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    "# How to simulate closed, noiseless systems\n",
    "**Simulate the dynamics of closed quantum systems**\n",
    "\n",
    "Boulder Opal enables you to simulate the dynamics of quantum systems that are subject to complex deterministic Hamiltonians. Simulation of quantum dynamics can benefit from graph-based calculation when elements of the computation undergo transformations linked to other nodes.  For instance, considering simulation of a quantum system subject to a distorted control pulse, we can combine the source of distortion into the computational graph in order to flexibly simulate the composite system.\n",
    "\n",
    "In this notebook we show how to use Boulder Opal to perform simulations of multilevel systems with complex coupling mechanisms using graph-based simulation.  This approach is preferable when a simulation becomes part of a larger computation where flexibility is prioritized. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "Here we show how to use Boulder Opal to create and execute a graph made up of nodes (corresponding to the different steps in the simulation) that represent functions of previous nodes (or of constant values).\n",
    "Please see the [currently available primitive nodes](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes).\n",
    "\n",
    "\n",
    "### 1. Define computational graph\n",
    "To describe the dynamics of a noiseless quantum system with Boulder Opal, start by setting up a graph object as described in the [How to represent quantum systems using graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/how-to-represent-quantum-systems-using-graphs) user guide. \n",
    "\n",
    "### 2. Set up quantum system\n",
    "Within the graph, define the piecewise-constant (PWC) system Hamiltonian. This is done by combining time-dependent signals with the corresponding operators for each term in the Hamiltonian. Signals are created using the `graph.pwc_signal` operation, while the operators are represented by constant matrices. \n",
    "\n",
    "### 3. Create simulation node\n",
    "Define a simulation node using the `graph.time_evolution_operators_pwc` operation. This calculates the unitary operation corresponding to the evolution of the system at times defined by the array `sample_times`. From these unitaries, one can calculate the state, or any system observable, at the specified times.   \n",
    "\n",
    "### 4. Execute graph-based simulation \n",
    "Execute the graph-based simulation by calling the `boulderopal.execute_graph` function. After the simulation is successfully completed, you can extract the results explicitly defined in the `output_node_names`, as described in the \n",
    "[How to represent quantum systems using graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/how-to-represent-quantum-systems-using-graphs) user guide.\n",
    "\n",
    "The graph-based approach also offers the possibility of running multiple simulations with a single call to `boulderopal.execute_graph`. For this, instead of defining a single Hamiltonian, you can define a batch of them, as examplified in the STIRAP example below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Generate entangled states in atomic chains\n",
    "\n",
    "In this example we show how to simulate the adiabatic dynamics of a multi-atomic system going from the ground state to an entangled state involving all atoms.\n",
    "We start by instantiating a graph and [adding operations to it](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes) in order to simulate the dynamics of an atomic chain.\n",
    "\n",
    "We consider a chain of $N=8$ atoms, each one modeled as a qubit, with $|0\\rangle$ representing the ground state and $|1\\rangle$ representing a Rydberg state.\n",
    "The total Hamiltonian of the system, as described by [A. Omran et al.](https://doi.org/10.1126/science.aax9743), is given by\n",
    "\n",
    "$$ H = \\frac{\\Omega(t)}{2} \\sum_{i=1}^N \\sigma_x^{(i)} - \\Delta(t) \\sum_{i=1}^N n_i - \\sum_{i=1}^N \\delta_i n_i + \\sum_{i<j}^N \\frac{V}{\\vert i-j \\vert^6}n_i n_j , $$\n",
    "\n",
    "with $\\sigma_x^{(i)} = \\vert 0 \\rangle \\langle 1 \\vert_i + \\vert 1 \\rangle \\langle 0 \\vert_i$, and $n_i = \\vert 1\\rangle\\langle 1 \\vert_i$.\n",
    "The fixed system parameters are the interaction strength between excited atoms, $V= 2\\pi \\times 24$ MHz, and the local energy shifts $\\delta_i =  - 2 \\pi \\times 4.5$ MHz for $i=1,N$ or 0 otherwise.\n",
    "\n",
    "We consider the system to be initially in its ground state,\n",
    "$ |\\psi(t=0)\\rangle = |00000000\\rangle$ ,\n",
    "and we aim to prepare the entangled target state\n",
    "$|\\psi_\\mathrm{target}\\rangle = \\frac{1}{\\sqrt{2}} \\Big( |01010101\\rangle + |10101010\\rangle \\Big) $.\n",
    "To achieve this superposition, the effective coupling strength to the Rydberg state $\\Omega(t)$ is modulated by a $\\sin^2$ envelope while the detuning $\\Delta(t)$ is linearly swept around zero, for a total time of $T = 1.1$ µs."
   ]
  },
  {
   "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",
    "import boulderopal as bo\n",
    "\n",
    "plt.style.use(qv.get_qctrl_style())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829145\") has started.\n",
      "Your task (action_id=\"1829145\") has completed.\n"
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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 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Physical parameters of the systems.\n",
    "N_qubits = 8\n",
    "interaction_strength = 24.0e6 * (2.0 * np.pi)  # Hz\n",
    "local_shift = -4.5e6 * (2.0 * np.pi)  # Hz\n",
    "omega_max = 10.0e6 * (2.0 * np.pi)  # Hz\n",
    "delta_max = 20.0e6 * (2.0 * np.pi)  # Hz\n",
    "total_duration = 1.1e-6\n",
    "segments = 50\n",
    "sample_times = np.linspace(0.0, total_duration, 100, endpoint=False)\n",
    "\n",
    "# Create the data flow graph describing the system.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Coupling strength to the Rydberg state operator.\n",
    "sigma_x_sum = sum(\n",
    "    graph.pauli_kronecker_product([(\"X\", k)], N_qubits) for k in range(N_qubits)\n",
    ")\n",
    "\n",
    "# Detuning operator.\n",
    "n_operator_list = [\n",
    "    0.5 * graph.pauli_kronecker_product([(\"I\", k)], N_qubits)\n",
    "    - 0.5 * graph.pauli_kronecker_product([(\"Z\", k)], N_qubits)\n",
    "    for k in range(N_qubits)\n",
    "]\n",
    "n_operator_sum = graph.sum(n_operator_list, 0)\n",
    "\n",
    "# Local energy shift operator.\n",
    "local_shifts = np.zeros(N_qubits)\n",
    "local_shifts[0] = local_shift\n",
    "local_shifts[-1] = local_shift\n",
    "local_shift_operator = sum(shift * n for shift, n in zip(local_shifts, n_operator_list))\n",
    "\n",
    "# Interaction operator.\n",
    "interaction_operator = 0\n",
    "for idx1 in range(N_qubits):\n",
    "    for idx2 in range(idx1):\n",
    "        n1_n2 = n_operator_list[idx1] @ n_operator_list[idx2]\n",
    "        interaction_operator += (n1_n2) / np.abs(idx1 - idx2) ** 6\n",
    "interaction_operator *= interaction_strength\n",
    "\n",
    "# Initial state.\n",
    "initial_state = graph.fock_state(2**N_qubits, 0)\n",
    "\n",
    "# Target GHZ state.\n",
    "idx_even = sum(2**n for n in range(0, N_qubits, 2))  # |0101...⟩\n",
    "idx_odd = sum(2**n for n in range(1, N_qubits, 2))  # |1010...⟩\n",
    "GHZ_state = np.zeros([2**N_qubits])\n",
    "GHZ_state[[idx_even, idx_odd]] = 1.0 / np.sqrt(2.0)\n",
    "\n",
    "# Signals for delta and omega.\n",
    "omega_signal = graph.signals.cosine_pulse_pwc(\n",
    "    duration=total_duration, segment_count=segments, amplitude=omega_max, name=\"omega\"\n",
    ")\n",
    "delta_signal = graph.signals.linear_ramp_pwc(\n",
    "    duration=total_duration, segment_count=segments, end_value=delta_max, name=\"delta\"\n",
    ")\n",
    "\n",
    "# Construct the Hamiltonian.\n",
    "omega_term = 0.5 * omega_signal * sigma_x_sum\n",
    "delta_term = -delta_signal * n_operator_sum\n",
    "constant_term = interaction_operator - local_shift_operator\n",
    "\n",
    "hamiltonian = omega_term + delta_term + constant_term\n",
    "\n",
    "# Calculate the evolution unitaries and evolve the initial state.\n",
    "unitaries = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=hamiltonian, sample_times=sample_times\n",
    ")\n",
    "evolved_states = unitaries @ initial_state[:, None]\n",
    "evolved_states.name = \"evolved_states\"\n",
    "\n",
    "# Project the evolved and target states to calculate the fidelity.\n",
    "fidelity = graph.abs(GHZ_state[None] @ evolved_states) ** 2\n",
    "fidelity.name = \"fidelity\"\n",
    "\n",
    "# Run simulation.\n",
    "graph_result = bo.execute_graph(\n",
    "    graph=graph, output_node_names=[\"omega\", \"delta\", \"evolved_states\", \"fidelity\"]\n",
    ")\n",
    "\n",
    "# Plot the controls.\n",
    "qv.plot_controls(\n",
    "    {\n",
    "        \"$\\\\Omega$\": graph_result[\"output\"][\"omega\"],\n",
    "        \"$\\\\Delta$\": graph_result[\"output\"][\"delta\"],\n",
    "    }\n",
    ")\n",
    "plt.suptitle(\"Pulses for $\\\\Omega$ and $\\\\Delta$\")\n",
    "\n",
    "# Retrieve and plot the evolved states and fidelity.\n",
    "evolved_states = graph_result[\"output\"][\"evolved_states\"][\"value\"].squeeze()\n",
    "fidelity = graph_result[\"output\"][\"fidelity\"][\"value\"].squeeze()\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(15, 5))\n",
    "axs[0].plot(sample_times * 1e6, np.abs(evolved_states) ** 2)\n",
    "axs[0].set_xlabel(\"Time (µs)\")\n",
    "axs[0].set_ylabel(\"Population\")\n",
    "axs[0].set_title(\"State populations dynamics\")\n",
    "axs[1].plot(sample_times * 1e6, fidelity)\n",
    "axs[1].set_xlabel(\"Time (µs)\")\n",
    "axs[1].set_ylabel(\"Fidelity\")\n",
    "axs[1].set_title(\"Fidelity dynamics\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Simulate the effect of pulse delay on STIRAP\n",
    "\n",
    "In this example we show how to simulate the dynamics of a three-level system undergoing stimulated Raman adiabatic passage (STIRAP) when subjected to pump and Stokes pulses. If the pulses are applied in a counter-intuitive manner, that is, $\\Omega_{23}(t)$ is applied before $\\Omega_{12}(t)$ (or $t_\\textrm{delay} >0$), the STIRAP pulse sequence will transfer the population in state $|1\\rangle$ to state $|3\\rangle$. In the calculation below, we will see the effect of $t_\\textrm{delay}$ on the infidelity of the process. Moreover, we will assume that the input controls are very coarse, consisting of very few segments, but they are passed through a Gaussian filter before acting on the three-level system.\n",
    "\n",
    "\n",
    "The Hamiltonian of the system is given by\n",
    "$$\n",
    "H(t) =\n",
    "\\frac{1}{2} \\Omega_{12}(t) \\Big(|1\\rangle\\langle 2| + |2\\rangle\\langle 1|\\Big)\n",
    "+\n",
    "\\frac{1}{2} \\Omega_{23}(t) \\Big(|2\\rangle\\langle 3| + |3\\rangle\\langle 2|\\Big)\n",
    ",\n",
    "$$\n",
    "where the time-dependent Rabi rates for the pump and Stoke pulses are applied for $t\\in(0,T)$ with a Gaussian profile:\n",
    "$$\n",
    "\\Omega_{12}(t) = \\Omega_\\max \\exp\\left(- \\frac{\\left(t - \\frac{T}{2} - \\frac{t_\\textrm{delay}}{2}\\right)^2}{2\\sigma^2}\\right)\n",
    "\\\\\n",
    "\\Omega_{23}(t) = \\Omega_\\max \\exp\\left(- \\frac{\\left(t - \\frac{T}{2} + \\frac{t_\\textrm{delay}}{2}\\right)^2}{2\\sigma^2}\\right)\n",
    "$$\n",
    "with a maximum amplitude $\\Omega_\\max$, a pulse width $\\sigma$, and a delay between them of $t_\\textrm{delay}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define matrices for the Hamiltonian operators.\n",
    "a_12 = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])\n",
    "a_23 = np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0]])\n",
    "\n",
    "# Define the target unitary: state |1⟩ goes to state |3⟩.\n",
    "target_operation = np.array([[0, 0, 0], [0, 0, 0], [1, 0, 0]])\n",
    "\n",
    "# Define system parameters.\n",
    "omega_max = 2 * np.pi * 5e6  # Hz\n",
    "total_duration = 10.0e-6  # s\n",
    "sigma = 0.5e-6\n",
    "gauss_filter_std = 0.5e-6\n",
    "input_segment_count = 12\n",
    "filtered_segment_count = 100\n",
    "\n",
    "times = np.linspace(0.0, total_duration, input_segment_count)\n",
    "durations = np.array([total_duration / input_segment_count] * input_segment_count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we create a batch of input Gaussian pulses (for different values of $t_\\textrm{delay}$), filter them, and use them to simulate the time evolution of the system. The batch of pulses allows the computations for all values of $t_\\textrm{delay}$ to be performed in parallel when the graph is executed. In this case, the first dimension of the $\\Omega$ pulse corresponds to the number of delay values in the batch (defined as 51 here) and the second dimension accounts for the time points sampled from the evolution (defined by `input_segment_count = 12` in this example). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define values of t_delay.\n",
    "t_delay_values = np.linspace(-total_duration / 2, total_duration / 2, 51)\n",
    "\n",
    "# Create batch of coarse input pulses.\n",
    "omega_12_pulse = omega_max * np.exp(\n",
    "    -0.5\n",
    "    * (times[None] - total_duration / 2.0 - t_delay_values[:, None] / 2.0) ** 2\n",
    "    / sigma**2\n",
    ")\n",
    "omega_23_pulse = omega_max * np.exp(\n",
    "    -0.5\n",
    "    * (times[None] - total_duration / 2.0 + t_delay_values[:, None] / 2.0) ** 2\n",
    "    / sigma**2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this particular example, we are interested only in the infidelities of the operation for each time delay, which can be extracted directly from the `graph.infidelity_stf` operation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829146\") has started.\n",
      "Your task (action_id=\"1829146\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Create the data flow graph describing the system.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create input signals.\n",
    "omega_12_signal = graph.pwc_signal(\n",
    "    values=omega_12_pulse, duration=total_duration, name=\"omega_12_signal\"\n",
    ")\n",
    "omega_23_signal = graph.pwc_signal(\n",
    "    values=omega_23_pulse, duration=total_duration, name=\"omega_23_signal\"\n",
    ")\n",
    "\n",
    "# Filter signals through a Gaussian filter.\n",
    "filtered_omega_12_signal = graph.convolve_pwc(\n",
    "    omega_12_signal, graph.gaussian_convolution_kernel(gauss_filter_std)\n",
    ")\n",
    "filtered_omega_23_signal = graph.convolve_pwc(\n",
    "    omega_23_signal, graph.gaussian_convolution_kernel(gauss_filter_std)\n",
    ")\n",
    "\n",
    "# Discretize filtered signals to output smoothed signals.\n",
    "sampled_filtered_pulse_12 = graph.discretize_stf(\n",
    "    stf=filtered_omega_12_signal,\n",
    "    duration=total_duration,\n",
    "    segment_count=filtered_segment_count,\n",
    "    name=\"filtered_omega_12_signal\",\n",
    ")\n",
    "sampled_filtered_pulse_23 = graph.discretize_stf(\n",
    "    stf=filtered_omega_23_signal,\n",
    "    duration=total_duration,\n",
    "    segment_count=filtered_segment_count,\n",
    "    name=\"filtered_omega_23_signal\",\n",
    ")\n",
    "\n",
    "# Create Hamiltonian terms.\n",
    "omega_12_term = filtered_omega_12_signal * a_12\n",
    "omega_23_term = filtered_omega_23_signal * a_23\n",
    "\n",
    "# Define the target operation.\n",
    "target = graph.target(operator=target_operation)\n",
    "\n",
    "# Calculate the infidelities.\n",
    "infidelities = graph.infidelity_stf(\n",
    "    sample_times=np.linspace(0, total_duration, filtered_segment_count),\n",
    "    hamiltonian=omega_12_term + omega_23_term,\n",
    "    target=target,\n",
    "    name=\"infidelities\",\n",
    ")\n",
    "\n",
    "# Run simulation.\n",
    "graph_result = bo.execute_graph(\n",
    "    graph=graph,\n",
    "    output_node_names=[\n",
    "        \"infidelities\",\n",
    "        \"omega_12_signal\",\n",
    "        \"omega_23_signal\",\n",
    "        \"filtered_omega_12_signal\",\n",
    "        \"filtered_omega_23_signal\",\n",
    "    ],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now perform the simulation and retrieve the returned control infidelities.  We then plot both the infidelities as well as a pair of the input/filtered pulses simulated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def batch_item(batch, idx):\n",
    "    \"\"\"\n",
    "    Extract a single item from a batched PWC.\n",
    "    \"\"\"\n",
    "    return {\"durations\": batch[\"durations\"], \"values\": batch[\"values\"][idx]}\n",
    "\n",
    "\n",
    "# Plot the input/filtered pulses.\n",
    "qv.plot_controls(\n",
    "    {\n",
    "        \"input $\\\\Omega_{12}$\": batch_item(\n",
    "            graph_result[\"output\"][\"omega_12_signal\"], 33\n",
    "        ),\n",
    "        \"input $\\\\Omega_{23}$\": batch_item(\n",
    "            graph_result[\"output\"][\"omega_23_signal\"], 33\n",
    "        ),\n",
    "        \"filtered $\\\\Omega_{12}$\": batch_item(\n",
    "            graph_result[\"output\"][\"filtered_omega_12_signal\"], 33\n",
    "        ),\n",
    "        \"filtered $\\\\Omega_{23}$\": batch_item(\n",
    "            graph_result[\"output\"][\"filtered_omega_23_signal\"], 33\n",
    "        ),\n",
    "    }\n",
    ")\n",
    "plt.suptitle(r\"Input and filtered pulses for $t_\\mathrm{delay} = 0.16 T$\")\n",
    "\n",
    "# Plot the infidelities obtained as a function of the pulse delay.\n",
    "plt.figure()\n",
    "plt.plot(t_delay_values / 1e-6, graph_result[\"output\"][\"infidelities\"][\"value\"])\n",
    "plt.xlabel(r\"Pulse delay $\\tau$ (µs)\")\n",
    "plt.ylabel(\"Infidelity\")\n",
    "plt.title(\"Infidelity as a function of the pulse delay\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the infidelity only goes to 0 when $t_\\textrm{delay} > 0$, but if the two pulses are too separated the infidelity increases again."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
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