{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "DkA0Fobtb9dM" }, "source": [ "##### Copyright 2022 The Cirq Developers" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2025-08-12T09:08:25.529166Z", "iopub.status.busy": "2025-08-12T09:08:25.528956Z", "iopub.status.idle": "2025-08-12T09:08:25.532227Z", "shell.execute_reply": "2025-08-12T09:08:25.531674Z" }, "id": "tUshu7YfcAAW" }, "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": "4ySIERZGZN0d" }, "source": [ "# QVM Basic Example" ] }, { "cell_type": "markdown", "metadata": { "id": "vGUeqO9jn1vc" }, "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": "cd6e59ef3edd" }, "source": [ "This notebook walks through running a simple circuit on the [Quantum Virtual Machine](./quantum_virtual_machine.ipynb), including the necessary constraints on a device-runnable circuit and how to satisfy them. " ] }, { "cell_type": "markdown", "metadata": { "id": "Lfira0gPf0Gd" }, "source": [ "## **Install** Cirq and qsim" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2025-08-12T09:08:25.534636Z", "iopub.status.busy": "2025-08-12T09:08:25.534413Z", "iopub.status.idle": "2025-08-12T09:08:41.104451Z", "shell.execute_reply": "2025-08-12T09:08:41.103569Z" }, "id": "zs5J6wAXqvtW" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "installing cirq...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "installed cirq.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "installing qsimcirq...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "installed qsimcirq.\n" ] } ], "source": [ "# @title Install `cirq_google` and `qsimcirq`\n", "\n", "try:\n", " import cirq\n", " import cirq_google\n", "except ImportError:\n", " print(\"installing cirq...\")\n", " !pip install --quiet cirq-google\n", " print(\"installed cirq.\")\n", " import cirq\n", " import cirq_google\n", "\n", "try:\n", " import qsimcirq\n", "except ImportError:\n", " print(\"installing qsimcirq...\")\n", " !pip install --quiet qsimcirq\n", " print(f\"installed qsimcirq.\")\n", " import qsimcirq\n", "\n", "# Other modules used in this colab\n", "import matplotlib.pyplot as plt\n", "import time" ] }, { "cell_type": "markdown", "metadata": { "id": "p2JAfQa8gVSe" }, "source": [ "## Create a **Quantum Virtual Machine**\n", "\n", "The following cell builds a Quantum Virtual Machine that mimics a particular Google quantum hardware device (currently Willow-pink, Rainbow or Weber) using the following customizable steps: \n", "- Constructing a `cirq.NoiseModel` object from device calibration data saved in Cirq. See [Representing Noise](../noise/representing_noise.ipynb) for more on noise models. \n", "- Building a `qsimcirq.QsimSimulator` that uses this noise model. See [Noisy Simulation](./noisy_simulation.ipynb) and [Noise simulation with qsim](/qsim/tutorials/noisy_qsimcirq) for more. \n", "- Creating a `cirq.Device` that imposes the same constraints on circuits that the original device would. See [Devices](../hardware/devices.ipynb) for more on these constraint objects. \n", "- Packaging the simulator and device into an object that implements the `cirq.Engine` interface that the hardware device would use. \n", "\n", "If you don't need this level of control, you can also instantiate a QVM with `cirq_google.engine.create_default_noisy_quantum_virtual_machine`, as in [QVM Creation Template](./qvm_builder_code.ipynb). " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2025-08-12T09:08:41.108140Z", "iopub.status.busy": "2025-08-12T09:08:41.107199Z", "iopub.status.idle": "2025-08-12T09:08:41.442593Z", "shell.execute_reply": "2025-08-12T09:08:41.441947Z" }, "id": "pbHCUPLpq5WE" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Your quantum virtual machine willow_pink is ready, here is the qubit grid: \n", "========================\n", "\n", " (0, 6)────(0, 7)────(0, 8)\n", " │ │ │\n", " │ │ │\n", " (1, 5)────(1, 6)────(1, 7)────(1, 8)\n", " │ │ │ │\n", " │ │ │ │\n", " (2, 4)────(2, 5)────(2, 6)────(2, 7)────(2, 8)────(2, 9)────(2, 10)\n", " │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │\n", " (3, 3)───(3, 4)────(3, 5)────(3, 6)────(3, 7)────(3, 8)────(3, 9)────(3, 10)\n", " │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │\n", " (4, 2)───(4, 3)───(4, 4)────(4, 5)────(4, 6)────(4, 7)────(4, 8)────(4, 9)────(4, 10)────(4, 11)───(4, 12)\n", " │ │ │ │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │ │ │ │\n", " (5, 1)───(5, 2)───(5, 3)───(5, 4)────(5, 5)────(5, 6)────(5, 7)────(5, 8)────(5, 9)────(5, 10)────(5, 11)───(5, 12)\n", " │ │ │ │ │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │ │ │ │ │\n", "(6, 0)───(6, 1)───(6, 2)───(6, 3)───(6, 4)────(6, 5)────(6, 6)────(6, 7)────(6, 8)────(6, 9)────(6, 10)────(6, 11)───(6, 12)───(6, 13)───(6, 14)\n", " │ │ │ │ │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │ │ │ │ │\n", " (7, 2)───(7, 3)───(7, 4)────(7, 5)────(7, 6)────(7, 7)────(7, 8)────(7, 9)────(7, 10)────(7, 11)───(7, 12)───(7, 13)\n", " │ │ │ │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │ │ │ │\n", " (8, 2)───(8, 3)───(8, 4)────(8, 5)────(8, 6)────(8, 7)────(8, 8)────(8, 9)────(8, 10)────(8, 11)───(8, 12)\n", " │ │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │ │\n", " (9, 4)────(9, 5)────(9, 6)────(9, 7)────(9, 8)────(9, 9)────(9, 10)────(9, 11)\n", " │ │ │ │ │ │ │\n", " │ │ │ │ │ │ │\n", " (10, 4)───(10, 5)───(10, 6)───(10, 7)───(10, 8)───(10, 9)───(10, 10)\n", " │ │ │ │\n", " │ │ │ │\n", " (11, 6)───(11, 7)───(11, 8)───(11, 9)\n", " │ │ │\n", " │ │ │\n", " (12, 6)───(12, 7)───(12, 8)\n" ] } ], "source": [ "# @title Choose a processor (\"willow_pink\" or \"rainbow\" or \"weber\")\n", "# (see cirq_google.engine.list_virtual_processors() for available names)\n", "processor_id = \"willow_pink\" # @param {type:\"string\"}\n", "\n", "# Construct a simulator with a noise model based on the specified processor.\n", "noise_props = cirq_google.engine.load_device_noise_properties(processor_id)\n", "noise_model = cirq_google.NoiseModelFromGoogleNoiseProperties(noise_props)\n", "sim = qsimcirq.QSimSimulator(noise=noise_model)\n", "\n", "# Create a device from the public device description\n", "device = cirq_google.engine.create_device_from_processor_id(processor_id)\n", "cal = cirq_google.engine.load_median_device_calibration(processor_id)\n", "# Build the simulated local processor from the simulator and device.\n", "sim_processor = cirq_google.engine.SimulatedLocalProcessor(\n", " processor_id=processor_id, sampler=sim, device=device, calibrations={cal.timestamp // 1000: cal}\n", ")\n", "# Package the processor to use an Engine interface\n", "sim_engine = cirq_google.engine.SimulatedLocalEngine([sim_processor])\n", "print(\n", " \"Your quantum virtual machine\",\n", " processor_id,\n", " \"is ready, here is the qubit grid:\",\n", " \"\\n========================\\n\",\n", ")\n", "print(sim_engine.get_processor(processor_id).get_device())" ] }, { "cell_type": "markdown", "metadata": { "id": "TJfN17frwo-0" }, "source": [ "## **Create** a circuit, **transform** it (to make it executable on Google quantum hardware) and **choose qubits** on the processor. \n", "\n", "The circuit you use needs to be _device ready_, which means it: \n", "- Is comprised of operations from the device's gate set. \n", "- Is applied to qubits that exist on the device. \n", "- Respects the connectivity of qubits on the device.\n", "\n", "Below is an example of a circuit that has the correct topology to be placed on the Willow-pink device, and how it is prepared to be run on the QVM." ] }, { "cell_type": "markdown", "metadata": { "id": "a_arTtfcwqrz" }, "source": [ "### Create a GHZ state builder circuit\n", "\n", "The generalized [Greenberger–Horne–Zeilinger (GHZ) state](https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state){:.external} has the form $\\frac{|00..0⟩ + |11..1⟩}{\\sqrt{2}}$ and, in this case, will be constructed using 17 qubits, with a Hadamard and a sequence of CNOT gates:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-08-12T09:08:41.445079Z", "iopub.status.busy": "2025-08-12T09:08:41.444838Z", "iopub.status.idle": "2025-08-12T09:08:41.459897Z", "shell.execute_reply": "2025-08-12T09:08:41.459295Z" }, "id": "mZFn6OmwwqaR" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: ────H───@───────────────────────────────────────────────────────────────M('out')───\n", " │ │\n", "1: ────────X───@───────────────────────────────────────────────────────────M──────────\n", " │ │\n", "2: ────────────X───@───────────────────────────────────────────────────────M──────────\n", " │ │\n", "3: ────────────────X───@───────────────────────────────────────────────────M──────────\n", " │ │\n", "4: ────────────────────X───@───────────────────────────────────────────────M──────────\n", " │ │\n", "5: ────────────────────────X───@───────────────────────────────────────────M──────────\n", " │ │\n", "6: ────────────────────────────X───@───────────────────────────────────────M──────────\n", " │ │\n", "7: ────────────────────────────────X───@───────────────────────────────────M──────────\n", " │ │\n", "8: ────────────────────────────────────X───@───────────────────────────────M──────────\n", " │ │\n", "9: ────────────────────────────────────────X───@───────────────────────────M──────────\n", " │ │\n", "10: ───────────────────────────────────────────X───@───────────────────────M──────────\n", " │ │\n", "11: ───────────────────────────────────────────────X───@───────────────────M──────────\n", " │ │\n", "12: ───────────────────────────────────────────────────X───@───────────────M──────────\n", " │ │\n", "13: ───────────────────────────────────────────────────────X───@───────────M──────────\n", " │ │\n", "14: ───────────────────────────────────────────────────────────X───@───────M──────────\n", " │ │\n", "15: ───────────────────────────────────────────────────────────────X───@───M──────────\n", " │ │\n", "16: ───────────────────────────────────────────────────────────────────X───M──────────\n" ] } ], "source": [ "# Define an abstract line of 17 qubits\n", "number_of_qubits = 17\n", "qubits = cirq.LineQubit.range(number_of_qubits)\n", "\n", "# Create a GHZ circuit on this qubit line\n", "ghz_circuit = cirq.Circuit(\n", " cirq.H(qubits[0]),\n", " *[cirq.CNOT(qubits[i - 1], qubits[i]) for i in range(1, number_of_qubits)],\n", " cirq.measure(*qubits, key='out'),\n", ")\n", "print(ghz_circuit)" ] }, { "cell_type": "markdown", "metadata": { "id": "tc5L80jjMknb" }, "source": [ "Notice that this circuit consists of a sequence of CNOT gates applied consecutively to a single chain of qubits. The connectivity required by the circuit is simple in the sense that it needs a line of qubits which are only connected to their adjacent neighbor in the sequence. As constructed, this consists of 17 `cirq.LineQubit`s indexed `0, 1, 2...16`. " ] }, { "cell_type": "markdown", "metadata": { "id": "gmgGLI7eZLQt" }, "source": [ "### Transform the circuit \n", "\n", "Before executing a circuit on (virtual) quantum hardware, the operations in the circuit need to be translated to use the types of gates the device supports. The `cirq.optimize_for_target_gateset` function does this for you, transforming the operations to use the `cirq.CZTargetGateset`, which is supported by the Willow-pink processor that this QVM is based on. Learn more about the gate set constraints of Google hardware at the [Hardware](../hardware) page." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2025-08-12T09:08:41.462221Z", "iopub.status.busy": "2025-08-12T09:08:41.461991Z", "iopub.status.idle": "2025-08-12T09:08:41.636875Z", "shell.execute_reply": "2025-08-12T09:08:41.636263Z" }, "id": "MqdssGOhY9-S" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: ────PhXZ(a=0.5,x=-0.5,z=1)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M('out')───\n", " │ │\n", "1: ────PhXZ(a=0.5,x=0.5,z=0)────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "2: ─────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "3: ──────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "4: ───────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "5: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "6: ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "7: ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "8: ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "9: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "10: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "11: ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "12: ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "13: ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "14: ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────M──────────\n", " │ │\n", "15: ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────M──────────\n", " │ │\n", "16: ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───M──────────\n" ] } ], "source": [ "# Convert the gates in the GHZ circuit to the \"CZ\" gateset, which the device uses.\n", "translated_ghz_circuit = cirq.optimize_for_target_gateset(\n", " ghz_circuit, context=cirq.TransformerContext(deep=True), gateset=cirq.CZTargetGateset()\n", ")\n", "print(translated_ghz_circuit)" ] }, { "cell_type": "markdown", "metadata": { "id": "JfFfiNkbDDQy" }, "source": [ "### Choose qubits on the virtual device\n", "\n", "Choose qubits on the device to execute your device ready circuit on. Look at the device map (as above) and choose a set of qubits that fit your circuit (eg a line or a block). The Willow-pink, Rainbow and Weber devices have different topologies, some qubit maps may be possible on only one of these devices. As noted, the GHZ example circuit as constructed will fit on a 17 qubit chain of adjacent qubits on the device, so you only need to find this consecutive line of qubits. See [Qubit Picking](../hardware/qubit_picking.ipynb) for more advice and methods for selecting qubits. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2025-08-12T09:08:41.639167Z", "iopub.status.busy": "2025-08-12T09:08:41.638946Z", "iopub.status.idle": "2025-08-12T09:08:41.643433Z", "shell.execute_reply": "2025-08-12T09:08:41.642877Z" }, "id": "k4PsLLFnDGN-" }, "outputs": [], "source": [ "# Choose qubits on the virtual device\n", "device_qubit_chain = [\n", " cirq.GridQubit(5, 6),\n", " cirq.GridQubit(5, 7),\n", " cirq.GridQubit(4, 7),\n", " cirq.GridQubit(4, 6),\n", " cirq.GridQubit(4, 5),\n", " cirq.GridQubit(5, 5),\n", " cirq.GridQubit(6, 5),\n", " cirq.GridQubit(6, 6),\n", " cirq.GridQubit(6, 7),\n", " cirq.GridQubit(6, 8),\n", " cirq.GridQubit(6, 9),\n", " cirq.GridQubit(7, 9),\n", " cirq.GridQubit(8, 9),\n", " cirq.GridQubit(8, 8),\n", " cirq.GridQubit(8, 7),\n", " cirq.GridQubit(7, 7),\n", " cirq.GridQubit(7, 8),\n", "]\n", "# Layout:\n", "#\n", "# q(4, 5)───q(4, 6)───q(4, 7)\n", "# │ │\n", "# │ │\n", "# q(5, 5) q(5, 6)───q(5, 7)\n", "# │\n", "# │\n", "# q(6, 5)───q(6, 6)───q(6, 7)───q(6, 8)───q(6, 9)\n", "# │\n", "# │\n", "# q(7, 7)───q(7, 8) q(7, 9)\n", "# │ │\n", "# │ │\n", "# q(8, 7)───q(8, 8)───q(8, 9)" ] }, { "cell_type": "markdown", "metadata": { "id": "UD28ccnyrezn" }, "source": [ "### Map the transformed circuit to the qubits you chose on the device\n", "\n", "The transformed GHZ circuit still needs to be re-mapped to use the selected qubits. The `transform_qubits` function of `cirq.Circuit` does this automatically, returning a new transformed circuit when given a qubit mapping function. \n", "\n", "Because the connectivity qubit chain in the GHZ circuit example follows the sequence of `cirq.LineQubit`s in `qubits`, it suffices to zip the circuit's qubits together with the chosen device qubits, since both are connected chains of 17 qubits. The dictionary built from these paired qubits can then be turned into a simple lambda function for use with `transform_qubits`, as follows:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2025-08-12T09:08:41.645432Z", "iopub.status.busy": "2025-08-12T09:08:41.645222Z", "iopub.status.idle": "2025-08-12T09:08:41.668146Z", "shell.execute_reply": "2025-08-12T09:08:41.667553Z" }, "id": "znPgxQ81rjb3" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4, 5): ──────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(4, 6): ─────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(4, 7): ────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(5, 5): ─────────────────────────────────────────────────────────────────┼─────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(5, 6): ───PhXZ(a=0.5,x=-0.5,z=1)───@───PhXZ(a=0,x=0,z=1)────────────────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M('out')───\n", " │ │ │ │\n", "(5, 7): ───PhXZ(a=0.5,x=0.5,z=0)────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(6, 5): ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(6, 6): ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(6, 7): ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(6, 8): ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(6, 9): ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │\n", "(7, 7): ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)────────────────M──────────\n", " │ │ │ │\n", "(7, 8): ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼───PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───M──────────\n", " │ │ │\n", "(7, 9): ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────┼─────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(8, 7): ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)─────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(8, 8): ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┼───PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)──────────────────────────────────────────────────────────────────────────────────────────M──────────\n", " │ │ │\n", "(8, 9): ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────PhXZ(a=0.5,x=0.5,z=0)────────────@───PhXZ(a=-0.5,x=0.5,z=-8.88e-16)───@───PhXZ(a=0,x=0,z=1)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────M──────────\n" ] } ], "source": [ "# Map the line of circuit qubits to the chosen line of device qubits.\n", "qubit_map = dict(zip(qubits, device_qubit_chain))\n", "# Then replace qubits in the circuit according to that map.\n", "device_ready_ghz_circuit = translated_ghz_circuit.transform_qubits(lambda q: qubit_map[q])\n", "print(device_ready_ghz_circuit)" ] }, { "cell_type": "markdown", "metadata": { "id": "dWYXJmyWqg3x" }, "source": [ "### **Running other circuits**\n", "\n", "In principle, you can run any custom [Circuit](../build/circuits.ipynb) with a quantum virtual machine, but realistically there are some constraints. As mentioned, the circuits need to be mappable to the device. Additionally, the number of qubits that are simulatable depends highly on the hardware available to you and how long you are able to run your simulation. As the QVM is instantiated as above, with a `qsimcirq.QSimSimulator`, it only uses the default, local [qsim](https://quantumai.google/qsim) simulator. However, qsim has plenty of support for being run in a [Google Cloud instance](/qsim/tutorials/gcp_before_you_begin){:.external}, with a variable amount of compute power. In order to get the most capacity possible for qsim, use [Multinode Simulation](/qsim/tutorials/multinode).\n", "\n", "For an example of building and running a much larger circuit, see the [QVM Stabilizer Example](./qvm_stabilizer_example.ipynb) tutorial. " ] }, { "cell_type": "markdown", "metadata": { "id": "Zxv0RtJuhaof" }, "source": [ "## **Execute** Your Circuit on the Quantum Virtual Machine\n", "\n", "You can run the now device-ready circuit, as you would with any other `cirq.Engine` instance, by getting a sampler from it and using the `run` function on the circuits. Your choice of `repetitions` is intrinsically related to the accuracy of your simulated results. We recommend 3000 repetitions for trial runs, and 10,000 repetitions for accuracy-critical runs, but you can stick to one to ten repetitions when testing a code pipeline. You can read more about this in [this paper](https://arxiv.org/abs/2111.02396){:.external}." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "cellView": "form", "execution": { "iopub.execute_input": "2025-08-12T09:08:41.670358Z", "iopub.status.busy": "2025-08-12T09:08:41.670135Z", "iopub.status.idle": "2025-08-12T09:08:54.311253Z", "shell.execute_reply": "2025-08-12T09:08:54.310569Z" }, "id": "bFjnNSqRZsFu" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Circuit successfully executed on your quantum virtual machine willow_pink\n", "QVM runtime: 12.64s (3000 repetitions)\n", "You can now print or plot \"results\"\n" ] } ], "source": [ "# @title Execute your device ready circuit on the Quantum Virtual Machine\n", "circuit = device_ready_ghz_circuit\n", "\n", "repetitions = 3000\n", "start = time.time()\n", "results = sim_engine.get_sampler(processor_id).run(circuit, repetitions=repetitions)\n", "elapsed = time.time() - start\n", "\n", "print('Circuit successfully executed on your quantum virtual machine', processor_id)\n", "print(f'QVM runtime: {elapsed:.04g}s ({repetitions} repetitions)')\n", "print('You can now print or plot \"results\"')" ] }, { "cell_type": "markdown", "metadata": { "id": "na6nqbvviW7U" }, "source": [ "## **Visualize** Output\n", "\n", "Finally, you can use a [state histogram](./state_histograms.ipynb) to plot the measured results." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2025-08-12T09:08:54.313783Z", "iopub.status.busy": "2025-08-12T09:08:54.313535Z", "iopub.status.idle": "2025-08-12T09:08:54.686352Z", "shell.execute_reply": "2025-08-12T09:08:54.685560Z" }, "id": "O92KP1EwZwV9" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = cirq.plot_state_histogram(results.histogram(key='out'))\n", "ax.get_xaxis().set_ticks([])\n", "plt.gcf().set_size_inches(10, 4)\n", "plt.show(ax)" ] }, { "cell_type": "markdown", "metadata": { "id": "XOTvkKq_Z1UY" }, "source": [ "The leftmost and rightmost bars correspond to $|00..0\\rangle$ and $|11..1\\rangle$, respectively, which matches expectation for a GHZ state. Natural $|1\\rangle → |0\\rangle$ decay causes $|11..1\\rangle$ to be much less common than $|00..0\\rangle$, and other states also appear due to the various error mechanisms in the hardware that are mimicked by the simulated noise model. Learn more about these errors [here](https://arxiv.org/abs/2111.02396){:.external}.\n" ] } ], "metadata": { "colab": { "collapsed_sections": [ "Lfira0gPf0Gd" ], "name": "qvm_basic_example.ipynb", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "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": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 0 }