2022-04-25T21:09:20.354166Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define parameters of the ion trap.\n",
    "ion_count = 2\n",
    "atomic_mass = 171  # Yb ions.\n",
    "center_of_mass_frequencies = [1.6e6, 1.5e6, 0.3e6]\n",
    "\n",
    "# Define laser parameters.\n",
    "maximum_rabi_rate = 2 * np.pi * 50e3  # Hz\n",
    "laser_detuning = 1.6e6 + 4.7e3  # Hz\n",
    "\n",
    "# Define gate parameters.\n",
    "duration = 3e-4  # s\n",
    "target_phases = np.array([[0, 0], [np.pi / 4, 0]])\n",
    "segment_count = 64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-25T21:09:20.419143Z",
     "start_time": "2022-04-25T21:09:20.354166Z"
    }
   },
   "outputs": [],
   "source": [
    "# Obtain setup parameters for the two tones.\n",
    "lamb_dicke_parameters_1, relative_detunings_1, *_ = bo.ions.obtain_ion_chain_properties(\n",
    "    atomic_mass=atomic_mass,\n",
    "    ion_count=ion_count,\n",
    "    center_of_mass_frequencies=center_of_mass_frequencies,\n",
    "    wavevector=[2 * np.pi * 2.0 / 355e-9, 0, 0],\n",
    "    laser_detuning=laser_detuning,\n",
    ").values()\n",
    "\n",
    "lamb_dicke_parameters_2, relative_detunings_2, *_ = bo.ions.obtain_ion_chain_properties(\n",
    "    atomic_mass=atomic_mass,\n",
    "    ion_count=ion_count,\n",
    "    center_of_mass_frequencies=center_of_mass_frequencies,\n",
    "    wavevector=[2 * np.pi * 2.4 / 355e-9, 0, 0],\n",
    "    laser_detuning=laser_detuning,\n",
    ").values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-25T21:09:28.696922Z",
     "start_time": "2022-04-25T21:09:28.668867Z"
    }
   },
   "outputs": [],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "# Define drive for the first tone.\n",
    "ion_drive_1 = graph.complex_optimizable_pwc_signal(\n",
    "    segment_count=segment_count,\n",
    "    maximum=maximum_rabi_rate,\n",
    "    duration=duration,\n",
    "    name=r\"$\\gamma^{(1)}$\",\n",
    ")\n",
    "\n",
    "# Define drive for the second tone.\n",
    "ion_drive_2 = graph.complex_optimizable_pwc_signal(\n",
    "    segment_count=segment_count,\n",
    "    maximum=maximum_rabi_rate,\n",
    "    duration=duration,\n",
    "    name=r\"$\\gamma^{(2)}$\",\n",
    ")\n",
    "\n",
    "# Calculate phases due to both drives.\n",
    "ms_phases = graph.ions.ms_phases_multitone(\n",
    "    drives=[ion_drive_1, ion_drive_2],\n",
    "    lamb_dicke_parameters=np.array([lamb_dicke_parameters_1, lamb_dicke_parameters_2]),\n",
    "    relative_detunings=np.array([relative_detunings_1, relative_detunings_2]),\n",
    "    name=\"phases\",\n",
    ")\n",
    "\n",
    "# Calculate displacements due to each drive, which is applied to both ions.\n",
    "ms_displacements_1 = graph.ions.ms_displacements(\n",
    "    drives=[ion_drive_1] * ion_count,\n",
    "    lamb_dicke_parameters=lamb_dicke_parameters_1,\n",
    "    relative_detunings=relative_detunings_1,\n",
    ")\n",
    "ms_displacements_2 = graph.ions.ms_displacements(\n",
    "    drives=[ion_drive_2] * ion_count,\n",
    "    lamb_dicke_parameters=lamb_dicke_parameters_2,\n",
    "    relative_detunings=relative_detunings_2,\n",
    ")\n",
    "\n",
    "# Calculate total infidelity due to the phases and both displacement contributions.\n",
    "infidelity = graph.ions.ms_infidelity(\n",
    "    phases=ms_phases,\n",
    "    displacements=ms_displacements_1 + ms_displacements_2,\n",
    "    target_phases=target_phases,\n",
    "    name=\"infidelity\",\n",
    ")\n",
    "\n",
    "# Run optimization.\n",
    "result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"infidelity\",\n",
    "    output_node_names=[r\"$\\gamma^{(1)}$\", r\"$\\gamma^{(2)}$\", \"phases\"],\n",
    "    optimization_count=4,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-25T21:09:35.785685Z",
     "start_time": "2022-04-25T21:09:34.866143Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Target phase:    0.7853981634\n",
      "Optimized phase: 0.7853981501\n",
      "Optimization cost: 1.332e-15\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Print phases and cost.\n",
    "print(f\"Target phase:    {target_phases[1][0]:.10f}\")\n",
    "print(f\"Optimized phase: {result['output'].pop('phases')['value'][1][0]:.10f}\")\n",
    "print(f\"Optimization cost: {result['cost']:.3e}\")\n",
    "\n",
    "# Plot optimized drives.\n",
    "qv.plot_controls(result[\"output\"])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}