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   "source": [
    "# How to optimize controls on large sparse Hamiltonians\n",
    "**Efficiently perform control optimization on sparse Hamiltonians**\n",
    "\n",
    "Boulder Opal exposes a highly-flexible [optimization engine](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/run_optimization) for general-purpose gradient-based optimization.  It can be directly applied to model-based control optimization for arbitrary-dimensional quantum systems. \n",
    "\n",
    "This optimization engine provides best-in-class time to solution, but the efficiency of the optimization will always decline with the system size.\n",
    "In cases where the Hamiltonian to be treated is sparse it is possible to recover performance via specialized methods.\n",
    "In this user guide we demonstrate the use of sparse-Hamiltonian methods for efficient optimizations in large systems.\n",
    "To learn the basics about control optimization, you can follow our [robust optimization tutorial](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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Define system Hamiltonian with a sparse representation\n",
    "\n",
    "The flexible Boulder Opal optimization engine expresses all optimization problems as data flow graphs, which describe how optimization variables (variables that can be tuned by the optimizer) are transformed into the cost function (the objective that the optimizer attempts to minimize). \n",
    "\n",
    "You can carry out the optimization of larger systems by using approximate integration methods that are more computationally effective than standard approaches.\n",
    "This is especially helpful when the Hamiltonian is sparse.\n",
    "\n",
    "Here you can define system Hamiltonian terms with a sparse representation with operations such as `graph.sparse_pwc_operator` or `graph.constant_sparse_pwc_operator`.\n",
    "These accept an operator as a Tensor or as a sparse matrix (for example, as a [`scipy.sparse.coo_matrix`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_matrix.html)).\n",
    "\n",
    "### 2. Use sparse-matrix methods in the computational graph\n",
    "\n",
    "You can then integrate the Schrödinger equation using the [Lanczos algorithm](https://en.wikipedia.org/wiki/Lanczos_algorithm) that is available in the operation `graph.state_evolution_pwc`.\n",
    "The Lanczos algorithm accepts a parameter called the `krylov_subspace_dimension`, which controls the accuracy of the operation.\n",
    "You can choose this parameter manually or use the operation `graph.estimated_krylov_subspace_dimension_lanczos` to obtain an estimate of its best choice for your Hamiltonian and error tolerance.\n",
    "\n",
    "All of these calculations are performed within the optimization graph.\n",
    "\n",
    "### 3. Run graph-based optimization\n",
    "\n",
    "With the graph object created, an optimization can be run using the `boulderopal.run_optimization` function. The cost, the outputs, and the graph must be provided. The function returns the results of the optimization. Note that this example code block uses naming that should be replaced with the naming used in your graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "is_executing": true
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   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo\n",
    "\n",
    "plt.style.use(qv.get_qctrl_style())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Optimized controls in a nearest-neighbor-coupled qubit chain\n",
    "\n",
    " To illustrate this, consider a system of four qubits where each qubit only interacts with the nearest neighbor through an XX coupling operator:\n",
    "\n",
    "$$ H = \\frac{1}{2} \\sum_{i=1}^3 \\Omega_i(t) \\sigma_{x,i} \\sigma_{x,i+1}. $$\n",
    "\n",
    "Suppose you start from the state $\\left| 0000 \\right\\rangle$ and want to create the state $\\left(\\left| 0000 \\right\\rangle +i\\left| 0011 \\right\\rangle -i\\left| 1100 \\right\\rangle+ \\left| 1111 \\right\\rangle \\right)/2$ by using optimized controls for $\\Omega_1(t)$, $\\Omega_2(t)$, and $\\Omega_3(t)$.\n",
    "\n",
    "The following code uses spare-matrix techniques and Lanczos algorithm to obtain an estimate for an integration accuracy of `1e-5` and then how to optimize the controls using it. The code also prints a comparison between the integration that uses the Lanczos algorithm and the exact integration, as well as the optimized controls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828668\") has completed.\n",
      "Your task (action_id=\"1828669\") has started.\n",
      "Your task (action_id=\"1828669\") has completed.\n",
      "\n",
      "Recommended Krylov subspace dimension:\t10\n",
      "Final state infidelity: 1.110e-14 (Lanczos integration)\n",
      "Final state infidelity: -1.217e-13 (Exact integration)\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x540 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define physical constraints.\n",
    "omega_max = 2 * np.pi * 5e6  # rad/s\n",
    "duration = 500e-9  # s\n",
    "segment_count = 20\n",
    "sample_times = np.linspace(0, duration, 100)\n",
    "target_state = np.zeros(2**4, complex)\n",
    "target_state[int(\"0000\", 2)] = 1 / 2\n",
    "target_state[int(\"0011\", 2)] = 1j / 2\n",
    "target_state[int(\"1100\", 2)] = -1j / 2\n",
    "target_state[int(\"1111\", 2)] = 1 / 2\n",
    "\n",
    "\n",
    "# Define coupling operators.\n",
    "def create_operators(graph):\n",
    "    sigma_x = graph.pauli_matrix(\"X\")\n",
    "    return [\n",
    "        0.5 * graph.embed_operators([(sigma_x, n), (sigma_x, n + 1)], [2] * 4)\n",
    "        for n in range(3)\n",
    "    ]\n",
    "\n",
    "\n",
    "# Build graph to estimate the Krylov subspace dimension.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Find the spectral range for the Hamiltonian with highest omega value.\n",
    "spectral_range = graph.spectral_range(operator=omega_max * sum(create_operators(graph)))\n",
    "\n",
    "# Find the suggested Krylov subspace dimension for that spectral range\n",
    "# with an error tolerance of 1e-5.\n",
    "graph.estimated_krylov_subspace_dimension_lanczos(\n",
    "    spectral_range=spectral_range,\n",
    "    duration=duration,\n",
    "    maximum_segment_duration=duration / segment_count,\n",
    "    error_tolerance=1e-5,\n",
    "    name=\"krylov_subspace_dimension\",\n",
    ")\n",
    "\n",
    "# Estimate recommended Krylov subspace dimension.\n",
    "krylov_subspace_dimension = bo.execute_graph(\n",
    "    graph=graph, output_node_names=\"krylov_subspace_dimension\"\n",
    ")[\"output\"][\"krylov_subspace_dimension\"][\"value\"]\n",
    "\n",
    "# Build optimization graph.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Define initial state.\n",
    "initial_state = graph.fock_state(16, 0)\n",
    "\n",
    "# Define individual control signals (Omegas).\n",
    "signals = [\n",
    "    graph.real_optimizable_pwc_signal(\n",
    "        segment_count=segment_count,\n",
    "        minimum=-omega_max,\n",
    "        maximum=omega_max,\n",
    "        duration=duration,\n",
    "        name=rf\"$\\Omega_{n+1}$\",\n",
    "    )\n",
    "    for n in range(3)\n",
    "]\n",
    "\n",
    "# Define individual terms of the Hamiltonian.\n",
    "operators = create_operators(graph)\n",
    "sparse_hamiltonian_terms = [\n",
    "    graph.sparse_pwc_operator(signal=signal, operator=operator)\n",
    "    for signal, operator in zip(signals, operators)\n",
    "]\n",
    "\n",
    "# Create total Hamiltonian by adding terms.\n",
    "hamiltonian = graph.sparse_pwc_sum(sparse_hamiltonian_terms)\n",
    "\n",
    "# Integrate the Schrödinger equation for the Hamiltonian,\n",
    "# using the recommended choice of Krylov subspace dimension.\n",
    "evolved_states = graph.state_evolution_pwc(\n",
    "    initial_state=initial_state,\n",
    "    hamiltonian=hamiltonian,\n",
    "    krylov_subspace_dimension=krylov_subspace_dimension,\n",
    "    sample_times=sample_times,\n",
    ")\n",
    "\n",
    "# Calculate the infidelities as a function of time.\n",
    "sparse_infidelities = graph.state_infidelity(\n",
    "    evolved_states, target_state, name=\"sparse_infidelities\"\n",
    ")\n",
    "\n",
    "# Use the final state infidelity as the cost.\n",
    "final_state_infidelity = sparse_infidelities[-1]\n",
    "final_state_infidelity.name = \"cost\"\n",
    "\n",
    "# Calculate the evolution using a dense Hamiltonian, for comparison.\n",
    "dense_hamiltonian_terms = [\n",
    "    signal * operator for signal, operator in zip(signals, operators)\n",
    "]\n",
    "dense_hamiltonian = graph.pwc_sum(dense_hamiltonian_terms)\n",
    "time_evolution_operators = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=dense_hamiltonian, sample_times=sample_times\n",
    ")\n",
    "dense_evolved_states = time_evolution_operators @ initial_state[:, None]\n",
    "dense_infidelities = graph.state_infidelity(\n",
    "    dense_evolved_states[..., 0], target_state, name=\"dense_infidelities\"\n",
    ")\n",
    "\n",
    "# Run optimization.\n",
    "result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"cost\",\n",
    "    output_node_names=[\"sparse_infidelities\", \"dense_infidelities\"]\n",
    "    + [rf\"$\\Omega_{n+1}$\" for n in range(3)],\n",
    "    optimization_count=5,\n",
    ")\n",
    "\n",
    "# Extract time-dependent infidelities.\n",
    "sparse_infidelities = result[\"output\"].pop(\"sparse_infidelities\")[\"value\"].flatten()\n",
    "dense_infidelities = result[\"output\"].pop(\"dense_infidelities\")[\"value\"].flatten()\n",
    "\n",
    "# Plot and print results.\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(sample_times / 1e-9, sparse_infidelities, label=\"Lanczos integration\")\n",
    "ax.plot(sample_times / 1e-9, dense_infidelities, \":\", label=\"Exact integration\")\n",
    "ax.legend()\n",
    "ax.set_xlabel(\"Time (ns)\")\n",
    "ax.set_ylabel(\"State infidelity\")\n",
    "\n",
    "print(f\"\\nRecommended Krylov subspace dimension:\\t{krylov_subspace_dimension}\")\n",
    "print(f\"Final state infidelity: {result['cost']:.3e} (Lanczos integration)\")\n",
    "print(f\"Final state infidelity: {dense_infidelities[-1]:.3e} (Exact integration)\")\n",
    "\n",
    "qv.plot_controls(result[\"output\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparison between the time evolution of the infidelity using the Lanczos and exact integrations (top). The difference between them is well within the `1e-5` accuracy. Optimized pulses obtained to generate the target state (bottom)."
   ]
  }
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