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   "source": [
    "# How to define continuous analytical Hamiltonians\n",
    "**Use analytical expressions to construct your Hamiltonian**\n",
    "\n",
    "The Boulder Opal [optimization](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/run_optimization) and [simulation](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/execute_graph) engines can be applied to a wide range of quantum systems thanks to the flexible [dataflow graph framework](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/get-an-introduction-to-graphs-in-boulder-opal).\n",
    "\n",
    "In particular, you can define analytical Hamiltonians by taking advantage of Bouldar Opal's basic mathematical operations.\n",
    "In this notebook we show how to define signals from their analytical expressions and use them for simulation or optimization.\n",
    "Note that the `signals` attribute in the Boulder Opal graph contains [a library of predefined analytical signals](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#signals) as piecewise-constant ([PWC](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/Pwc)) or sampleable ([STF](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/Stf)) functions that you can directly use without having to define them from the ground up.\n",
    "For more information, you can also read the [How to create analytical signals for simulation and optimization](https://docs.q-ctrl.com/boulder-opal/toolkit/design/represent-time-varying-signals/how-to-create-analytical-signals-for-simulation-and-optimization) user guide."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Create an identity Stf node and define analytical signals\n",
    "\n",
    "Once a graph has been set up to describe the computation, use the `graph.identity_stf` operation to create an STF representing the identity function $f(t) = t$.\n",
    "\n",
    "Apply a sequence of [mathematical functions](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#mathematical-functions) to the identity function to create STF nodes representing your desired signals.\n",
    "\n",
    "### 2. Construct the Hamiltonian\n",
    "\n",
    "Create the Hamiltonian terms by multiplying the signals by the appropriate operators.\n",
    "You can directly use STF nodes created this way with operations such as `graph.time_evolution_operators_stf` or `graph.infidelity_stf`, or you can discretize them into PWCs with `graph.discretize_stf`.\n",
    "For more information on STFs and PWCs, see the [Working with time-dependent functions in Boulder Opal](https://docs.q-ctrl.com/boulder-opal/toolkit/design/represent-time-varying-signals/implement-time-dependent-functions-in-boulder-opal) topic.\n",
    "\n",
    "### 3. Execute the graph for the simulation/optimization\n",
    "With the graph object created, a simulation can be run using the `boulderopal.execute_graph` function. The outputs and the graph must be provided. The function returns the results of the simulation. \n",
    "\n",
    "Alternatively, an optimization can be run using the `boulderopal.run_optimization` function or the `boulderopal.run_stochastic_optimization` function. The cost, the outputs, and the graph must be provided. The function returns the results of the optimization. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Simulation with analytical signals \n",
    "\n",
    "In this example, we will simulate a Landau–Zener transition in a two-level system.\n",
    "\n",
    "The Hamiltonian for the system is \n",
    "$$\n",
    "H(t) = \\Omega(t) \\sigma_x + \\Delta(t) \\sigma_z ,\n",
    "$$\n",
    "where $\\Omega(t)$ is the Rabi coupling and $\\Delta(t)$ is the detuning.\n",
    "\n",
    "For the Rabi coupling we will implement a pulse of the form\n",
    "$$\n",
    "\\Omega(t) = \\Omega_0 \\sin^2 (\\pi t / T) ,\n",
    "$$\n",
    "and for the detuning a sweep of the form\n",
    "$$\n",
    "\\Delta(t) = - \\Delta_0 \\cos(\\pi t / T) ,\n",
    "$$\n",
    "where $\\Omega_0$ and $\\Delta_0$ are the maximum values of the Rabi coupling and detuning,\n",
    "and $T$ is the signal duration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "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": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829420\") has started.\n",
      "Your task (action_id=\"1829420\") 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 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the data flow graph describing the system.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Define the duration of the signals.\n",
    "duration = 2e-6  # s\n",
    "\n",
    "# Define the number of samples for the discretizations.\n",
    "sample_count = 512\n",
    "sample_times = np.linspace(0.0, duration, sample_count)\n",
    "\n",
    "# Define maximum values for the signals.\n",
    "omega_max = 1.5e6  # rad/s\n",
    "delta_max = 2.1e6  # rad/s\n",
    "\n",
    "# Define the signals.\n",
    "t = graph.identity_stf()\n",
    "omega = omega_max * graph.sin(np.pi * t / duration) ** 2\n",
    "delta = -delta_max * graph.cos(np.pi * t / duration)\n",
    "\n",
    "# Construct the Hamiltonian.\n",
    "hamiltonian = omega * graph.pauli_matrix(\"X\") + delta * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Compute the time-evolution unitaries.\n",
    "unitaries = graph.time_evolution_operators_stf(\n",
    "    hamiltonian=hamiltonian, sample_times=sample_times\n",
    ")\n",
    "\n",
    "# Define the initial state.\n",
    "initial_state = graph.fock_state(2, 0)[:, None]\n",
    "\n",
    "# Evolve the initial state with the unitary to get the final state.\n",
    "evolved_states = unitaries @ initial_state\n",
    "evolved_states.name = \"states\"\n",
    "\n",
    "# Discretize the signals as STFs can't be directly exported.\n",
    "graph.discretize_stf(omega, duration, sample_count, name=r\"$\\Omega$\")\n",
    "graph.discretize_stf(delta, duration, sample_count, name=r\"$\\Delta$\")\n",
    "\n",
    "# Run simulation.\n",
    "result = bo.execute_graph(\n",
    "    graph=graph, output_node_names=[\"states\", r\"$\\Omega$\", r\"$\\Delta$\"]\n",
    ")\n",
    "\n",
    "# Plot the analytical signals used.\n",
    "qv.plot_controls(\n",
    "    {name: result[\"output\"][name] for name in [r\"$\\Omega$\", r\"$\\Delta$\"]}, smooth=True\n",
    ")\n",
    "plt.suptitle(\"Landau–Zener signals\")\n",
    "\n",
    "# Plot the population dynamics.\n",
    "populations = np.abs(result[\"output\"][\"states\"][\"value\"].squeeze()) ** 2\n",
    "qv.plot_population_dynamics(\n",
    "    sample_times, {rf\"$|{k}\\rangle$\": populations[:, k] for k in range(2)}\n",
    ")\n",
    "plt.suptitle(\"Landau–Zener transition dynamics\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Optimization with analytical signals \n",
    "\n",
    "In this example, we will implement an X gate in a noisy single-qubit system, by optimizing the parameters of two signals. \n",
    "\n",
    "The Hamiltonian for the system is \n",
    "$$\n",
    "H(t) = \\alpha(t) \\sigma_{z} + \\frac{1}{2}\\left(\\gamma(t)\\sigma_{-} + \\gamma^*(t)\\sigma_{+}\\right) + \\delta \\sigma_{z} + \\zeta(t) \\sigma_{z} , \n",
    "$$\n",
    "where $\\alpha(t)$ and $\\gamma(t)$ are signals with optimizable parameters, $\\delta$ is the qubit detuning, and $\\zeta(t)$ is a dephasing noise process.\n",
    "\n",
    "The $\\alpha(t)$ signals acting on $\\sigma_{z}$ is an arctangent ramp, defined by\n",
    "$$\n",
    "\\alpha(t) = \\alpha_0 \\arctan\\left( \\frac{t - t_0}{t_\\mathrm{ramp}} \\right)  ,\n",
    "$$\n",
    "where $\\pm a_0$ are the asymptotic values of the signal, $t_0$ is the center time, and $t_\\mathrm{ramp}$ is the characteristic duration of the ramp.\n",
    "\n",
    "The $\\gamma(t)$ signal acting on $\\sigma_{-}$ is a Gaussian signal, defined by\n",
    "$$\n",
    "\\gamma(t) = \\gamma_0 \\exp \\left(- \\frac{(t-t_0)^2}{2\\sigma^2} \\right)  ,\n",
    "$$\n",
    "where $\\gamma_0$ is the amplitude, \n",
    "$\\sigma$ is the width of the Gaussian, and\n",
    "$t_0$ is the center of the signal.\n",
    "\n",
    "\n",
    "We will fix the characteristic ramp time $t_\\mathrm{ramp}$ and Gaussian width $\\sigma$, and aim to find optimal values for the rest of signal parameters to implement the target quantum gate.\n",
    "\n",
    "In this case, we will discretize the smooth analytical signals into [piecewise-constant functions](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/Pwc) to simulate a discrete interface with an experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829421\") has started.\n",
      "Your task (action_id=\"1829421\") has completed.\n",
      "Optimized cost: 6.748e-04\n",
      "Optimal signal parameters\n",
      "\tα(t) amplitude:\t-3.943e+06 rad/s\n",
      "\tα(t) center:\t1.317e-06 s\n",
      "\tγ(t) amplitude:\t-1.729e+06-6.041e+06j rad/s\n",
      "\tγ(t) center:\t1.431e-06 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x540 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "# Define the duration of the signals.\n",
    "duration = 3e-6  # s\n",
    "sample_count = 64\n",
    "\n",
    "# Define α(t) as an arctan ramp.\n",
    "t = graph.identity_stf()\n",
    "alpha_ramp = duration / 8\n",
    "alpha_zero = graph.optimizable_scalar(\n",
    "    lower_bound=-3e7, upper_bound=3e7, name=\"alpha_amplitude\"\n",
    ")\n",
    "alpha_center = graph.optimizable_scalar(\n",
    "    lower_bound=0.0, upper_bound=duration, name=\"alpha_center\"\n",
    ")\n",
    "alpha_stf = alpha_zero * graph.arctan((t - alpha_center) / alpha_ramp)\n",
    "\n",
    "# Define γ(t) as a Gaussian pulse.\n",
    "gamma_max = 2.0 * np.pi * 1e6\n",
    "gamma_width = duration / 8\n",
    "gamma_modulus = graph.optimizable_scalar(lower_bound=-gamma_max, upper_bound=gamma_max)\n",
    "gamma_phase = graph.optimizable_scalar(\n",
    "    lower_bound=0,\n",
    "    upper_bound=2.0 * np.pi,\n",
    "    is_lower_unbounded=False,\n",
    "    is_upper_unbounded=False,\n",
    ")\n",
    "gamma_amplitude = gamma_modulus * graph.exp(1j * gamma_phase)\n",
    "gamma_amplitude.name = \"gamma_amplitude\"\n",
    "\n",
    "gamma_center_time = graph.optimizable_scalar(\n",
    "    lower_bound=0.0, upper_bound=duration, name=\"gamma_center\"\n",
    ")\n",
    "gamma_stf = graph.signals.gaussian_pulse_stf(\n",
    "    gamma_amplitude, gamma_width, gamma_center_time\n",
    ")\n",
    "\n",
    "# Discretize the signals.\n",
    "alpha = graph.discretize_stf(alpha_stf, duration, sample_count, name=r\"$\\alpha$\")\n",
    "gamma = graph.discretize_stf(gamma_stf, duration, sample_count, name=r\"$\\gamma$\")\n",
    "\n",
    "# Create Hamiltonian.\n",
    "hamiltonian = alpha * graph.pauli_matrix(\"Z\") + graph.hermitian_part(\n",
    "    gamma * graph.pauli_matrix(\"M\")\n",
    ")\n",
    "\n",
    "# Add detuning term.\n",
    "delta = 2 * np.pi * 0.25e6  # rad/s\n",
    "hamiltonian += delta * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Define target gate.\n",
    "target = graph.target(operator=graph.pauli_matrix(\"X\"))\n",
    "\n",
    "# Add dephasing noise term.\n",
    "zeta = 2 * np.pi * 20e3  # rad/s\n",
    "dephasing = zeta * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Robust infidelity.\n",
    "robust_infidelity = graph.infidelity_pwc(\n",
    "    hamiltonian=hamiltonian,\n",
    "    noise_operators=[dephasing],\n",
    "    target=target,\n",
    "    name=\"robust_infidelity\",\n",
    ")\n",
    "\n",
    "result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"robust_infidelity\",\n",
    "    output_node_names=[\n",
    "        \"alpha_amplitude\",\n",
    "        \"alpha_center\",\n",
    "        \"gamma_amplitude\",\n",
    "        \"gamma_center\",\n",
    "        r\"$\\alpha$\",\n",
    "        r\"$\\gamma$\",\n",
    "    ],\n",
    "    optimization_count=8,\n",
    ")\n",
    "\n",
    "print(f\"Optimized cost: {result['cost']:.3e}\")\n",
    "\n",
    "# Print out the converged signal parameters.\n",
    "print(\"Optimal signal parameters\")\n",
    "print(f\"\\tα(t) amplitude:\\t{result['output']['alpha_amplitude']['value']:.3e} rad/s\")\n",
    "print(f\"\\tα(t) center:\\t{result['output']['alpha_center']['value']:.3e} s\")\n",
    "print(f\"\\tγ(t) amplitude:\\t{result['output']['gamma_amplitude']['value']:.3e} rad/s\")\n",
    "print(f\"\\tγ(t) center:\\t{result['output']['gamma_center']['value']:.3e} s\")\n",
    "\n",
    "# Plot the optimal analytical signals found.\n",
    "qv.plot_controls({name: result[\"output\"][name] for name in [r\"$\\alpha$\", r\"$\\gamma$\"]})\n",
    "plt.suptitle(\"Optimal signals\")\n",
    "plt.show()"
   ]
  }
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