examples/analog_hamiltonian_simulation/05_Running_Analog_Hamiltonian_Simulation_with_local_simulator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "20e6ca17",
   "metadata": {},
   "source": [
    "# Running analog Hamiltonian simulation with local simulator\n",
    "\n",
    "We recommend to test and debug an analog Hamiltonian simulation (AHS) program on the local simulator before submitting it to a QPU. In this notebook, we introduce several features of the local simulator that will be useful to streamline this testing process.\n",
    "\n",
    "To begin, we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d1173d71",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "from braket.devices import LocalSimulator\n",
    "from braket.ahs.driving_field import DrivingField\n",
    "\n",
    "from ahs_utils import show_register, show_global_drive, plot_avg_density_2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5e39b46",
   "metadata": {},
   "source": [
    "## 2D checkerboard phase \n",
    "We consider a $3\\times3$ square grid with 9 atoms. As shown in [this notebook](https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb), we can realize the 2D checkerboard phase via adiabatically tuning the Rabi frequency and detuning. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "06439adb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "register = AtomArrangement()\n",
    "separation = 6.7e-6  # in meters \n",
    "\n",
    "for k in range(3):\n",
    "    for l in range(3):\n",
    "        register.add((k * separation, l * separation))\n",
    "\n",
    "\n",
    "time_points = [0, 2.5e-7, 2.75e-6, 3e-6]\n",
    "amplitude_min = 0       # rad / s\n",
    "amplitude_max = 1.57e7  # rad / s\n",
    "\n",
    "detuning_min = -5.5e7   # rad / s\n",
    "detuning_max = 5.5e7    # rad / s\n",
    "\n",
    "amplitude_values = [amplitude_min, amplitude_max, amplitude_max, amplitude_min]  # piecewise linear\n",
    "detuning_values = [detuning_min, detuning_min, detuning_max, detuning_max]  # piecewise linear\n",
    "phase_values = [0, 0, 0, 0]  # piecewise constant\n",
    "\n",
    "\n",
    "drive = DrivingField.from_lists(time_points, amplitude_values, detuning_values, phase_values)\n",
    "    \n",
    "show_register(register)\n",
    "show_global_drive(drive)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b90c4ceb",
   "metadata": {},
   "source": [
    "The AHS program can be constructed by assembling the atomic register with the driving field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f1878620",
   "metadata": {},
   "outputs": [],
   "source": [
    "ahs_program = AnalogHamiltonianSimulation(\n",
    "    register=register, \n",
    "    hamiltonian=drive\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9ca31a1",
   "metadata": {},
   "source": [
    "We can then run the program on the local simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a70c804e",
   "metadata": {},
   "outputs": [],
   "source": [
    "device = LocalSimulator(\"braket_ahs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d760b11b",
   "metadata": {},
   "source": [
    "Below we explicitly specify `shots=10000` and `steps=100` respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7a3ebaec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elapsed time = 3.253291130065918 seconds\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "result_full = device.run(ahs_program, shots=10000, steps=100).result()\n",
    "print(f\"The elapsed time = {time.time()-start_time} seconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "dac877bf",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_avg_density_2D(result_full.get_avg_density(), register)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f8623ff",
   "metadata": {},
   "source": [
    "## Run AHS program in the blockade subspace\n",
    "\n",
    "The above simulation is performed using the *full* Hamiltonian with size $2^{9}\\times 2^{9}$. However, because of Rydberg blockade, if neighboring atoms are within each other's Rydberg blockade radius $R_b$, they are very unlikely to be excited to the Rydberg states simultaneously. Given that (see [this notebook](https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb))\n",
    "\\begin{align}\n",
    "R_b = \\left[\\frac{C_6}{\\sqrt{\\Delta^2+\\Omega^2}}\\right]^{1/6},\n",
    "\\end{align}\n",
    "\n",
    "we have 6.752 $\\mu m$ < $R_b$ < 6.796 $\\mu m$ throughout the program, which is always larger than $6.7~ \\mu m$, the distances between neighboring atoms. Hence we can approximate the full Hamiltonian of the system with a smaller *effective* Hamiltonian. We can take advantage of this fact to speed up the simulation by setting the parameter `blockade_radius` as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c92cd79b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elapsed time = 0.199995756149292 seconds\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "result_blockade = device.run(ahs_program, shots=10000, blockade_radius=6.796e-6, steps=100).result()\n",
    "print(f\"The elapsed time = {time.time()-start_time} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6ce420c",
   "metadata": {},
   "source": [
    "Indeed, the runtime for the simulation with the effective Hamiltonian is one magnitude less than the one with the original Hamiltonian. We can visually confirm that the checkerboard phase is created successfully using the Rydberg blockade approximation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4152af92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_avg_density_2D(result_blockade.get_avg_density(), register)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f058f7d",
   "metadata": {},
   "source": [
    "In order to quantify the difference in the final average Rydberg densities from the two simulations, we can calculate the root-mean-square difference (RMS) defined as \n",
    "\\begin{align}\n",
    "\\text{RMS} = \\sqrt{\\frac{1}{N}\\sum_{i=1}^N(\\bar{n}_i^\\text{full}-\\bar{n}_i^\\text{blockade})^2}.\n",
    "\\end{align}\n",
    "Here $\\bar{n}_i^\\text{full}$ and $\\bar{n}_i^\\text{blockade}$ are the final Rydberg density at the $i$-th site for the simulation with the full Hamiltonian and the effective Hamiltonian respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "cf902009",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RMS_blockade for the final Rydberg densities = 0.024428330547406077\n"
     ]
    }
   ],
   "source": [
    "n_full = result_full.get_avg_density()\n",
    "n_blockade = result_blockade.get_avg_density()\n",
    "\n",
    "RMS_blockade = np.sqrt(np.mean((np.array(n_full)-np.array(n_blockade))**2))\n",
    "print(f\"The RMS_blockade for the final Rydberg densities = {RMS_blockade}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5663c2d",
   "metadata": {},
   "source": [
    "Since the RMS is only around 2%, we are assured that the simulation with the effective Hamiltonian of smaller size gives quantitatively the same results as the one with the full Hamiltonian."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a7270af",
   "metadata": {},
   "source": [
    "## Tuning other parameters in the local simulator\n",
    "\n",
    "Another way to speed up the simulation, without using the blockade approximation, is to adjust other parameters of the local simulator, such as `steps`, the number of time points in the simulation. Previously, we have set `steps=100`, but it can be adjusted to be `40` as shown below. We expect that the less time point used in the simulation, the faster it will finish."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "49b3b95a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The elapsed time = 1.4084961414337158 seconds\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "result_reduced_nsteps = device.run(ahs_program, shots=10000, steps=40).result()\n",
    "print(f\"The elapsed time = {time.time()-start_time} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61267635",
   "metadata": {},
   "source": [
    "This indeed speed up the simulation as expected. We can confirm that the simulation produces result that is close to our expectation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "32ad6d32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_avg_density_2D(result_reduced_nsteps.get_avg_density(), register)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4861e840",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The RMS_reduced_nsteps for the final Rydberg densities = 0.08276531076886416\n"
     ]
    }
   ],
   "source": [
    "n_reduced_nsteps = result_reduced_nsteps.get_avg_density()\n",
    "\n",
    "RMS_reduced_nsteps = np.sqrt(np.mean((np.array(n_full)-np.array(n_reduced_nsteps))**2))\n",
    "print(f\"The RMS_reduced_nsteps for the final Rydberg densities = {RMS_reduced_nsteps}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff29f595",
   "metadata": {},
   "source": [
    "We note that if the Hamiltonian is almost constant throughout the AHS program, simulation with smaller `steps`, such as `80` or `50`, is likely sufficient to give qualitatively good result, as demonstrated here. On the other hand, if the Hamiltonian is varying drastically throughout the program, one may need to have higher `steps` around 200 or more.\n",
    "\n",
    "We see that although the runtime is reduced compared to the simulation with default parameters, it is still much longer than the simulation performed with the effective Hamiltonian that uses blockade approximation. The reason is that the local simulator will need to construct Hamiltonian used for the simulation, and this takes majority part of the runtime. \n",
    "\n",
    "We also note that when the dimension of the Hamiltonian is larger than $2^{10}\\times2^{10}$, the AHS local simulator use `scipy.integrate.ode` as the backend solver and support the following arguments: <code>atol</code>, <code>rtol</code>, <code>solver_method</code>, <code>order</code>, <code>nsteps</code>, <code>first_step</code>, <code>max_step</code> and <code>min_step</code>. For more information, please refer to the following <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.ode.html\">documentation page</a>. \n",
    "\n",
    "When the dimension of the Hamiltonian is less than or equal to $2^{10}\\times2^{10}$, we use a solver based on the <a href=\"https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_method\">implicit Runge-Kutta method</a> written in `numpy`, which is more efficient than the `scipy.integrate.ode` solver in this case. The solver based on `numpy` does not support the arguments listed above."
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