{ "cells": [ { "cell_type": "markdown", "id": "9f82bf0f", "metadata": {}, "source": [ "# Ordered phases in Rydberg systems\n", "\n", "In this example notebook, we show how one can prepare ordered phases in Rydberg systems, focusing on the 1D $Z_2$ phase and the 2D checkerboard phase. We will use an adiabatic time-evolution to prepare these many-body ground states.\n", "\n", "## Adiabatic evolution\n", "\n", "The adiabatic theorem of quantum mechanics states that \n", "\n", ">A physical system remains in its *instantaneous* eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. (Born & Fock, 1928)\n", "\n", "In other words, a slow-enough change in the parameters of the Hamiltonian will not induce transitions between its ground state and excited states: If the system starts in the ground state of the Hamiltonian at the beginning, it will smoothly transition into the ground state of the Hamiltonian at the end.\n", "\n", "The adiabatic theorem plays a key role in preparing the desired many-body ground states in the Rydberg system, the Hamiltonian of which can be expressed as\n", "\n", "\\begin{align}\n", "H(t) = \\sum_{k=1}^N \\frac{\\Omega(t)}{2}\\left(|g_k\\rangle\\langle r_k| + |r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t){n}_k + \\sum_{j=1}^{N-1}\\sum_{k=j+1}^N V_{jk}{n}_j{n}_k,\n", "\\end{align}\n", "\n", "where, for simplicity, we set the phase and the shifting field (See notebook 00 for detailed description of this Hamiltonian) to be zero throughout this notebook. We schedule the driving amplitude $\\Omega(t)$ to start from zero ($\\Omega(t=0)=0$). Hence, with negative detuning ($\\Delta_\\text{global}(t=0)<0$), the initial state where all atoms are in the ground state ($\\langle n_k\\rangle =0$) is the lowest energy eigenstate of the Hamiltonian, the many-body ground state.\n", "\n", "To arrive at a target Hamiltonian where the excited states of the atoms are favored, we ramp up the detuning $\\Delta_\\text{global}$ from large negative to large positive. During the ramp, we apply a large driving amplitude $\\Omega$ to open an energy gap between the first excited state and the ground state. According to the adiabatic theorem, if the ramping is slow enough, the system remains in the many-body ground state throughout the evolution. At the end of the AHS program, the Rabi frequency will be turned off and since $\\Delta_\\text{global}>0$, all the atoms tend to stay in the Rydberg state to lower the energy of the system. However, due to the strong Rydberg interaction, only one atom can be excited to the Rydberg state within its blockade radius.\n", "\n", "For a 1D chain of atoms, if we adjust the separation between the atoms such that only neighboring atoms are within the blockade radius, then we will arrive at a state where every second atom is excited, this is called the \"$Z_2$ phase\". For a 2D square array of atoms, a similar \"checkerboard phase\" emerges. The common feature of these phases is that the atoms are excited to the Rydberg states in an alternative pattern, complying with the blockade constraint, as shown in the figure below. In the figure, the shaded circles show *half* of the blockade radius such that sites with overlapped circles blockade each other. We show configurations, with black and white sites represent Rydberg and ground state atoms respectively, that comply with the blockade constraint. \n", "\n", "![Blockade_examples.png](Blockade_examples.png)\n", "\n", "We will realize these phases in this notebook. To begin, we import the necessary packages." ] }, { "cell_type": "code", "execution_count": 1, "id": "9124196d", "metadata": {}, "outputs": [], "source": [ "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n", "from braket.tracking import Tracker\n", "tracker = Tracker().start()" ] }, { "cell_type": "markdown", "id": "156c4218", "metadata": {}, "source": [ "In this notebook, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes and other functionalities." ] }, { "cell_type": "code", "execution_count": 2, "id": "08909afa", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from braket.ahs.atom_arrangement import AtomArrangement\n", "\n", "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n", "\n", "from ahs_utils import show_register, show_global_drive, show_final_avg_density, get_drive \n", "\n", "from braket.devices import LocalSimulator" ] }, { "cell_type": "markdown", "id": "5b5eee4d", "metadata": {}, "source": [ "## 1D $Z_2$ phase \n", "\n", "Here we consider a 1D chain of 9 atoms with neighboring atoms separated by $6.1\\mu m$. The setup of the system can be generated as follows" ] }, { "cell_type": "code", "execution_count": 3, "id": "6702f2b8", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "register = AtomArrangement()\n", "separation = 6.1e-6 # in meters \n", "num_atoms = 9\n", "\n", "for k in range(num_atoms):\n", " register.add([k * separation, 0])\n", " \n", "show_register(register)" ] }, { "cell_type": "markdown", "id": "33174b8a", "metadata": {}, "source": [ "In order to prepare the $Z_2$ ordered state for the atomic chain, we shall design an AHS program that drives the system adiabatically. As described above, we start from $\\Omega(t=0)=0$ with $\\Delta(t=0)<0$, followed by turning on $\\Omega(t)$ and ramping up $\\Delta(t)$. We will turn off the driving amplitude at the end of the program. This program can be specified as follows." ] }, { "cell_type": "code", "execution_count": 4, "id": "12184869", "metadata": {}, "outputs": [], "source": [ "time_points = [0, 2.5e-7, 2.75e-6, 3e-6]\n", "amplitude_min = 0\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 = get_drive(time_points, amplitude_values, detuning_values, phase_values)" ] }, { "cell_type": "markdown", "id": "ee92d637", "metadata": {}, "source": [ "We can plot the waveforms of these driving fields to make sure that they are correctly specified." ] }, { "cell_type": "code", "execution_count": 5, "id": "e8d369e3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "show_global_drive(drive);" ] }, { "cell_type": "markdown", "id": "ecd5fce7", "metadata": {}, "source": [ "Finally, we construct out AHS program from the atomic registers, and the Hamiltonian defined above. " ] }, { "cell_type": "code", "execution_count": 6, "id": "ef5318d9", "metadata": {}, "outputs": [], "source": [ "ahs_program = AnalogHamiltonianSimulation(\n", " register=register, \n", " hamiltonian=drive\n", ")" ] }, { "cell_type": "markdown", "id": "37e89b67", "metadata": {}, "source": [ "Before running the program on Quera's Aquila device (See notebook 01), we can first run it on the local simulator to make sure the outcome is the expected $Z_2$ state. Below we have explicitly specified the values of `steps` and `shots`, which are the number of time steps in the simulation and the number of sampling for the final stats, respectively. One could increase the accuracy of the result by increasing the values of these arguments, at the expense of longer runtime. " ] }, { "cell_type": "code", "execution_count": 7, "id": "18447781", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "device = LocalSimulator(\"braket_ahs\")\n", "result = device.run(ahs_program, shots=1000, steps=100).result()\n", "show_final_avg_density(result)" ] }, { "cell_type": "markdown", "id": "daf77070", "metadata": {}, "source": [ "We see that the average Rydberg density approximately forms the $Z_2$ pattern. The discrepancy can be attributed to finite size of the system and nonadiabaticity throughout the evolution. We expect that as one increase the system size and the duration of the AHS program, the final Rydberg density will approach the ideal $Z_2$ pattern.\n", "\n", "The $Z_2$ phase can be characterized by the density correlation $g_{ij}$ of the $i$-th and the $j$-th atom, which is defined as\n", "\n", "\\begin{align}\n", "g_{ij} = \\langle n_i n_j\\rangle - \\langle n_i\\rangle\\langle n_j\\rangle,\n", "\\end{align}\n", "\n", "where $\\langle\\cdot\\rangle$ is the average over the shots." ] }, { "cell_type": "code", "execution_count": 8, "id": "4ba0163e", "metadata": {}, "outputs": [], "source": [ "def get_density_correlation_Z2(result):\n", " post_sequences = np.array([list(measurement.post_sequence) for measurement in result.measurements])\n", " return np.cov(post_sequences.T)\n", "\n", "gij = get_density_correlation_Z2(result)" ] }, { "cell_type": "markdown", "id": "c405519e", "metadata": {}, "source": [ "The Rydberg density correlation function can be visualized as follows." ] }, { "cell_type": "code", "execution_count": 9, "id": "dd0c5d4a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(gij, cmap='bwr', vmin=-0.25, vmax=+0.25)\n", "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n", "plt.xlabel(\"atom index\")\n", "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n", "plt.ylabel(\"atom index\")\n", "plt.title('Rydberg density correlation')\n", "plt.gca().set_aspect('equal')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "276bb5b6", "metadata": {}, "source": [ "For more explanation and interpretation of the Rydberg density correlation functions, see \"Probing many-body dynamics on a 51-atom quantum simulator\" by [Bernien et al. (2017)](https://arxiv.org/abs/1707.04344). " ] }, { "cell_type": "markdown", "id": "fc7d3074", "metadata": {}, "source": [ "## 2D checkerboard phase \n", "\n", "In two dimension, Rydberg system can exhibit the checkerboard phase, which is analogous to the $Z_2$ phase in 1D. For simplicity, here we create a $3\\times 3$ square lattice." ] }, { "cell_type": "code", "execution_count": 10, "id": "22477060", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "register_2D = AtomArrangement()\n", "separation = 6.7e-6 # in meters \n", "\n", "for k in range(3):\n", " for l in range(3):\n", " register_2D.add((k * separation, l * separation))\n", "\n", "show_register(register_2D)" ] }, { "cell_type": "markdown", "id": "eb0fcacf", "metadata": {}, "source": [ "We will use the same driving field as the one for generating the $Z_2$ phase. We then assemble the 2D array with the driving field, and run the AHS program on the local simulator. " ] }, { "cell_type": "code", "execution_count": 11, "id": "df3a2aae", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ahs_program_2D = AnalogHamiltonianSimulation(\n", " register=register_2D, \n", " hamiltonian=drive\n", ")\n", "\n", "result_2D = device.run(ahs_program_2D, shots=1000, steps=200).result()\n", "show_final_avg_density(result_2D)" ] }, { "cell_type": "markdown", "id": "08e49477", "metadata": {}, "source": [ "We see that the overall pattern mimics the checkerboard pattern, but the central site suffers strong discrepancy. This is due to the finite size of the system and the finite duration of the AHS program, which cause non-adiabatic errors.\n", "\n", "For more explanation and interpretation of the 2-d results, see \"Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator\" by [Ebadi et al. (2020)](http://arxiv.org/abs/2012.12281). " ] }, { "cell_type": "markdown", "id": "68ffc633", "metadata": {}, "source": [ "## Realizing $Z_2$ and checkerboard phase on a QPU\n", "\n", "In previous sections, we have demonstrated two AHS programs for realizing many-body ground states. The results from the local simulator show that the results of the programs meet our expectations. Here we will run the same AHS program on the Aquila device. " ] }, { "cell_type": "markdown", "id": "525d3c27", "metadata": {}, "source": [ "
\n", "Note: Some atoms may be missing even if the shot was successful. We recommend comparing pre_sequence of each shot with the requested atom filling in the AHS program specification. \n", "
" ] }, { "cell_type": "code", "execution_count": 12, "id": "31901542", "metadata": {}, "outputs": [], "source": [ "from braket.aws import AwsDevice \n", "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")" ] }, { "cell_type": "code", "execution_count": 13, "id": "07a73135", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "result_1D_aquila = device.run(ahs_program, shots=100).result()\n", "show_final_avg_density(result_1D_aquila)" ] }, { "cell_type": "markdown", "id": "69fc4e5d", "metadata": {}, "source": [ "We can calculate the density correlation function for the result obtained from Aquila" ] }, { "cell_type": "code", "execution_count": 14, "id": "e07e91f5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gij_aquila = get_density_correlation_Z2(result_1D_aquila)\n", "\n", "plt.imshow(gij_aquila, cmap='bwr', vmin=-0.25, vmax=+0.25)\n", "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n", "plt.xlabel(\"atom index\")\n", "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n", "plt.ylabel(\"atom index\")\n", "plt.title('Rydberg density correlation')\n", "plt.gca().set_aspect('equal')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "id": "fcc2c8b3", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "result_2D_aquila = device.run(ahs_program_2D, shots=100).result()\n", "show_final_avg_density(result_2D_aquila)" ] }, { "cell_type": "markdown", "id": "1c5e689d", "metadata": {}, "source": [ "In summary, in this notebook we have demonstrated how to realize the 1D $Z_2$ phase and 2D checkerboard phase via adiabatic transition on the Rydberg systems. These are interesting many body phases in their own right, and serve as the starting points for the more involved use cases. " ] }, { "cell_type": "code", "execution_count": 16, "id": "eba213ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Task Summary\n", "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 200, 'tasks': {'COMPLETED': 2}}}\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: 2.60 USD\n" ] } ], "source": [ "print(\"Task Summary\")\n", "print(tracker.quantum_tasks_statistics())\n", "print('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", "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")" ] }, { "cell_type": "code", "execution_count": null, "id": "a6a296d5", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }