{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Perform model-based robust optimization for the cross-resonance gate\n",
    "**Increasing robustness against crosstalk in a two-qubit entangling operation**\n",
    "\n",
    "Boulder Opal provides tools to simplify the process of [control optimization](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-error-robust-quantum-logic-gates/learn-to-design-robust-single-qubit-gates-using-computational-graphs) even for complex multiqubit systems.  Superconducting qubits in particular have been shown to benefit from the application of robust control solutions for the suppression of drift and crosstalk-induced errors endemic to real hardware.  With an appropriate Hamiltonian model of the system it's possible to create noise-robust control solutions which ultimately deliver improved gate fidelity as a means to increase quantum volume.\n",
    "\n",
    "In this application note we will demonstrate the utility of robust control to improve the performance of cross-resonance entangling gates degraded by crosstalk errors.  We will cover:\n",
    "- Modelling crosstalk as a noise channel\n",
    "- Performing model-based control optimization on a pair of coupled multilevel systems\n",
    "- Validating performance by calculating susceptibility to quasi-static crosstalk errors\n",
    "\n",
    "Ultimately this notebook demonstrates how to improve the quantum volume of superconducting quantum computers by delivering gate-level performance enhancements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports and initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import qctrlvisualizer as qv\n",
    "\n",
    "import boulderopal as bo\n",
    "\n",
    "plt.style.use(qv.get_qctrl_style())\n",
    "\n",
    "colors = {\n",
    "    \"Primitive\": \"black\",\n",
    "    \"Optimized\": qv.QCTRL_STYLE_COLORS[0],\n",
    "    \"Robust\": qv.QCTRL_STYLE_COLORS[1],\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Creating a Boulder Opal cross-resonance gate robust to crosstalk\n",
    "Consider a system of two transmon qubits coupled by a common transmission line. Qubit 1 is defined as the control qubit, and qubit 2 is the target qubit. The control qubit is driven by the in-phase and quadrature microwave drive with a frequency that matches the target qubit frequency. In a frame rotating with the drive frequency and after applying the rotating wave approximation (RWA) the Hamiltonian is of the form:\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\hbar} H = (\\Delta + \\epsilon) b_1^\\dagger b_1 +\n",
    "\\frac{\\alpha_1}{2} (b_1^\\dagger)^2 b_1^2 +\n",
    "\\epsilon b_2^\\dagger b_2+\n",
    "\\frac{\\alpha_2}{2} (b_2^\\dagger)^2 b_2^2 +\n",
    " g \\left( b_1^\\dagger b_2 + b_1 b_2^\\dagger \\right) +\\frac{1}{2}\\left(\\Omega(t)b_1 + \\text{H.c.}\\right),\n",
    "$$\n",
    "\n",
    "where $b_i$ is the annihilation operator of the $i$th qubit, $\\Delta=\\omega_1-\\omega_2$ is the detuning between the two qubits where $\\omega_i$ is the frequency of the $i$th qubit, $\\epsilon$ is the mismatch between the drive frequency and the target qubit frequency, $g$ is the effective coupling strength between the qubits, $\\Omega$ is the drive modulus and $\\alpha_i$ is the anharmonicity of the $i$th qubit.\n",
    "\n",
    "The target operation is the $\\pi/2$ cross-resonance gate which operates in the space of the two lowest levels:\n",
    "\n",
    "$$U_\\mathrm{CR}\\left(\\frac{\\pi}{2}\\right)=\\frac{1}{\\sqrt{2}}\\left(\\mathbb{I}-i\\sigma_1^z\\sigma_2^x\\right)=[ZX]^{1/2}.$$\n",
    "\n",
    "Since the above operation is defined up to phase factors of the individual qubits, this may lead to a large infidelity. Consequently, a final (optimizable) phase shift on each qubit is introduced to overcome the infidelity inflation due to these phase factors.\n",
    "\n",
    "This application note addresses robustness to crosstalk. Crosstalk between the qubits leads to unwanted effects that may mimic the effect of noise. The crosstalk Hamiltonian has the form\n",
    "$$\n",
    "\\frac{1}{\\hbar} H_\\mathrm{ct}\n",
    "  = c_\\mathrm{ct}\n",
    "  \\frac{\\Omega(t)}{2}b_2 + \\text{H.c.},\n",
    "$$\n",
    "where $c_\\mathrm{ct}$ is the (complex) relative crosstalk.\n",
    "\n",
    "In this section, we optimize the implementation of the target gate under the effect of crosstalk. This is performed within the framework of the four-level approximation, where only the first four levels of each qubit are considered. Moreover, only up to three excitations overall are permitted, which further reduces the Hilbert space from $16$ states to $10$ states.\n",
    "\n",
    "To set up the optimization, first define operators and constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constants in the lab frame.\n",
    "omega_1 = 5.114 * 2 * np.pi * 1e9  # Hz\n",
    "omega_2 = 4.914 * 2 * np.pi * 1e9  # Hz\n",
    "alpha_1 = -330 * 2 * np.pi * 1e6  # Hz\n",
    "alpha_2 = -330 * 2 * np.pi * 1e6  # Hz\n",
    "g = 3.8 * 2 * np.pi * 1e6  # Hz\n",
    "Delta = omega_1 - omega_2\n",
    "epsilon = 0\n",
    "\n",
    "# Limits for drive amplitudes.\n",
    "drive_max = 200 * 2 * np.pi * 1e6  # Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, define the operators in the Hamiltonian and the target gate. The target gate is defined in the dressed frame, that is, the basis where the constant Hamiltonian term\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\hbar} H_0 = (\\Delta + \\epsilon) b_1^\\dagger b_1 +\n",
    "\\frac{\\alpha_1}{2} (b_1^\\dagger)^2 b_1^2 +\n",
    "\\epsilon b_2^\\dagger b_2+\n",
    "\\frac{\\alpha_2}{2} (b_2^\\dagger)^2 b_2^2 +\n",
    " g \\left( b_1^\\dagger b_2 + b_1 b_2^\\dagger \\right),\n",
    "$$\n",
    "\n",
    "is diagonal. The transformation between the frames is defined through $H_0 S = S D$, with the unitary operator $S$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lowering operator.\n",
    "b = np.diag(np.sqrt(np.arange(1, 4)), 1)\n",
    "# Number operator.\n",
    "n = np.diag(np.arange(4))\n",
    "# Projector onto the two lowest states.\n",
    "qubit_proj = np.diag([1, 1, 0, 0])\n",
    "\n",
    "# Pauli operators.\n",
    "sigma_x = np.zeros(n.shape)\n",
    "sigma_x[:2, :2] = np.array([[0, 1], [1, 0]])\n",
    "sigma_z = np.zeros(n.shape)\n",
    "sigma_z[:2, :2] = np.array([[1, 0], [0, -1]])\n",
    "\n",
    "# Embedding the single-qubit number operators into the two-qubit system of dimension 16.\n",
    "n1 = np.kron(n, np.eye(4))\n",
    "n2 = np.kron(np.eye(4), n)\n",
    "\n",
    "proj = np.kron(qubit_proj, qubit_proj)\n",
    "\n",
    "# Block-diagonal permutations. We find the indices of the 10 two-qutrit\n",
    "# states with the fewest total excitations. This truncates the\n",
    "# Hilbert space to a total of three excitations or less.\n",
    "perm = np.argsort(np.diag(n1 + n2))\n",
    "perm_trunc = perm[:10]\n",
    "block_n = [np.where(np.diag(n1 + n2) == n)[0].tolist() for n in range(4)]\n",
    "truncate = np.ix_(perm_trunc, perm_trunc)\n",
    "\n",
    "# Define truncated operators.\n",
    "b_1 = np.kron(b, np.eye(4))[truncate]\n",
    "bd_1 = b_1.T.conj()\n",
    "b_2 = np.kron(np.eye(4), b)[truncate]\n",
    "bd_2 = b_2.T.conj()\n",
    "bdb_1 = n1[truncate]\n",
    "bdb_2 = n2[truncate]\n",
    "bdb_12 = np.kron(b.T.conj(), b)[truncate]\n",
    "bdb_21 = np.kron(b, b.T.conj())[truncate]\n",
    "bd2b2_1 = (n1 @ n1 - n1)[truncate]\n",
    "bd2b2_2 = (n2 @ n2 - n2)[truncate]\n",
    "\n",
    "sigma_z_1 = np.kron(sigma_z, np.eye(4))[truncate]\n",
    "sigma_z_2 = np.kron(np.eye(4), sigma_z)[truncate]\n",
    "\n",
    "# Frame transformation HS = SD.\n",
    "hamiltonian_with_no_drives = (\n",
    "    (Delta + epsilon) * bdb_1\n",
    "    + epsilon * bdb_2\n",
    "    + alpha_1 * bd2b2_1 / 2\n",
    "    + alpha_2 * bd2b2_2 / 2\n",
    "    + g * (bdb_12 + bdb_21)\n",
    ")\n",
    "S = np.eye(10)\n",
    "base_index = 0\n",
    "for i in block_n:\n",
    "    inds = np.arange(base_index, base_index + len(i))\n",
    "    eigenvalues, eigenvectors = np.linalg.eigh(\n",
    "        hamiltonian_with_no_drives[:, inds][inds, :]\n",
    "    )\n",
    "    for k, j in enumerate(eigenvectors.T):\n",
    "        ind = np.abs(np.abs(j) - 1.0).argmin()\n",
    "        S[:, base_index + ind][inds] = j * np.sign(j[ind])\n",
    "    base_index += len(i)\n",
    "\n",
    "# The phase shift operators in the simulation/optimization frame.\n",
    "phase_shift_operator1 = S @ (sigma_z_1 / 2) @ S.T.conj()\n",
    "phase_shift_operator2 = S @ (sigma_z_2 / 2) @ S.T.conj()\n",
    "\n",
    "# Target in the simulation/optimization frame.\n",
    "zx_half = np.linalg.multi_dot(\n",
    "    [S, ((proj - 1j * np.kron(sigma_z, sigma_x)) / np.sqrt(2))[truncate], S.T.conj()]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating control pulses\n",
    "\n",
    "Next, define the optimization configuration and the control schemes: Primitive, Optimized and Robust."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optimization constraints.\n",
    "duration = 0.4e-6  # s\n",
    "crosstalk_constant = 0.1\n",
    "\n",
    "scheme_configurations = {\n",
    "    \"Primitive\": {\n",
    "        \"primitive_flag\": True,\n",
    "        \"noise_flag\": False,\n",
    "        \"segment_count\": 1,\n",
    "        \"optimization_count\": 10,\n",
    "    },\n",
    "    \"Optimized\": {\n",
    "        \"primitive_flag\": False,\n",
    "        \"noise_flag\": False,\n",
    "        \"segment_count\": 200,\n",
    "        \"optimization_count\": 4,\n",
    "    },\n",
    "    \"Robust\": {\n",
    "        \"primitive_flag\": False,\n",
    "        \"noise_flag\": True,\n",
    "        \"segment_count\": 200,\n",
    "        \"optimization_count\": 4,\n",
    "    },\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimization specification in the next cell involves several steps:\n",
    "- create the (noiseless) Hamiltonian,\n",
    "- create the noise operators,\n",
    "- define the cost function to be minimized by the optimizer, which is the infidelity of the system's evolution,\n",
    "- introduce the final (optimizable) phase shift on each qubit,\n",
    "- compute the infidelity of the Hamiltonian with optimizable phase shifts.\n",
    "\n",
    "The outputs are the optimized values of $\\Omega(t)$ ($x$ and $y$ components) across the gate duration, the optimized phase shifts, and the infidelities with and without the phase shifts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scheme_optimization(primitive_flag, noise_flag, segment_count, optimization_count):\n",
    "    graph = bo.Graph()\n",
    "\n",
    "    # Construct drive term.\n",
    "    if primitive_flag:\n",
    "        drive = graph.real_optimizable_pwc_signal(\n",
    "            segment_count=segment_count,\n",
    "            duration=duration,\n",
    "            maximum=drive_max,\n",
    "            minimum=-drive_max,\n",
    "            name=\"drive\",\n",
    "        )\n",
    "    else:\n",
    "        drive = graph.complex_optimizable_pwc_signal(\n",
    "            segment_count=segment_count,\n",
    "            duration=duration,\n",
    "            maximum=drive_max,\n",
    "            name=\"drive\",\n",
    "        )\n",
    "\n",
    "    drive_term = graph.hermitian_part(drive * b_1)\n",
    "\n",
    "    # Construct remaining Hamiltonian term.\n",
    "    fixed_hamiltonian_term = (\n",
    "        (Delta + epsilon) * bdb_1\n",
    "        + epsilon * bdb_2\n",
    "        + alpha_1 * bd2b2_1 / 2\n",
    "        + alpha_2 * bd2b2_2 / 2\n",
    "        + g * (bdb_12 + bdb_21)\n",
    "    )\n",
    "\n",
    "    hamiltonian = drive_term + fixed_hamiltonian_term\n",
    "\n",
    "    # Create noise operators.\n",
    "    if noise_flag:\n",
    "        crosstalk_1x = crosstalk_constant * graph.real(drive) * (b_2 + bd_2) / 2\n",
    "        crosstalk_1y = crosstalk_constant * graph.imag(drive) * 1j * (b_2 - bd_2) / 2\n",
    "        noise_operators = [crosstalk_1x, crosstalk_1y]\n",
    "    else:\n",
    "        noise_operators = []\n",
    "\n",
    "    # Create infidelity.\n",
    "    infidelity = graph.infidelity_pwc(\n",
    "        hamiltonian=hamiltonian,\n",
    "        noise_operators=noise_operators,\n",
    "        target=graph.target(operator=zx_half),\n",
    "        name=\"infidelity\",\n",
    "    )\n",
    "\n",
    "    # Introduce optimizable phase shifts on each qubit.\n",
    "    phase_shifts = graph.optimization_variable(\n",
    "        count=2,\n",
    "        lower_bound=-np.pi,\n",
    "        upper_bound=np.pi,\n",
    "        is_lower_unbounded=True,\n",
    "        is_upper_unbounded=True,\n",
    "        name=\"phases\",\n",
    "    )\n",
    "    phase_shift_hamiltonian = graph.constant_pwc(\n",
    "        phase_shifts[0] * phase_shift_operator1\n",
    "        + phase_shifts[1] * phase_shift_operator2,\n",
    "        duration=1.0,\n",
    "    )\n",
    "\n",
    "    u_phase = graph.time_evolution_operators_pwc(\n",
    "        hamiltonian=phase_shift_hamiltonian, sample_times=np.array([1.0])\n",
    "    )\n",
    "    # Create infidelity with phase shifts\n",
    "    cost = graph.infidelity_pwc(\n",
    "        hamiltonian=hamiltonian,\n",
    "        noise_operators=noise_operators,\n",
    "        target=graph.target(operator=u_phase[0] @ zx_half),\n",
    "        name=\"infidelity_with_phase_shift\",\n",
    "    )\n",
    "\n",
    "    return bo.run_optimization(\n",
    "        graph=graph,\n",
    "        optimization_count=optimization_count,\n",
    "        cost_node_name=\"infidelity_with_phase_shift\",\n",
    "        output_node_names=[\n",
    "            \"infidelity\",\n",
    "            \"infidelity_with_phase_shift\",\n",
    "            \"drive\",\n",
    "            \"phases\",\n",
    "        ],\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, perform the optimization. The following cell optimizes a primitive pulse as a benchmark, along with the optimized and the robust controls. The infidelities for each control scheme are presented with and without the phase shift."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828083\") has started.\n",
      "Your task (action_id=\"1828083\") has completed.\n",
      "Your task (action_id=\"1828088\") has started.\n",
      "Your task (action_id=\"1828088\") has completed.\n",
      "Your task (action_id=\"1828091\") has started.\n",
      "Your task (action_id=\"1828091\") has completed.\n",
      "\n",
      "\tPrimitive\n",
      "Infidelity: 7.321e-01\n",
      "Infidelity with phase shift: 1.825e-01\n",
      "\n",
      "\tOptimized\n",
      "Infidelity: 4.963e-01\n",
      "Infidelity with phase shift: 4.383e-07\n",
      "\n",
      "\tRobust\n",
      "Infidelity: 5.529e-01\n",
      "Infidelity with phase shift: 3.921e-05\n"
     ]
    }
   ],
   "source": [
    "scheme_results = {}\n",
    "\n",
    "for scheme, config in scheme_configurations.items():\n",
    "    scheme_results[scheme] = scheme_optimization(**config)\n",
    "\n",
    "for scheme, result in scheme_results.items():\n",
    "    print(f\"\\n\\t{scheme}\")\n",
    "    print(f\"Infidelity: {result['output']['infidelity']['value']:.3e}\")\n",
    "    print(\n",
    "        \"Infidelity with phase shift: \"\n",
    "        f\"{result['output']['infidelity_with_phase_shift']['value']:.3e}\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even in the presence of crosstalk, the infidelity arising from the robust pulse (with phase shifts) is extremely low. Visualize the control schemes using the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for scheme, result in scheme_results.items():\n",
    "    qv.plot_controls({\"$\\\\Omega$\": result[\"output\"][\"drive\"]})\n",
    "    plt.suptitle(scheme)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plots display the control pulses ($\\Omega_x$ and $\\Omega_y$) for the primitive, optimized and robust schemes, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verifying accuracy and robustness of Boulder Opal cross-resonance gate\n",
    "\n",
    "Use the controls obtained above to calculate the exact time evolution determined by the Hamiltonian in the four-level approximation. In the cell below, the evolution dynamics is calculated for each scheme with a batch of crosstalk amplitudes. We then extract both the noise-free and the noisy dynamics from the result.\n",
    "\n",
    "First, verify the noise-free operations: compare the noise-free operational infidelities and examine the evolution of an equal superposition of the four lowest 2-qubit states, $|\\psi_0\\rangle =\\frac{1}{2}\\left(|00\\rangle-i|01\\rangle+i|10\\rangle+|11\\rangle\\right)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828096\") has completed.\n",
      "Your task (action_id=\"1828098\") has started.\n",
      "Your task (action_id=\"1828098\") has completed.\n",
      "Your task (action_id=\"1828099\") has started.\n",
      "Your task (action_id=\"1828099\") has completed.\n",
      "\n",
      "Noise-free operational infidelities\n",
      "\tPrimitive :\t1.825e-01\n",
      "\tOptimized :\t4.383e-07\n",
      "\tRobust    :\t2.576e-07\n"
     ]
    }
   ],
   "source": [
    "initial_state = (np.array([[1, -1j, 1j, 0, 1, 0, 0, 0, 0, 0]]) / 2).T\n",
    "crosstalk_count = 101\n",
    "crosstalk_array = np.linspace(-1, 1, crosstalk_count)\n",
    "scheme_infidelities = {}\n",
    "scheme_probabilities = {}\n",
    "\n",
    "for scheme, result in scheme_results.items():\n",
    "    graph = bo.Graph()\n",
    "\n",
    "    # Construct drive term.\n",
    "    drive_values = result[\"output\"][\"drive\"][\"values\"]\n",
    "    drive = graph.pwc_signal(values=drive_values, duration=duration)\n",
    "    drive_term = graph.hermitian_part(drive * b_1)\n",
    "\n",
    "    # Construct crosstalk terms.\n",
    "    drive_batched = graph.pwc_signal(\n",
    "        values=drive_values * crosstalk_array[:, None], duration=duration\n",
    "    )\n",
    "    crosstalk_1x = crosstalk_constant * graph.real(drive_batched) * (b_2 + bd_2) / 2\n",
    "    crosstalk_1y = (\n",
    "        crosstalk_constant * graph.imag(drive_batched) * 1j * (b_2 - bd_2) / 2\n",
    "    )\n",
    "\n",
    "    # Construct remaining Hamiltonian terms.\n",
    "    fixed_hamiltonian_term = (\n",
    "        (Delta + epsilon) * bdb_1\n",
    "        + epsilon * bdb_2\n",
    "        + alpha_1 * bd2b2_1 / 2\n",
    "        + alpha_2 * bd2b2_2 / 2\n",
    "        + g * (bdb_12 + bdb_21)\n",
    "    )\n",
    "\n",
    "    # Generate Hamiltonian and evolution operator.\n",
    "    hamiltonian = crosstalk_1x + crosstalk_1y + drive_term + fixed_hamiltonian_term\n",
    "\n",
    "    u_H = graph.time_evolution_operators_pwc(\n",
    "        hamiltonian=hamiltonian, sample_times=np.array([duration])\n",
    "    )\n",
    "\n",
    "    # Construct phase correction terms.\n",
    "    phase1 = result[\"output\"][\"phases\"][\"value\"][0]\n",
    "    phase2 = result[\"output\"][\"phases\"][\"value\"][1]\n",
    "    phase_shift_hamiltonian = graph.constant_pwc(\n",
    "        phase1 * phase_shift_operator1 + phase2 * phase_shift_operator2, duration=1.0\n",
    "    )\n",
    "    u_phase = graph.time_evolution_operators_pwc(\n",
    "        hamiltonian=phase_shift_hamiltonian, sample_times=np.array([1.0])\n",
    "    )\n",
    "\n",
    "    # Obtain infidelity.\n",
    "    infidelity_with_phase_shift = graph.unitary_infidelity(\n",
    "        u_H[:, -1], u_phase[0] @ zx_half, name=\"infidelity\"\n",
    "    )\n",
    "\n",
    "    # Obtain noise-free state evolution.\n",
    "    final_unitary = graph.conjugate(u_phase) @ u_H\n",
    "    final_state = final_unitary[crosstalk_count // 2, 0] @ initial_state\n",
    "    probabilities = graph.abs(final_state[:, 0]) ** 2\n",
    "    probabilities.name = \"probabilities\"\n",
    "\n",
    "    # Calculate simulation.\n",
    "    graph_result = bo.execute_graph(\n",
    "        graph=graph, output_node_names=[\"infidelity\", \"probabilities\"]\n",
    "    )\n",
    "\n",
    "    scheme_infidelities[scheme] = graph_result[\"output\"][\"infidelity\"][\"value\"]\n",
    "    scheme_probabilities[scheme] = graph_result[\"output\"][\"probabilities\"][\"value\"]\n",
    "\n",
    "print(\"\\nNoise-free operational infidelities\")\n",
    "for scheme, infidelity in scheme_infidelities.items():\n",
    "    print(f\"\\t{scheme:10s}:\\t{infidelity[crosstalk_count // 2]:.3e}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n",
    "fig.suptitle(\"Final populations\", y=1)\n",
    "\n",
    "for ax, (scheme, probs) in zip(axs, scheme_probabilities.items()):\n",
    "    populations = [probs[1], probs[2], 1 - probs[1] - probs[2]]\n",
    "    ax.bar(\n",
    "        [r\"$|01\\rangle$\", r\"$|10\\rangle$\", \"Rest\"], populations, color=colors[scheme]\n",
    "    )\n",
    "    ax.set_ylim(0.0, 0.55)\n",
    "    ax.set_title(scheme)\n",
    "    ax.set_xlabel(\"State\")\n",
    "\n",
    "axs[0].set_ylabel(\"Probability\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure shows the final state after operating the respective gates on the initial state $|\\psi_0\\rangle =\\frac{1}{2}\\left(|00\\rangle-i|01\\rangle+i|10\\rangle+|11\\rangle\\right)$. The final state after an ideal operation of the CR gate should be the Bell state $|\\psi_f\\rangle =\\frac{1}{\\sqrt{2}}\\left(|01\\rangle+|10\\rangle\\right)$. The populations are displayed to assess each scheme. Clearly, there is non-negligible population leakage in the primitive scheme, while both the Optimized and Robust schemes perform almost perfectly (up to a small asymmetry).\n",
    "\n",
    "Next, assess the robustness of the different control solutions to crosstalk noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.suptitle(\"Scheme robustness\")\n",
    "for scheme, infidelity in scheme_infidelities.items():\n",
    "    plt.plot(crosstalk_array, infidelity, label=scheme, color=colors[scheme])\n",
    "plt.legend()\n",
    "plt.xlabel(\"Relative crosstalk\")\n",
    "plt.ylabel(\"Infidelity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure demonstrates the different noise (crosstalk) susceptibilities (in terms of operational infidelity) of the Primitive, Optimized and Robust controls. The Robust scheme has a much broader low-infidelity region."
   ]
  }
 ],
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   "title_cell": "Table of Contents",
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