examples/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb

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 "cells": [
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   "cell_type": "markdown",
   "id": "92c948f0-6dd3-4955-b4eb-2926a79ecf7e",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Introduction to Aquila\n",
    "\n",
    "In the previous notebook, we have introduced the concept of Analog Hamiltonian Simulation (AHS) and how to run an AHS program on the neutral atom local simulator. In this notebook, we illustrate how to run an AHS program on QuEra's Aquila, a Rydberg based QPU, via Amazon Braket. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4df5b53",
   "metadata": {},
   "source": [
    "## QuEra's Aquila\n",
    "\n",
    "In order to use the Aquila device, let us first connect to it, and query its parameters with its unique Amazon Resource Number (ARN)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57ac4e1c",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> You need to pip install the <a href=\"https://github.com/amazon-braket/amazon-braket-sdk-python#installing-the-amazon-braket-python-sdk\" class=\"alert-link\">Braket SDK</a>. If you are new to Amazon Braket, make sure you have completed the necessary <a href=\"https://docs.aws.amazon.com/braket/latest/developerguide/braket-get-started.html\" class=\"alert-link\">Get Started steps</a>. If you are using a Braket hosted notebook instance, this SDK comes pre-installed with the notebooks.\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f3c3385",
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    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:35.108494Z",
     "start_time": "2023-08-29T21:36:35.104203Z"
    }
   },
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "\n",
    "tracker = Tracker().start()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7175daec",
   "metadata": {},
   "source": [
    "In this notebook, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3cd780d0",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'braketSchemaHeader': {'name': 'braket.device_schema.quera.quera_ahs_paradigm_properties',\n",
      "                        'version': '1'},\n",
      " 'lattice': {'area': {'height': Decimal('0.000076'),\n",
      "                      'width': Decimal('0.000075')},\n",
      "             'geometry': {'numberSitesMax': 256,\n",
      "                          'positionResolution': Decimal('1E-8'),\n",
      "                          'spacingRadialMin': Decimal('0.000004'),\n",
      "                          'spacingVerticalMin': Decimal('0.000004')}},\n",
      " 'performance': {'lattice': {'atomCaptureProbabilityTypical': Decimal('0.001'),\n",
      "                             'atomCaptureProbabilityWorst': Decimal('0.002'),\n",
      "                             'atomDetectionErrorFalseNegativeTypical': Decimal('0.001'),\n",
      "                             'atomDetectionErrorFalseNegativeWorst': Decimal('0.005'),\n",
      "                             'atomDetectionErrorFalsePositiveTypical': Decimal('0.001'),\n",
      "                             'atomDetectionErrorFalsePositiveWorst': Decimal('0.005'),\n",
      "                             'atomLossProbabilityTypical': Decimal('0.005'),\n",
      "                             'atomLossProbabilityWorst': Decimal('0.01'),\n",
      "                             'atomPositionError': Decimal('2E-7'),\n",
      "                             'fillingErrorTypical': Decimal('0.008'),\n",
      "                             'fillingErrorWorst': Decimal('0.05'),\n",
      "                             'positionErrorAbs': Decimal('2.25E-7'),\n",
      "                             'sitePositionError': Decimal('1E-7'),\n",
      "                             'vacancyErrorTypical': Decimal('0.001'),\n",
      "                             'vacancyErrorWorst': Decimal('0.005')},\n",
      "                 'rydberg': {'rydbergGlobal': {'T1Ensemble': Decimal('0.000075'),\n",
      "                                               'T1Single': Decimal('0.000075'),\n",
      "                                               'T2BlockadedRabiEnsemble': Decimal('0.000007'),\n",
      "                                               'T2BlockadedRabiSingle': Decimal('0.000008'),\n",
      "                                               'T2EchoEnsemble': Decimal('0.000007'),\n",
      "                                               'T2EchoSingle': Decimal('0.000008'),\n",
      "                                               'T2RabiEnsemble': Decimal('0.000007'),\n",
      "                                               'T2RabiSingle': Decimal('0.000008'),\n",
      "                                               'T2StarEnsemble': Decimal('0.00000475'),\n",
      "                                               'T2StarSingle': Decimal('0.000005'),\n",
      "                                               'detuningError': Decimal('1000000.0'),\n",
      "                                               'detuningInhomogeneity': Decimal('1000000.0'),\n",
      "                                               'groundDetectionError': Decimal('0.05'),\n",
      "                                               'groundPrepError': Decimal('0.01'),\n",
      "                                               'rabiAmplitudeRampCorrection': [{'rabiCorrection': Decimal('0.92'),\n",
      "                                                                                'rampTime': Decimal('5E-8')},\n",
      "                                                                               {'rabiCorrection': Decimal('0.97'),\n",
      "                                                                                'rampTime': Decimal('7.5E-8')},\n",
      "                                                                               {'rabiCorrection': Decimal('1.0'),\n",
      "                                                                                'rampTime': Decimal('1E-7')}],\n",
      "                                               'rabiFrequencyErrorRel': Decimal('0.03'),\n",
      "                                               'rabiFrequencyGlobalErrorRel': Decimal('0.02'),\n",
      "                                               'rabiFrequencyInhomogeneityRel': Decimal('0.02'),\n",
      "                                               'rydbergDetectionError': Decimal('0.1'),\n",
      "                                               'rydbergPrepErrorBest': Decimal('0.05'),\n",
      "                                               'rydbergPrepErrorWorst': Decimal('0.07')},\n",
      "                             'rydbergLocal': {'crosstalk': Decimal('0.02'),\n",
      "                                              'detuningErrorRms': Decimal('0.02'),\n",
      "                                              'errorRateIncoherentBright': Decimal('36000.0'),\n",
      "                                              'errorRateIncoherentDark': Decimal('720.0'),\n",
      "                                              'siteCoefficientErrorRms': Decimal('0.1')}}},\n",
      " 'qubitCount': 256,\n",
      " 'rydberg': {'c6Coefficient': Decimal('5.42E-24'),\n",
      "             'rydbergGlobal': {'detuningRange': (Decimal('-125000000.0'),\n",
      "                                                 Decimal('125000000.0')),\n",
      "                               'detuningResolution': Decimal('0.2'),\n",
      "                               'detuningSlewRateMax': Decimal('6000000000000000.0'),\n",
      "                               'phaseRange': (Decimal('-99.0'),\n",
      "                                              Decimal('99.0')),\n",
      "                               'phaseResolution': Decimal('5E-7'),\n",
      "                               'rabiFrequencyRange': (Decimal('0.0'),\n",
      "                                                      Decimal('15800000.0')),\n",
      "                               'rabiFrequencyResolution': Decimal('400.0'),\n",
      "                               'rabiFrequencySlewRateMax': Decimal('400000000000000.0'),\n",
      "                               'timeDeltaMin': Decimal('5E-8'),\n",
      "                               'timeMax': Decimal('0.000004'),\n",
      "                               'timeMin': Decimal('0.0'),\n",
      "                               'timeResolution': Decimal('1E-9')},\n",
      "             'rydbergLocal': {'detuningRange': (Decimal('-125000000.0'),\n",
      "                                                Decimal('0.0')),\n",
      "                              'detuningSlewRateMax': Decimal('2500000000000000.0'),\n",
      "                              'numberLocalDetuningSitesMax': Decimal('256'),\n",
      "                              'siteCoefficientRange': (Decimal('0.0'),\n",
      "                                                       Decimal('1.0')),\n",
      "                              'spacingRadialMin': Decimal('0.000004'),\n",
      "                              'timeDeltaMin': Decimal('5E-8'),\n",
      "                              'timeResolution': Decimal('1E-9')}}}\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint as pp\n",
    "\n",
    "from braket.aws import AwsDevice\n",
    "from braket.devices import Devices\n",
    "\n",
    "device = AwsDevice(Devices.QuEra.Aquila)\n",
    "capabilities = device.properties.paradigm\n",
    "pp(capabilities.dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea413e47",
   "metadata": {},
   "source": [
    "The preceding numbers represent numerical capabilities and constraints for which AHS programs can be run on Aquila. In the following sections, we will go through these device capabilities and build an AHS program that complies with these constraints."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0b5f568",
   "metadata": {},
   "source": [
    "## Building an AHS program for Aquila\n",
    "\n",
    "We have seen the basic components of an AHS program in the previous example, including the register, the driving fields and local detuning. In order to run an AHS program on Aquila, however, these components have to meet certain requirements. In this section, we introduce other constraints via building up a valid program for Aquila step by step. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6535a209",
   "metadata": {},
   "source": [
    "### Register\n",
    "In contrast to the local simulator which can only simulate a handful of atoms (qubits), Aquila can simulate systems with a few hundred. The coordinates of the atoms (qubits), however, have to meet certain constraints. We can check the requirements as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "edf0d67c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:36.082365Z",
     "start_time": "2023-08-29T21:36:36.074743Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'area': {'height': Decimal('0.000076'), 'width': Decimal('0.000075')},\n",
      " 'geometry': {'numberSitesMax': 256,\n",
      "              'positionResolution': Decimal('1E-8'),\n",
      "              'spacingRadialMin': Decimal('0.000004'),\n",
      "              'spacingVerticalMin': Decimal('0.000004')}}\n"
     ]
    }
   ],
   "source": [
    "lattice_constraints = capabilities.lattice\n",
    "pp(lattice_constraints.dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dadd661",
   "metadata": {},
   "source": [
    "The detailed description of these sections can be inspected as follows"
   ]
  },
  {
   "cell_type": "code",
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   "id": "409362f9",
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     "end_time": "2023-08-29T21:36:36.090365Z",
     "start_time": "2023-08-29T21:36:36.082665Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    The area of the FOV\n",
      "    Attributes:\n",
      "        width (Decimal): Largest allowed difference between x\n",
      "            coordinates of any two sites (measured in meters)\n",
      "        height (Decimal): Largest allowed difference between y\n",
      "            coordinates of any two sites (measured in meters)\n",
      "    \n",
      "\n",
      "    Spacing or number of sites or rows\n",
      "    Attributes:\n",
      "        spacingRadialMin (Decimal): Minimum radial spacing between any\n",
      "            two sites in the lattice (measured in meters)\n",
      "        spacingVerticalMin (Decimal): Minimum spacing between any two\n",
      "            rows in the lattice (measured in meters)\n",
      "        positionResolution (Decimal): Resolution with which site positions\n",
      "            can be specified (measured in meters)\n",
      "        numberSitesMax (int): Maximum number of sites that can be placed\n",
      "            in the lattice\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(lattice_constraints.area.__doc__)\n",
    "print(lattice_constraints.geometry.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b15d2f13",
   "metadata": {},
   "source": [
    "As we can see, the requirements for the setup in an AHS program can be summarized as follows\n",
    "1. The number of sites in the setup cannot be greater than `capabilities.lattice.geometry.numberSitesMax`\n",
    "2. The atoms have to be separated by at least `capabilities.lattice.geometry.spacingRadialMin` meters\n",
    "3. The rows in the setup have to be separated by at least `capabilities.lattice.geometry.spacingVerticalMin` meters\n",
    "4. The resolution for the coordinates of the atoms cannot be greater than `capabilities.lattice.geometry.positionResolution` meters\n",
    "5. The setup cannot be wider than `capabilities.lattice.area.width` meters\n",
    "6. The setup cannot be taller than `capabilities.lattice.area.height` meters\n",
    "\n",
    "Below, we demonstrate a valid setup that meets these requirements, which has 105 atoms grouped as 35 equilateral triangles that are well separated from each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "487a6b5e",
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     "end_time": "2023-08-29T21:36:36.435379Z",
     "start_time": "2023-08-29T21:36:36.136196Z"
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   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from ahs_utils import show_register\n",
    "\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "\n",
    "separation = 5e-6\n",
    "block_separation = 15e-6\n",
    "k_max = 5\n",
    "m_max = 5\n",
    "\n",
    "register = AtomArrangement()\n",
    "for k in range(k_max):\n",
    "    for m in range(m_max):\n",
    "        register.add((block_separation * m, block_separation * k + separation / np.sqrt(3)))\n",
    "        register.add(\n",
    "            (\n",
    "                block_separation * m - separation / 2,\n",
    "                block_separation * k - separation / (2 * np.sqrt(3)),\n",
    "            )\n",
    "        )\n",
    "        register.add(\n",
    "            (\n",
    "                block_separation * m + separation / 2,\n",
    "                block_separation * k - separation / (2 * np.sqrt(3)),\n",
    "            )\n",
    "        )\n",
    "\n",
    "show_register(register, show_atom_index=False, blockade_radius=1.5 * separation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62acf66e",
   "metadata": {},
   "source": [
    "In the above figure, each blue link connects a pair of atoms that blockade each other. Since the triangles are well separated from each other, and the driving field (see below) is acting on all atoms uniformly, effectively we are repeating the same experiment on the same setup (an equilateral triangle) 35 times in one shot. If the setup of interest is small and contains only a few atoms, we could try to fit in a few identical copies of the setup in the bounding box while avoiding the interference between them. In this way, we are effectively taking more shots for the AHS program of interest."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75e18060",
   "metadata": {},
   "source": [
    "### Driving field\n",
    "\n",
    "Aquila can simulate the following Hamiltonian \n",
    "\n",
    "\\begin{align}\n",
    "H_\\text{Rydberg}(t) = \\sum_{k=1}^N H_{\\text{drive}, k}(t) + \\sum_{k=1}^N H_{\\text{local detuning}, k}(t) + \\sum_{j=1}^{N-1}\\sum_{k = j+1}^N H_{\\text{vdW}, j, k}.\n",
    "\\end{align}\n",
    "Here the third term is the van der Waals interaction term which is fixed once the setup is defined. The first term is the driving field,\n",
    "\\begin{align}\n",
    "H_{\\text{drive}, k}(t) = \\frac{\\Omega(t)}{2}\\left(e^{i\\phi(t)}|g_k\\rangle\\langle r_k| + e^{-i\\phi(t)}|r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t)n_k,\n",
    "\\end{align}\n",
    "which act on all the atoms in the setup. Here $n_k = |r_k\\rangle\\langle r_k|$ is the number operator of atom $k$.  The specification of the driving field has to satisfy several conditions, which can be queried as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "91e004b1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:36.445086Z",
     "start_time": "2023-08-29T21:36:36.437107Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'detuningRange': (Decimal('-125000000.0'), Decimal('125000000.0')),\n",
      " 'detuningResolution': Decimal('0.2'),\n",
      " 'detuningSlewRateMax': Decimal('6000000000000000.0'),\n",
      " 'phaseRange': (Decimal('-99.0'), Decimal('99.0')),\n",
      " 'phaseResolution': Decimal('5E-7'),\n",
      " 'rabiFrequencyRange': (Decimal('0.0'), Decimal('15800000.0')),\n",
      " 'rabiFrequencyResolution': Decimal('400.0'),\n",
      " 'rabiFrequencySlewRateMax': Decimal('400000000000000.0'),\n",
      " 'timeDeltaMin': Decimal('5E-8'),\n",
      " 'timeMax': Decimal('0.000004'),\n",
      " 'timeMin': Decimal('0.0'),\n",
      " 'timeResolution': Decimal('1E-9')}\n"
     ]
    }
   ],
   "source": [
    "rydbergGlobal = capabilities.rydberg.rydbergGlobal\n",
    "pp(rydbergGlobal.dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b67aec2",
   "metadata": {},
   "source": [
    "The detailed description for each quantity of `rydbergGlobal` can be inspected as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d0bca3f4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:36.448920Z",
     "start_time": "2023-08-29T21:36:36.443536Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    Constraints for the parameters of the driving field that drives the\n",
      "        ground-to-Rydberg transition uniformly on all atoms\n",
      "    Attributes:\n",
      "        rabiFrequencyRange (Tuple[Decimal,Decimal]): Achievable Rabi frequency range for the global\n",
      "            Rydberg drive waveform (measured in rad/s)\n",
      "        rabiFrequencyResolution (Decimal): Resolution with which global Rabi frequency amplitude\n",
      "            can be specified (measured in rad/s)\n",
      "        rabiFrequencySlewRateMax (Decimal): Maximum slew rate for changing the global Rabi\n",
      "            frequency (measured in (rad/s)/s)\n",
      "        detuningRange(Tuple[Decimal,Decimal]): Achievable detuning range for the global Rydberg\n",
      "            pulse (measured in rad/s)\n",
      "        detuningResolution(Decimal): Resolution with which global detuning can be specified\n",
      "            (measured in rad/s)\n",
      "        detuningSlewRateMax (Decimal): Maximum slew rate for detuning (measured in (rad/s)/s)\n",
      "        phaseRange(Tuple[Decimal,Decimal]): Achievable phase range for the global Rydberg pulse\n",
      "            (measured in rad)\n",
      "        phaseResolution(Decimal): Resolution with which global Rabi frequency phase can be\n",
      "            specified (measured in rad)\n",
      "        timeResolution(Decimal): Resolution with which times for global Rydberg drive parameters\n",
      "            can be specified (measured in s)\n",
      "        timeDeltaMin(Decimal): Minimum time step with which times for global Rydberg drive\n",
      "            parameters can be specified (measured in s)\n",
      "        timeMin (Decimal): Minimum duration of Rydberg drive (measured in s)\n",
      "        timeMax (Decimal): Maximum duration of Rydberg drive (measured in s) Note: This may be \n",
      "            longer than the T2 coherence time.\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(rydbergGlobal.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0f2d5a4",
   "metadata": {},
   "source": [
    "As we can see, the requirements for the driving field in the AHS program can be summarized as follows\n",
    "\n",
    "1. The Rabi frequency $\\Omega(t)$ has to be within the range `rydbergGlobal.rabiFrequencyRange`, in the unit of rad/s\n",
    "2. The resolution for the Rabi frequency cannot be greater than `rydbergGlobal.rabiFrequencyResolution` rad/s\n",
    "3. The slew rate for the Rabi frequency cannot be greater than `rydbergGlobal.rabiFrequencySlewRateMax` (rad/s)/s\n",
    "\n",
    "4. The phase $\\phi(t)$ has to be within the range `rydbergGlobal.phaseRange`, in the unit of rad\n",
    "5. The resolution for the phase cannot be greater than `rydbergGlobal.phaseResolution` rad\n",
    "\n",
    "6. The detuning $\\Delta(t)$ has to be within the range `rydbergGlobal.detuningRange`, in the unit of rad\n",
    "7. The resolution for the detuning cannot be greater than `rydbergGlobal.detuningResolution` rad\n",
    "8. The slew rate for the detuning cannot be greater than `rydbergGlobal.detuningSlewRateMax` rad/s\n",
    "\n",
    "9. The duration of the driving field cannot be less than `rydbergGlobal.timeMin` seconds\n",
    "10. The duration of the driving field cannot be more than `rydbergGlobal.timeMax` seconds\n",
    "11. The time points have to be separated by at least `rydbergGlobal.timeDeltaMin` seconds\n",
    "12. The resolution for the time points cannot be greater than `rydbergGlobal.timeResolution` seconds\n",
    "\n",
    "Besides, there are a few additional requirements\n",
    "1. The Rabi frequency $\\Omega(t)$ has to start with 0 rad/s\n",
    "2. The Rabi frequency $\\Omega(t)$ has to end with 0 rad/s\n",
    "3. The phase $\\phi(t)$ has to start with 0 rad\n",
    "4. All the fields in the driving field have to have the same duration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbf846fd",
   "metadata": {},
   "source": [
    "In this example, we are interested in driving the atoms with constant Rabi frequency $\\Omega_\\text{const}=1.5\\times10^7$ rad/s for a duration of $T_\\text{const}=\\frac{\\pi}{\\sqrt{3}\\Omega}\\approx2.09\\times10^{-7}$ seconds such that each atom has average Rydberg density equal to 1/3. Since the Rabi frequency corresponds to blockade radius $R_b\\approx8.44\\times10^{-6}$ meters, which is greater than the sides of the equilateral triangles ($5\\times10^{-6}$ meters), the atoms of the same triangle blockade one another. On the other hand, $R_b$ is smaller than the distance between nearest atoms of neighboring triangles, which is around $10\\times10^{-6}$ meters, hence the neighboring triangles are not interacting with each other, as desired. \n",
    "\n",
    "However, for the AHS program submitted to Aquila, the Rabi frequency cannot be a constant because of the constraint that it has to start and end with 0 rad/s. Hence we will need to create a time series $\\Omega(t)$ such that $\\int_0^T\\Omega(t)dt=\\Omega_\\text{const}T_\\text{const}=\\frac{\\pi}{\\sqrt{3}}$, while satisfying $\\Omega(0)=\\Omega(T)=0$. This could be achieved via the utility function `rabi_pulse` below where we demonstrate how to create the desired driving field for Aquila."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdce8a28",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> The maximally allowed duration (\"timeMax\") of the AHS program may be higher than the coherence time of the atoms. The reported peformance metrics of Aquila correspond to a 4-microsecond AHS program. For more details on performance metrics, see <a href=https://github.com/amazon-braket/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/09_Noisy_quantum_dynamics_for_Rydberg_atom_arrays.ipynb> \"Noisy quantum evolution with Rydberg atoms\" notebook </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "11bd0f7e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:36.461492Z",
     "start_time": "2023-08-29T21:36:36.452053Z"
    }
   },
   "outputs": [],
   "source": [
    "from braket.ahs.driving_field import DrivingField\n",
    "from braket.timings.time_series import TimeSeries\n",
    "\n",
    "omega_const = 1.5e7  # rad / s\n",
    "rabi_pulse_area = np.pi / np.sqrt(3)  # rad\n",
    "omega_slew_rate_max = float(rydbergGlobal.rabiFrequencySlewRateMax)  # rad/s^2\n",
    "time_separation_min = float(rydbergGlobal.timeDeltaMin)  # s\n",
    "\n",
    "amplitude = TimeSeries.trapezoidal_signal(\n",
    "    rabi_pulse_area,\n",
    "    omega_const,\n",
    "    0.99 * omega_slew_rate_max,\n",
    "    time_separation_min=time_separation_min,\n",
    ")\n",
    "\n",
    "detuning = TimeSeries.constant_like(amplitude, 0.0)\n",
    "phase = TimeSeries.constant_like(amplitude, 0.0)\n",
    "\n",
    "drive = DrivingField(amplitude=amplitude, detuning=detuning, phase=phase)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3efaeb42",
   "metadata": {},
   "source": [
    "We can inspect the driving field in the following way "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5db7e231",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:37.056941Z",
     "start_time": "2023-08-29T21:36:36.461025Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ahs_utils import show_global_drive\n",
    "\n",
    "show_global_drive(drive);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c84b2ad",
   "metadata": {},
   "source": [
    "Here we used constant-zero phase and detuning, but, for more involved programs, its time series can be customized similarly to how we set the amplitude of the Rabi frequency here."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f89f17f6",
   "metadata": {},
   "source": [
    "### Local detuning\n",
    "\n",
    "Apart from the driving field, Aquila also supports the local detuning, the second term in the Hamiltonian $H_\\text{Rydberg}(t)$, which reads\n",
    "\\begin{align}\n",
    "H_{\\text{local detuning}, k}(t) = -\\Delta_\\text{local}(t)h_k \\,n_k.\n",
    "\\end{align}\n",
    "Here $\\Delta_\\text{local}(t)$ is the time-dependent magnitude of the frequency shift, and $h_k$ is the atom-dependent pattern, which is a dimensionless number between 0 and 1. The specification of the local detuning has to satisfy several conditions, which can be queried as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ab92778e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'detuningRange': (Decimal('-125000000.0'), Decimal('0.0')),\n",
      " 'detuningSlewRateMax': Decimal('2500000000000000.0'),\n",
      " 'numberLocalDetuningSitesMax': Decimal('256'),\n",
      " 'siteCoefficientRange': (Decimal('0.0'), Decimal('1.0')),\n",
      " 'spacingRadialMin': Decimal('0.000004'),\n",
      " 'timeDeltaMin': Decimal('5E-8'),\n",
      " 'timeResolution': Decimal('1E-9')}\n"
     ]
    }
   ],
   "source": [
    "rydbergLocal = capabilities.rydberg.rydbergLocal\n",
    "if rydbergLocal:\n",
    "    pp(rydbergLocal.dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b35ec30",
   "metadata": {},
   "source": [
    "The detailed description for each quantity of `rydbergLocal` can be inspected as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9ca150a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    Constraints for the parameters of the local detuning\n",
      "    Attributes:\n",
      "        detuningRange(Tuple[Decimal,Decimal]):\n",
      "            Achievable detuning range for the local detuning pattern (measured in rad/s)\n",
      "        detuningSlewRateMax(Decimal):\n",
      "            Maximum slew rate for changing the local detuning (measured in (rad/s)/s)\n",
      "        siteCoefficientRange(Tuple[Decimal,Decimal]):\n",
      "            Achievable site coefficient range for the local detuning pattern (unitless)\n",
      "        numberLocalDetuningSitesMax(Decimal):\n",
      "            Maximum number of sites available for the local detuning pattern\n",
      "        spacingRadialMin(Decimal):\n",
      "            Minimum radial spacing between any two sites with non-zero local detuning\n",
      "            (measured in meter)\n",
      "        timeResolution(Decimal):\n",
      "            Resolution with which times for local detuning time series can be specified\n",
      "            (measured in s)\n",
      "        timeDeltaMin(Decimal):\n",
      "            Minimum step between times for local detuning time series (measured in s)\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "if rydbergLocal:\n",
    "    print(rydbergLocal.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30fda238",
   "metadata": {},
   "source": [
    "As we can see, the requirements for the local detuning in the AHS program can be summarized as follows\n",
    "\n",
    "1. The local detuning $\\Delta_\\text{local}(t)$ has to be within the range `rydbergLocal.detuningRange`, in the unit of rad\n",
    "2. The slew rate for the local detuning cannot be greater than `rydbergLocal.detuningSlewRateMax` rad/s\n",
    "3. The atom-dependent pattern $h_k$, a dimensionless quantity, has to be within the range `rydbergLocal.siteCoefficientRange`\n",
    "4. The number of sites in the atom-dependent pattern cannot be greater than `rydbergLocal.numberLocalDetuningSitesMax`\n",
    "5. The atoms with non-zero local detuning have to separated by at least `rydbergLocal.spacingRadialMin` meters\n",
    "6. The resolution for the time points cannot be greater than `rydbergLocal.timeResolution` seconds\n",
    "7. The time points have to be separated by at least `rydbergLocal.timeDeltaMin` seconds\n",
    "\n",
    "Besides, there are a few additional requirements\n",
    "1. The local detuning $\\Delta_\\text{local}(t)$ has to start with 0 rad/s\n",
    "2. The local detuning $\\Delta_\\text{local}(t)$ has to end with 0 rad/s\n",
    "3. The local detuning has to have to have the same duration as the driving field\n",
    "\n",
    "\n",
    "For simplicity, we will not use the local detuning in this example. The use cases that require the local detuning will be presented in other notebooks. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d37e943",
   "metadata": {},
   "source": [
    "### AHS program\n",
    "\n",
    "We can assemble the register and Hamiltonian to an AHS program "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4d5ab540",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:37.065205Z",
     "start_time": "2023-08-29T21:36:37.057662Z"
    }
   },
   "outputs": [],
   "source": [
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "\n",
    "ahs_program = AnalogHamiltonianSimulation(register=register, hamiltonian=drive)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bbedb27-3568-4803-a1ed-7b26dc60c946",
   "metadata": {},
   "source": [
    "### Task \n",
    "\n",
    "Before submitting the AHS program to Aquila, we need to discretize the program to ensure that it complies with resolution-specific validation rules. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "59fb7f60",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:37.074834Z",
     "start_time": "2023-08-29T21:36:37.063616Z"
    }
   },
   "outputs": [],
   "source": [
    "discretized_ahs_program = ahs_program.discretize(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09b11fc2",
   "metadata": {},
   "source": [
    "We note that the number of shots has to be within the range specified by `device.properties.service.shotsRange`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "46d2da98",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:37.171997Z",
     "start_time": "2023-08-29T21:36:37.070137Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1000)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "device.properties.service.shotsRange"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4895c99a",
   "metadata": {},
   "source": [
    "The AHS program can be submitted to the device to create a quantum task on the Braket service."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "825eda10",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> Some atoms may be missing even if the shot was successful. We recommend comparing <code>pre_sequence</code> of each shot with the requested atom filling in the AHS program specification.  \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0e6528d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:37.172190Z",
     "start_time": "2023-08-29T21:36:37.087898Z"
    }
   },
   "outputs": [],
   "source": [
    "n_shots = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c395c2a1-8ce2-4521-8d92-16efad87ac9e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:38.720662Z",
     "start_time": "2023-08-29T21:36:37.092240Z"
    }
   },
   "outputs": [],
   "source": [
    "task = device.run(discretized_ahs_program, shots=n_shots)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60c6be46",
   "metadata": {},
   "source": [
    "The quantum task metadata can be inspected in the following way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "158f1044-4cfa-4fc1-a26e-5581900f8783",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:36:38.886620Z",
     "start_time": "2023-08-29T21:36:38.723687Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARN: arn:aws:braket:us-east-1:260818742045:quantum-task/b5041ea5-83d8-4de6-9aa5-741105177699\n",
      "status: QUEUED\n"
     ]
    }
   ],
   "source": [
    "metadata = task.metadata()\n",
    "task_arn = metadata[\"quantumTaskArn\"]\n",
    "task_status = metadata[\"status\"]\n",
    "\n",
    "print(f\"ARN: {task_arn}\")\n",
    "print(f\"status: {task_status}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54a39bff",
   "metadata": {},
   "source": [
    "It is suggested to save the quantum task ARN for retrieving the quantum task result in a later time. For example if the saved quantum task ARN reads `arn:aws:braket:us-east-1:545821822555:quantum-task/12345`, the quantum task can be retrieved as follows.\n",
    "    \n",
    "```\n",
    "from braket.aws import AwsQuantumTask\n",
    "task = AwsQuantumTask(arn=\"arn:aws:braket:us-east-1:545821822555:quantum-task/12345\")    \n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "Alternatively, we can access the quantum tasks through [the tasks page of Amazon Braket console](https://us-east-1.console.aws.amazon.com/braket/home?region=us-east-1#/tasks)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d496c2bb-89ec-4475-bf7d-ae75ef13cdde",
   "metadata": {},
   "source": [
    "## Analyzing the result from Aquila\n",
    "\n",
    "The results (once the quantum task is completed) can be downloaded directly into an object in the python session."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d8176e09-deeb-485d-96e9-5046f9d03fc5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:38:59.818842Z",
     "start_time": "2023-08-29T21:36:38.884294Z"
    }
   },
   "outputs": [],
   "source": [
    "result = task.result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae5eac68",
   "metadata": {},
   "source": [
    "The call `task.result()` is blocking execution until the quantum task is completed and results are loaded from Amazon Braket. After the quantum task is completed, the measurement result is saved in `result.measurements` which is a list of `ShotResult`, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "afb85bab",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:38:59.826095Z",
     "start_time": "2023-08-29T21:38:59.820695Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShotResult(status=<AnalogHamiltonianSimulationShotStatus.SUCCESS: 'Success'>, pre_sequence=array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1]), post_sequence=array([1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0,\n",
       "       1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1,\n",
       "       0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,\n",
       "       0, 1, 1, 0, 1, 1, 0, 1, 1]))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.measurements[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91a9823b",
   "metadata": {},
   "source": [
    "`ShotResult` contains three pieces of information\n",
    "\n",
    "1. `status` indicates if the shot is successful\n",
    "2. `pre_sequence` contains the measurement result *before* running the AHS program. Here `0` indicates an empty site, while `1` indicates a filled site with an atom in the ground state\n",
    "3. `post_sequence` contains the measurement result *after* running the AHS program. Here `0` indicates an empty site, or an atom in the Rydberg state, while `1` indicates an atom in the ground state\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88687ac9",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> Some atoms may be missing even if the shot was successful. We recommend comparing <code>pre_sequence</code> of each shot with the requested atom filling in the AHS program specification.  \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0d7eade",
   "metadata": {},
   "source": [
    "To confirm that at the end of the AHS program, the average Rydberg density for the atoms in the triangles are around 1/3 for each atom, we can first collect the  measurement result and aggregate over all triangles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4ed4a31c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:38:59.840764Z",
     "start_time": "2023-08-29T21:38:59.830328Z"
    }
   },
   "outputs": [],
   "source": [
    "counts = result.get_counts()\n",
    "average_density = [0, 0, 0]\n",
    "average_num_triangles = [0, 0, 0, 0]\n",
    "for key, val in counts.items():\n",
    "    for i in range(0, 3 * k_max * m_max, 3):\n",
    "        short_seq = key[i : i + 3]\n",
    "        for j in range(3):\n",
    "            if short_seq[j] == \"r\":\n",
    "                average_density[j] += val\n",
    "\n",
    "        average_num_triangles[short_seq.count(\"r\")] += val\n",
    "\n",
    "\n",
    "average_density = np.array(average_density) / (k_max * m_max * n_shots)\n",
    "average_num_triangles = np.array(average_num_triangles) / n_shots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15d35f76",
   "metadata": {},
   "source": [
    "Note that although we only perform 100 shots for the given AHS program, since we have made the full usage of the area in the Aquila device, effectively, we have made 3,500 shots for the experiment of interest! We can plot the result as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "8fa10c84",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:39:00.075101Z",
     "start_time": "2023-08-29T21:38:59.841759Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n",
    "ax1.bar(range(len(average_density)), average_density)\n",
    "ax1.set_xticks(range(3))\n",
    "ax1.set_xticklabels(range(3))\n",
    "ax1.set_xlabel(\"Indices of atoms\")\n",
    "ax1.set_ylabel(\"Average Rydberg density\")\n",
    "\n",
    "ax2.bar(range(len(average_num_triangles)), average_num_triangles)\n",
    "ax2.set_xlabel(\"Number of Rydberg atoms\")\n",
    "ax2.set_ylabel(\"Average number of triangles\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e73773e1",
   "metadata": {},
   "source": [
    "In the left panel, we show the average Rydberg density for each atom in the triangles. We see that indeed the average Rydberg density for the atoms in the triangles are around 1/3 as expected. In the right panel, we show the number of triangles with certain number of Rydberg atoms (0, 1, 2 or 3) averaged over the shots. It can be seen that almost no triangle has more than 1 Rydberg atoms since the atoms in the same triangle blockade each other. \n",
    "\n",
    "In summary, in this notebook we have demonstrated how to connect to QuEra's Aquila device, and define a valid AHS program for the device. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9180c117",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:39:00.079238Z",
     "start_time": "2023-08-29T21:39:00.073857Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum Task Summary\n",
      "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 100, 'tasks': {'COMPLETED': 1}}}\n",
      "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
      "Estimated cost to run this example: 1.30 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Quantum Task Summary\")\n",
    "print(tracker.quantum_tasks_statistics())\n",
    "print(\n",
    "    \"Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\"\n",
    ")\n",
    "print(\n",
    "    f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a9a8a075",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:39:00.081322Z",
     "start_time": "2023-08-29T21:39:00.078548Z"
    }
   },
   "outputs": [],
   "source": []
  }
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