{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "id": "S97D7gQHMdG_" }, "outputs": [], "source": [ "##### Copyright 2021 The Cirq Developers" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "cellView": "form", "id": "Y6Wh1qtGMghL" }, "outputs": [], "source": [ "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "id": "gNBCrapEMgxB" }, "source": [ "# Quantum scrambling experiment example" ] }, { "cell_type": "markdown", "metadata": { "id": "tlnEweYsMgzj" }, "source": [ "\n", " \n", " \n", " \n", " \n", "
\n", " View on QuantumAI\n", " \n", " Run in Google Colab\n", " \n", " View source on GitHub\n", " \n", " Download notebook\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "PnYvZgIoMg2O" }, "source": [ "This tutorial shows an experiment example from the publication [Information scrambling in computationally complex quantum circuits](https://arxiv.org/abs/2101.08870) (henceforth \"OTOC paper\"), in particular how to recreate Figure 1." ] }, { "cell_type": "markdown", "metadata": { "id": "xmJUa-i__Vl9" }, "source": [ "## Background on quantum scrambling" ] }, { "cell_type": "markdown", "metadata": { "id": "D-6CzQFH84Tr" }, "source": [ "Quantum scrambling describes how interaction in a quantum system disperses local information into its many degrees of freedom. Analogous to classical chaos, scrambling manifests itself as a [butterfly effect](https://en.wikipedia.org/wiki/Butterfly_effect) wherein a local perturbation is rapidly amplified over time. The perturbation is modeled by a local operator $\\hat{O}$ (the *butterfly operator*) acting on a qubit (the *butterfly qubit*). Under a dynamical process $\\hat{U} = \\hat{U}(t)$, the butterfly operator evolves in the Heisenberg picture as\n", "\n", "$$\n", "\\hat{O} (t) = \\hat{U}^\\dagger \\hat{O} \\hat{U}\n", "$$\n", "\n", "Expanding the butterfly operator in a basis\n", "\n", "$$\n", "\\hat{O} (t) = \\sum_{i = 1}^{n_p} w_i B_i \n", "$$\n", "\n", "where $B_i = B^{(1)}_i \\otimes \\cdots \\otimes B^{(n)}_i$ are basis elements and $w_i$ are coefficients, we can describe the two different mechanisms of quantum scrambling as follows:\n", "\n", "- *Operator spreading* occurs when basis elements $B_i$ require a higher weight (fewer non-identity terms) on average to describe $\\hat{O}(t)$.\n", "- *Operator entanglement* occurs when a larger $n_p$ (summation index) is required to describe $\\hat{O}(t)$.\n", "\n", "We experimentally evaluate the out-of-time order correlator (OTOC) $C(t)$ between $\\hat{O}(t)$ and a *measurement operator* $\\hat{M}$ which is a Pauli operator acting on another qubit (the *measurement qubit*)\n", "\n", "$$\n", "C(t) := \\langle \\hat{O} ^\\dagger (t) M^\\dagger \\hat{O} (t) M \\rangle\n", "$$\n", "\n", "over a collection of quantum circuits with microscopic differences (e.g., in the phases of gates). Operator scrambling is then reflected in the average OTOC value $\\bar{C}(t)$ over different circuits:\n", "\n", "- $\\bar{C}(t) = 1$ when $\\hat{O}(t)$ and $\\hat{M}$ do not overlap.\n", "- $\\bar{C}(t) < 1$ when $\\hat{O}(t)$ and $\\hat{M}$ overlap.\n", "- $\\bar{C}(t) \\rightarrow 0$ in the fully scrambled limit where the commutation between $\\hat{O}(t)$ and $\\hat{M}$ is completely randomized.\n", "\n", "Note that if operator entanglement is also present ($n_p \\gg 1$), $\\bar{C}(t)$ approaches $0$ for all circuits and their fluctuation vanishes as well.\n", "\n", "In what follows, we show how to build OTOC circuits, run them and compute $\\bar{C}$, then visualize results and detect operator spreading." ] }, { "cell_type": "markdown", "metadata": { "id": "BRfLi9YSMg4v" }, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "id": "x_5UjhI-f0qz" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Installing ReCirq...\n", "\u001b[K |████████████████████████████████| 1.5 MB 8.9 MB/s \n", "\u001b[K |████████████████████████████████| 380 kB 34.4 MB/s \n", "\u001b[K |████████████████████████████████| 5.8 MB 22.9 MB/s \n", "\u001b[K |████████████████████████████████| 33.7 MB 49 kB/s \n", "\u001b[K |████████████████████████████████| 1.3 MB 43.8 MB/s \n", "\u001b[K |████████████████████████████████| 15.7 MB 75 kB/s \n", "\u001b[K |████████████████████████████████| 229 kB 68.5 MB/s \n", "\u001b[?25h Building wheel for recirq (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Building wheel for lark-parser (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Building wheel for pytket-cirq (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Building wheel for pubchempy (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Building wheel for Py-BOBYQA (setup.py) ... \u001b[?25l\u001b[?25hdone\n", "Installed ReCirq!\n" ] } ], "source": [ "try:\n", " import recirq\n", "except ImportError:\n", " print(\"Installing ReCirq...\")\n", " !pip install git+https://github.com/quantumlib/recirq --quiet\n", " print(\"Installed ReCirq!\")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "lFI7APiqMhFy" }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import cirq\n", "import cirq_google as cg\n", "from recirq import otoc" ] }, { "cell_type": "markdown", "metadata": { "id": "fh6P5258GXQX" }, "source": [ "Note: Leave the `project_id` and/or `processor_id` blank to use a noisy simulator." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "cellView": "form", "id": "UaBOLd1ZNZwC" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "No project_id provided and environment variable GOOGLE_CLOUD_PROJECT not set.\n", "Using a noisy simulator.\n" ] } ], "source": [ "import os\n", "\n", "# The Google Cloud Project id to use.\n", "project_id = '' #@param {type:\"string\"}\n", "\n", "\n", "use_noisy_simulator = False\n", "if project_id == '' and 'GOOGLE_CLOUD_PROJECT' not in os.environ:\n", " print(\"No project_id provided and environment variable \"\n", " \"GOOGLE_CLOUD_PROJECT not set.\")\n", " use_noisy_simulator = True\n", "else: \n", " os.environ['GOOGLE_CLOUD_PROJECT'] = project_id\n", "\n", " def authenticate_user():\n", " \"\"\"Runs the user through the Colab OAuth process.\n", "\n", " Checks for Google Application Default Credentials and runs interactive login \n", " if the notebook is executed in Colab. In case the notebook is executed in Jupyter notebook\n", " or other IPython runtimes, no interactive login is provided, it is assumed that the \n", " `GOOGLE_APPLICATION_CREDENTIALS` env var is set or `gcloud auth application-default login`\n", " was executed already.\n", "\n", " For more information on using Application Default Credentials see \n", " https://cloud.google.com/docs/authentication/production\n", " \"\"\"\n", " in_colab = False\n", " try:\n", " from IPython import get_ipython\n", " in_colab = 'google.colab' in str(get_ipython())\n", " except: \n", " # Notebook is not executed within IPython. Assuming external authentication.\n", " return \n", "\n", " if in_colab: \n", " from google.colab import auth \n", " print(\"Getting OAuth2 credentials.\")\n", " print(\"Press enter after entering the verification code.\")\n", " auth.authenticate_user(clear_output=False)\n", " print(\"Authentication complete.\")\n", " else: \n", " print(\"Notebook is not executed with Colab, assuming Application Default Credentials are setup.\") \n", "\n", " authenticate_user()\n", " print(\"Successful authentication to Google Cloud.\")\n", "\n", "processor_id = \"\" #@param {type:\"string\"}\n", "use_noisy_simulator = use_noisy_simulator or processor_id == \"\" \n", "if use_noisy_simulator:\n", " print(\"Using a noisy simulator.\")\n", " sampler = cg.PhasedFSimEngineSimulator.create_with_random_gaussian_sqrt_iswap(\n", " mean=cg.SQRT_ISWAP_INV_PARAMETERS,\n", " sigma=cg.PhasedFSimCharacterization(\n", " theta=0.01, zeta=0.10, chi=0.01, gamma=0.10, phi=0.02\n", " ),\n", " )\n", " device = cg.Bristlecone\n", "else:\n", " sampler = cg.get_engine_sampler(processor_id, gate_set_name=\"sqrt_iswap\")\n", " device = cg.get_engine_device(processor_id=processor_id)" ] }, { "cell_type": "markdown", "metadata": { "id": "yLqyFVH2zn8D" }, "source": [ "## Build the OTOC circuits" ] }, { "cell_type": "markdown", "metadata": { "id": "pb8GcwQ2As7q" }, "source": [ "### Picking qubits" ] }, { "cell_type": "markdown", "metadata": { "id": "2DbErcZ_FpKX" }, "source": [ "First we specify a line of qubits to use. If running on the `cirq_google.Engine`, use the latest calibration report to identify a good line of qubits." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "GZIsJoNX1omO" }, "outputs": [], "source": [ "if not use_noisy_simulator:\n", " calibration = cg.get_engine_calibration(processor_id=processor_id)\n", " calibration.heatmap(key=\"two_qubit_sycamore_gate_xeb_average_error_per_cycle\").plot();" ] }, { "cell_type": "markdown", "metadata": { "id": "JIEEO9xaxRNW" }, "source": [ "Note that the ancilla qubit must be adjacent to the first qubit, and the first qubit is treated as the measurement qubit described above." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "id": "q1LLo6M-Ay9A" }, "outputs": [], "source": [ "qubit_indices = [(4, 1), (4, 2), (5, 2), (5, 3), (6, 3), (7, 3), (7, 4), (7, 5)]\n", "ancilla_index = (5, 1)\n", "\n", "qubits = [cirq.GridQubit(*idx) for idx in qubit_indices]\n", "ancilla = cirq.GridQubit(*ancilla_index)\n", "num_qubits = len(qubits)" ] }, { "cell_type": "markdown", "metadata": { "id": "NQ6VzBfoKrO9" }, "source": [ "### Qubit interactions and experiment parameters" ] }, { "cell_type": "markdown", "metadata": { "id": "GysFXBXWGsRe" }, "source": [ "Now we specify how qubits interact (in other words, the pattern of two-qubit gates). For the 1D chain in this example, only two layers of two-qubit gates (CZ is used here) are needed to enact all interactions." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "id": "3ggOo2SEAqcQ" }, "outputs": [], "source": [ "# Staggered two-qubit interaction pattern.\n", "int_sets = [\n", " {(qubits[i], qubits[i + 1]) for i in range(0, num_qubits - 1, 2)},\n", " {(qubits[i], qubits[i + 1]) for i in range(1, num_qubits - 1, 2)},\n", "]\n", "\n", "# Use CZ for the two-qubit interaction.\n", "forward_ops = {\n", " (qubit_indices[i], qubit_indices[i + 1]): cirq.Circuit([cirq.CZ(qubits[i], qubits[i + 1])])\n", " for i in range(num_qubits - 1)\n", "}\n", "\n", "# CZ is self-inverse.\n", "reverse_ops = forward_ops.copy()" ] }, { "cell_type": "markdown", "metadata": { "id": "7Px_M7C-PYIE" }, "source": [ "Finally, we specify a number of trials to average over when computing $\\bar{C}(t)$, and a list of cycles which corresponds to discrete time values $t$ at which to compute $\\bar{C}$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "id": "9H-iVaQCAtxy" }, "outputs": [], "source": [ "num_trials = 4 # For averaging.\n", "cycles = range(0, 20 + 1, 2) # Number of circuit cycles." ] }, { "cell_type": "markdown", "metadata": { "id": "uEqqYN9xKyAn" }, "source": [ "### Build the circuits" ] }, { "cell_type": "markdown", "metadata": { "id": "YYWW1LwCPlBm" }, "source": [ "With the specified parameters, we use `recirq.otoc.build_otoc_circuits` to create the set of circuits. First we show an example for a given number of cycles and given butterfly qubit." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "id": "cjKvpxu3Pz1X" }, "outputs": [], "source": [ "# Example number of cycles and butterfly qubit.\n", "cycle = cycles[1]\n", "q_b = qubits[2]\n", "\n", "otoc_circuits = otoc.build_otoc_circuits(\n", " qubits,\n", " ancilla,\n", " cycle,\n", " int_sets,\n", " forward_ops=forward_ops,\n", " reverse_ops=reverse_ops,\n", " butterfly_qubits=q_b,\n", " cycles_per_echo=2,\n", " sq_gates=np.random.choice(8, (num_qubits, max(cycles))),\n", " use_physical_cz=True,\n", ")" ] }, { "cell_type": "markdown", "metadata": { "id": "k--g5ClBX1Sq" }, "source": [ "The output is an instance of `recirq.otoc.otoc_circuits.OTOCCircuits` which contains lists of circuits with $X$, $Y$, and $Z$ butterfly operators on the butterfly qubit. Additionally, a list of circuits with no butterfly operator (equivalently, with the identity $I$ as the butterfly operator) is included to renormalize results." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "id": "Wwf0-n0kQEFr" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ancilla qubit: (5, 1)\n", "Measurement qubit: (4, 1)\n", "Butterfly qubit: (5, 2)\n", "\n", "Example OTOC circuit:\n", "\n" ] }, { "data": { "text/html": [ "
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Compare this circuit to Fig. 1(a) & (b) of the [OTOC paper](https://arxiv.org/abs/2101.08870)." ] }, { "cell_type": "markdown", "metadata": { "id": "TNPdutdoRM9Q" }, "source": [ "Now we create all OTOC circuits for the experiment, varying the number of cycles and the butterfly qubit." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "id": "mdARggzhzoHp" }, "outputs": [], "source": [ "np.random.seed(0) # Random seed for OTOC circuits.\n", "\n", "circuit_list = []\n", "for i in range(num_trials):\n", " circuits_i = []\n", "\n", " for cycle in cycles:\n", " circuits_ic = []\n", " \n", " for k, q_b in enumerate(qubits[1:]):\n", " circs = otoc.build_otoc_circuits(\n", " qubits,\n", " ancilla,\n", " cycle,\n", " int_sets,\n", " forward_ops=forward_ops,\n", " reverse_ops=reverse_ops,\n", " butterfly_qubits=q_b,\n", " cycles_per_echo=2,\n", " sq_gates=np.random.choice(8, (num_qubits, max(cycles))),\n", " use_physical_cz=True,\n", " )\n", "\n", " # If q_b is the measurement qubit, add both the normalization \n", " # circuits and the circuits with X as the butterfly operator. \n", " # Otherwise only add circuits with Y being the butterfly operator.\n", " if k == 0:\n", " circuits_ic.extend(circs.butterfly_I)\n", " circuits_ic.extend(circs.butterfly_X)\n", " else:\n", " circuits_ic.extend(circs.butterfly_Y)\n", "\n", " circuits_i.append(circuits_ic)\n", " circuit_list.append(circuits_i)" ] }, { "cell_type": "markdown", "metadata": { "id": "I3jboTmsHM3j" }, "source": [ "The `circuit_list` is a three-dimensional array where the first axis corresponds to the trial, the second axis corresponds to the number of cycles, and the third axis corresponds the butterfly operator / qubit ($Q_b$)." ] }, { "cell_type": "markdown", "metadata": { "id": "Lf8B1rUc-qxE" }, "source": [ "## Run the circuits" ] }, { "cell_type": "markdown", "metadata": { "id": "tvEfmDVrOA1T" }, "source": [ "Now we run the circuits and process the results." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "id": "zRsJMaG3EkgD" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1408/1408 [14:50<00:00, 1.46s/it]" ] } ], "source": [ "# Compile to sqrt_iswap.\n", "from tqdm import tqdm\n", "\n", "progress = tqdm(total=np.array(circuit_list, dtype=object).size)\n", "for i, circuits_trial in enumerate(circuit_list):\n", " for j, circuits_cycle in enumerate(circuits_trial):\n", " for k, circuit_otoc in enumerate(circuits_cycle):\n", " circuit_list[i][j][k] = cg.optimized_for_sycamore(circuit_otoc, optimizer_type=\"sqrt_iswap\")\n", " progress.update()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "id": "bHNgLiy85DXg" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " On trial 4 / 4, cycle 11 / 11." ] } ], "source": [ "results = []\n", "for i, circuits_i in enumerate(circuit_list):\n", " results_i = np.zeros((num_qubits, len(cycles)))\n", "\n", " for c, circuits_ic in enumerate(circuits_i):\n", " print(\"\\r\", f\"On trial {i + 1} / {num_trials}, cycle {c + 1} / {len(cycles)}.\", end=\"\")\n", "\n", " job = sampler.run_batch(\n", " programs=circuits_ic, \n", " params_list=[{} for _ in range(len(circuits_ic))], \n", " repetitions=int(2_000 + 10_000 * (c / max(cycles)) ** 3),\n", " )\n", "\n", " # Compute ⟨σ_y⟩ (or normalization ⟨I⟩).\n", " for d in range(num_qubits):\n", " p = np.mean(job[4 * d ][0].measurements[\"z\"])\n", " p -= np.mean(job[4 * d + 1][0].measurements[\"z\"])\n", " p -= np.mean(job[4 * d + 2][0].measurements[\"z\"])\n", " p += np.mean(job[4 * d + 3][0].measurements[\"z\"])\n", " results_i[d, c] = 0.5 * p\n", " results.append(results_i)" ] }, { "cell_type": "markdown", "metadata": { "id": "c3uPMvlF-sth" }, "source": [ "## Plot the results" ] }, { "cell_type": "markdown", "metadata": { "id": "HjyMwu0Xotyy" }, "source": [ "First we plot the normalization factor and $\\langle \\sigma_y \\rangle$ on each butterfly qubit." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "id": "gW4Xa6wN050n" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "# Average the data for the `num_trials` random circuits.\n", "results_ave = np.mean(results, axis=0)\n", "\n", "# Plot the result with no butterfly operator.\n", "plt.plot(cycles, results_ave[0, :], \"o-\", color=\"black\", mec=\"black\", mfc=\"white\", label=\"Normalization\")\n", "\n", "# Plot results for each butterfly qubit.\n", "for i in range(1, num_qubits):\n", " plt.plot(cycles, results_ave[i, :], \"o-\", mec=\"black\", label=\"$Q_b =$ {}\".format(qubits[i]))\n", "\n", "plt.title(f\"$Q_a = {ancilla}$\")\n", "plt.xlabel(\"Cycles\")\n", "plt.ylabel(r\"$\\langle \\sigma_y \\rangle$\")\n", "plt.legend(bbox_to_anchor=(1, 1));" ] }, { "cell_type": "markdown", "metadata": { "id": "yXgKQN5s_Gqu" }, "source": [ "Compare this plot to Fig. 1(c) (left panel) of the [OTOC paper](https://arxiv.org/abs/2101.08870). The values of $\\langle \\sigma_y \\rangle$ decay below 1 before $\\hat{O}$ and $\\hat{M}$ overlap due to noise. The curve labeled \"normalization\" contains no butterfly operator and its decay is solely due to noise. By renormalizing, we can analyze the effects due to quantum scrambling." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "id": "pNgVw9Z-3KC9" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light", "tags": [] }, "output_type": "display_data" } ], "source": [ "for i in range(1, num_qubits):\n", " plt.plot(cycles, results_ave[i, :] / results_ave[0, :], \"o-\", mec=\"black\", label=\"$Q_b =$ {}\".format(qubits[i]))\n", "\n", "plt.title(f\"$Q_a = {ancilla}$\")\n", "plt.xlabel(\"Cycles\")\n", "plt.ylabel(r\"Average OTOC, $\\bar{C}$\")\n", "plt.legend(bbox_to_anchor=(1, 1));" ] }, { "cell_type": "markdown", "metadata": { "id": "s9HR9YKmpAuy" }, "source": [ "Note that for each location of $Q_b$, $\\bar{C}$ retains values near 1 before sufficient circuit cycles have occured to allow an overlap between $\\hat{O}$ and $\\hat{M}$. Beyond these cycles, $\\bar{C}$ converges to $0$, indicating that $\\hat{O}$ and $\\hat{M}$ have overlapped and no longer commute. These observations show behavior consistent with operator spreading as described at the start of this tutorial. Compare this plot to Fig. 1(c) (right panel) of the [OTOC paper](https://arxiv.org/abs/2101.08870)." ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "otoc_example.ipynb", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 0 }