Short answer: Quantum volume is a single-number benchmark that reports the largest random circuit of equal width and depth a quantum computer can run successfully. A 2019 Physical Review A paper introduced it, and later work from 2021 and 2023 examines what passing the test means, how the statistics should be handled, and what makes a benchmark valid. It is a useful comparison tool, but one number cannot describe a whole machine.
What it measures
The 2019 paper introduces quantum volume as a single-number metric measured with a concrete protocol on near-term machines of modest size, up to about 50 qubits. The authors measured it on several transmon devices and found values as high as 16. They say it quantifies the largest random circuit of equal width and depth that the computer successfully implements, is linked to system error rates, and is empirically reduced by uncontrolled interactions in the system. Machines with high-fidelity operations, high connectivity, large calibrated gate sets and circuit rewriting toolchains are expected to score higher. They describe it as a pragmatic way to compare progress toward better system-wide gate error rates.
How the test is defined
A 2023 arXiv paper on benchmarking rules gives the formula: the base-2 logarithm of the quantum volume is the largest width m for which the smaller of m and the achievable depth d(m) is maximal, using Haar-random circuits. The achievable depth is the largest depth at which the heavy-output probability exceeds 2/3. Heavy outputs are the bit strings whose probabilities are above the median of the distribution obtained by classically simulating the random circuit. The paper adds that experiments must follow set rules, including a statistical test on the passing result with at least 100 circuits.
What passing implies
A 2021 arXiv paper describes the test as a full-system benchmark sensitive to qubit number, fidelity, connectivity and other quantities believed important for useful devices. It says the test was designed to give a single-number measure of general capability, but that a complete understanding of its limitations and operational meaning was still missing. The authors study its design, sensitivity to errors and passing criteria, show transient behaviour at small qubit numbers, and give an efficient algorithm for estimating the expected heavy-output probability under different error models and compiler optimisations. They find the original confidence interval construction underachieves the desired coverage for single-shot experiments and overachieves for typical shot counts, and propose a new construction that reaches the stated coverage and needs fewer circuits to pass. They demonstrate it on an experimental dataset of quantum volume 2 to the power 10 from a Quantinuum System Model H1-1 machine.
What makes a benchmark valid
The 2023 paper proposes rules for a good benchmark. It should be well defined, with a clear set of rules; holistic, indicating performance over many device attributes in as few metrics as possible; and platform independent. It uses quantum volume as the worked example, including how different success statistics change what the result implies.
What this does not tell you
Quantum volume uses random circuits, so it does not say how a machine will do on a specific application. The results cited are from the papers' own devices and datasets, and a higher number from one platform is not automatically a better machine for every task.
FAQ
What does quantum volume measure?
The largest random circuit of equal width and depth the computer implements successfully.
How is success decided?
The heavy-output probability must exceed 2/3, with a statistical test over at least 100 circuits.
Is it a complete measure of a computer?
The 2021 paper says its full operational meaning was still not completely understood.
Has the statistics been improved?
The 2021 paper proposes a new confidence interval that reaches stated coverage with fewer circuits.
What are the rules for a good benchmark?
Well defined, holistic and platform independent, per the 2023 paper.
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