**Because evolution is
unitary**.

## Random quantum volume circuits for benchmarking

Nick Gardner

## About quantum volume

This past spring **I contributed a function to Mitiq for sampling random quantum volume circuits**. Quantum volume is a single-number benchmark for near-term quantum computers proposed in 2019 by researchers at IBM (see here for a nice overview). The **quantum volume** of a quantum computer quantifies the largest random circuit of equal width (number of qubits) and depth (layers of gates) which that quantum computer can successfully implement. As a **benchmark**, it is meant to serve as a more accurate single-number summary of the quality of a quantum computer than simpler quantities such as the number of qubits, or average gate fidelity. Various features of a quantum computing system jointly contribute to its quantum volume score, including how many qubits it has, the fidelity of its operations, and the degree of connectivity of its qubit layout.

## Random quantum volume circuits

The **random quantum circuits** used in quantum volume experiments consist of *d* layers of the following computation performed on *d* qubits: randomly permute all qubits, then apply random two-qubit unitary transformations to every pair of adjacent qubits (leaving one qubit out each time if the number of qubits is odd). Success in executing the circuit is defined in terms of the **heavy output generation problem** (can the computer produce a set of output strings more than two-thirds of which are “heavy”–have a greater than the median probability of being generated–for that random circuit?).

## Adding quantum volume circuits to Mitiq

The functions I implemented for **Mitiq** generate this type of random circuit and calculate (classically) its set of heavy output strings.

**This was my first real project in the world of quantum computing software**, and thanks to the Mitiq team it was a great experience–I learned a ton and am excited to work on future Mitiq projects. Thank you especially to Andrea, Nathan, and Misty for being so welcoming and helpful!

## About me

I am a graduate student at Stanford interested in quantum computing, focusing on quantum error correction. I’ve begun contributing to Mitiq within the Stanford University course “Quantum Computing: Open-Source Project Experience” (CS59SI).