Quantum volume: how one number tries to score a quantum computer

Short answer: Quantum volume is a single-number benchmark introduced in a 2019 paper by IBM researchers. It quantifies the largest random circuit of equal width and depth that a quantum computer successfully implements. A 2022 analysis in the journal Quantum says a complete understanding of the test's limitations and operational meaning is still missing. The figures here come from the papers and, for the 2019 paper, from its vendor authors.

What is the core definition of quantum volume?

The 2022 analysis describes the test as designed to produce a single-number measure of a quantum computer's general capability. It specifically quantifies the largest random circuit of equal width and depth that the computer successfully implements. This definition distinguishes it from simple qubit counts or isolated gate fidelities. The 2019 authors describe it as a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments.

How is the metric measured in practice?

The 2019 paper describes a concrete protocol designed for near-term quantum computers of modest size, typically with qubit numbers around 50. The paper's authors report measuring it on several state-of-the-art transmon devices, finding values as high as 16. The protocol is sensitive to qubit number, fidelity, connectivity, and other quantities believed to be important in building useful devices. The 2022 paper calls it a full-system benchmark. The paper's title refers to validating quantum computers using randomized model circuits.

What factors influence the resulting score?

Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes. The 2019 paper says the metric is empirically reduced by uncontrolled interactions within the system. The 2022 paper presents an algorithm for estimating the expected heavy output probability under different error models and compiler optimization options. The paper also describes transient behaviors for small qubit numbers. The 2022 paper explores sensitivity to errors, passing criteria and what passing implies.

What are the limitations and operational meanings?

A complete understanding of the quantum volume test's limitations and operational meaning is still missing. The original confidence interval construction has been shown to underachieve the desired coverage level for single shots. Additionally, the test exhibits transient behaviors for small qubit numbers, including specific ideal measurement output distributions. The 2022 paper presents an algorithm that predicts performance goals for future systems. Quantum volume is a benchmark, not a certification, and we make no claim about any commercial system.

FAQ

What is quantum volume?

A single-number metric that quantifies the largest random circuit of equal width and depth that the computer successfully implements, introduced in 2019 by IBM researchers.

What did the 2019 paper measure?

It reports measuring quantum volume on several state-of-the-art transmon devices, finding values as high as 16. These are IBM authors' own results.

What affects the score?

The paper links it to system error rates and says it is reduced by uncontrolled interactions. It expects systems with high-fidelity operations, high connectivity, large calibrated gate sets and circuit rewriting toolchains to have higher quantum volumes.

What are its limits?

A 2022 paper says a complete understanding of the test's limitations and operational meaning is still missing, and that the original confidence interval construction underachieves the desired coverage level for single shots.

Does a high score mean a machine is ready for real work?

The papers do not say so. It is a benchmark, and this article makes no claim about any commercial system.