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Quantum Volume and Benchmarking

Quantum volume is a benchmark built to answer the question a raw qubit count cannot: how capable is this machine, really. It measures the largest square random circuit, equal in width and depth, that a quantum computer can run and still produce a correct result, and because a circuit’s depth is limited by the machine’s error rate, quantum volume folds qubit count, gate fidelity, and connectivity into one number. That is exactly why it exists. A vendor can double its qubit count while its machine gets no better at finishing a computation, and quantum volume is designed to catch that, because it only rises when the qubits are clean enough and well-connected enough to run a deeper circuit. It is the reason a serious reader treats “1,000 qubits” as an incomplete claim and asks for a benchmark that reflects the whole system, which is the same discipline that runs through How to Tell Real Quantum Progress From Hype.

Source: Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta, “Validating quantum computers using randomized model circuits,” Physical Review A 100, 032328, 2019, arXiv:1811.12926.

The short version:

• Raw qubit count measures width only. It says nothing about whether the qubits are clean enough or connected enough to run a useful computation, so it overstates capability.
• Quantum volume measures the largest square random circuit, equal width and depth, that a machine runs successfully, so it captures error rate and connectivity along with qubit count.
• Because depth is capped by the error rate, a machine with many noisy qubits and a machine with few clean ones can have the same quantum volume, which is the honest comparison.
• CLOPS, circuit layer operations per second, measures a different axis: how fast the machine runs those circuits, so speed and capability are tracked separately.
• These benchmarks describe NISQ-era machines, which are still far from a cryptographically relevant one, so a rising quantum volume is progress, not proximity to breaking cryptography.

Picture judging a delivery company by counting its trucks. A firm with a hundred trucks sounds bigger than a firm with ten, but if half the hundred break down mid-route and the drivers cannot reach each other to reroute, the smaller, reliable fleet delivers more packages. Truck count is width, and it hides whether the trucks actually finish their routes. Quantum volume is the benchmark that measures finished routes instead of trucks. It combines how many trucks there are, how often they break down, and how well they coordinate into a single figure for how much the whole operation can actually deliver, which is the number that tells you something real.

What is quantum volume?

Quantum volume is a single-number metric that quantifies the largest random circuit of equal width and depth a quantum computer can implement successfully. It was introduced in 2019 by a team at IBM, and its own abstract defines it plainly: quantum volume “quantifies the largest random circuit of equal width and depth that the computer successfully implements,” and it “is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system.” The benchmark works by running a family of randomized model circuits and checking, statistically, whether the machine’s output stays close enough to the ideal result to count as a success at a given size.

Source: Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta, “Validating quantum computers using randomized model circuits,” Physical Review A 100, 032328, 2019, arXiv:1811.12926.

The “equal width and depth” requirement is the clever heart of the design. Width is the number of qubits, and depth is the number of gate layers, and by forcing them equal, the benchmark ensures a machine cannot score well just by having many qubits it cannot actually use together. To pass at a larger size, the machine needs both more qubits and the fidelity to run them through more gate layers without the errors piling up, so quantum volume rewards balanced improvement across the whole system rather than a lopsided qubit-count record.

Why does raw qubit count mislead?

Raw qubit count misleads because it measures only one dimension of a machine, its width, while a useful computation also requires depth, and depth is limited by something the qubit count does not reveal: the error rate. A cryptographic attack, and indeed almost any valuable quantum algorithm, is a deep sequence of operations, and a single uncorrected error partway through corrupts the result. A machine with a large number of noisy qubits cannot run a deep circuit, because the errors accumulate faster than the computation progresses, so its enormous width buys nothing beyond a shallow circuit’s worth of computation.

That is why a qubit-count headline can rise while the machine’s real capability stands still. Adding qubits without lowering the error rate widens a machine that still cannot run a deeper circuit, so the number that matters, the depth it can sustain, does not move. Quantum volume was built precisely to expose that gap. Because it caps depth at the machine’s error rate and ties the score to both width and depth at once, a vendor cannot inflate it by adding noisy qubits, and a rising quantum volume is real evidence that the whole system improved. The original paper measured values as high as 16 on the state-of-the-art transmon devices of its day, a reminder of how modest real usable depth was even as qubit counts climbed.

Source: Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta, “Validating quantum computers using randomized model circuits,” Physical Review A 100, 032328, 2019, arXiv:1811.12926.

What exactly does quantum volume measure?

Quantum volume rolls several distinct properties of a machine into one figure, which is both its strength and the reason to understand what sits inside it. The properties it captures:

1. Qubit count (width). More qubits raise the ceiling on the circuit size, but only if the other properties keep pace.
2. Gate error rate (fidelity). Cleaner gates let the machine run deeper before errors overwhelm the output, and low fidelity caps the score no matter how many qubits there are.
3. Connectivity. If any qubit can interact with any other, circuits compile efficiently; if qubits only reach their neighbors, extra operations are needed to move information around, which adds error and lowers the achievable depth.
4. Gate set and compilation. A richer set of calibrated gates and a good circuit-rewriting toolchain reduce the operations needed, which raises the score.

Source: Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, Jay M. Gambetta, “Validating quantum computers using randomized model circuits,” Physical Review A 100, 032328, 2019, arXiv:1811.12926.

The consequence is that two machines with very different qubit counts can post the same quantum volume, and that is the benchmark working as intended. A machine with many noisy, poorly connected qubits and a machine with fewer clean, well-connected ones can be genuinely comparable in usable capability, and quantum volume says so where a qubit count would falsely rank the first ahead. The number is a fair, holistic comparison in a way the headline count never is.

What does CLOPS measure, and why is speed separate?

CLOPS, which stands for circuit layer operations per second, measures how fast a quantum computer runs the benchmark circuits, and it exists because capability and speed are different things that both matter. Quantum volume tells you the largest circuit a machine can run correctly, but it says nothing about how many such circuits the machine executes per unit time, and a machine that runs a large circuit once an hour is far less useful than one that runs the same circuit thousands of times a second. CLOPS captures that throughput, so the pair of metrics separates “how capable” from “how fast.”

The separation matters for the cryptographic question in particular, because a real attack is not one circuit but an enormous, deep computation that has to complete before decoherence and drift accumulate. Speed feeds directly into whether the whole run finishes in a tolerable time, which is why the resource estimates for breaking RSA quote a runtime alongside a qubit count. Reading capability and speed as separate axes keeps you from the twin errors of assuming a fast machine is capable or a capable machine is fast. Both benchmarks together give a fuller picture than either alone, and neither is captured by a qubit count.

How do these benchmarks relate to the quantum threat?

These benchmarks describe the machines of the NISQ era, the current period of noisy, intermediate-scale quantum computers without full error correction, and reading them correctly is what keeps a rising benchmark from being misread as a cryptographic threat. Quantum volume and CLOPS measure how well a machine runs modest circuits without error correction, which is a genuine and important axis of progress. A cryptographically relevant quantum computer lives on a different axis entirely, because it needs error-corrected logical qubits running a circuit billions of operations deep, far beyond anything a NISQ benchmark reaches.

So a doubling of quantum volume is real progress and still says nothing about whether cryptography is at risk, because the benchmark tops out well short of the depth a Shor’s attack requires. The useful way to hold both facts is to treat quantum volume and CLOPS as the right measures for judging NISQ-era machines against each other, and to switch to a different scorecard, logical qubit count, gate fidelity below the error-correction threshold, and demonstrated error correction, when the question is cryptographic risk. Confusing the two scorecards is the single most common way a benchmark headline gets over-read, and separating them is the core move in How to Tell Real Quantum Progress From Hype.

Common misconceptions

• “More qubits always means a more powerful quantum computer.” Qubit count is width only, and a machine’s usable depth is capped by its error rate. Quantum volume exists precisely because adding noisy qubits can leave real capability unchanged.
• “Quantum volume is just another name for qubit count.” It forces circuit width and depth to be equal, so it captures error rate and connectivity too. A machine cannot raise its quantum volume by adding qubits it cannot run deeper circuits on.
• “A high quantum volume means cryptography is at risk.” Quantum volume measures NISQ-era machines without error correction and tops out far below the depth a cryptographic attack needs. It is progress on one axis, not proximity to a CRQC.
• “Quantum volume and speed are the same metric.” They are separate. Quantum volume measures the largest circuit a machine runs correctly, while CLOPS measures how fast it runs those circuits, and a machine can be capable but slow or fast but limited.
• “Two machines with the same quantum volume must have the same number of qubits.” They need not. A machine with many noisy qubits and one with fewer clean ones can share a quantum volume, which is the benchmark giving an honest comparison a qubit count would distort.

Questions people ask

What is quantum volume in plain terms? It is a single number for how capable a quantum computer is, defined as the largest square random circuit, equal in width and depth, that the machine can run and still get right. Because depth is limited by the error rate, it captures fidelity and connectivity rather than qubit count alone (arXiv:1811.12926).

Why are raw qubit counts a poor measure? Because qubit count is width, and a useful computation needs depth, which the error rate limits. A machine with many noisy qubits cannot run a deep circuit, so a large count can hide poor real capability. Quantum volume ties the score to both width and depth to expose that gap.

What is CLOPS? Circuit layer operations per second, a benchmark for how fast a machine runs the circuits quantum volume measures. It tracks speed separately from capability, because a capable-but-slow machine and a fast-but-limited one are different, and a cryptographic attack needs both capability and speed to finish in tolerable time.

Does a rising quantum volume mean a CRQC is near? No. Quantum volume measures NISQ-era machines without error correction and tops out far below the depth a cryptographic attack needs. It is genuine progress, but a CRQC is judged on logical qubits, fidelity below the error-correction threshold, and demonstrated error correction, which are a different scorecard.

Can two machines with different qubit counts have the same quantum volume? Yes, and that is the benchmark working correctly. A machine with many noisy, poorly connected qubits and one with fewer clean, well-connected ones can be genuinely comparable in usable capability, and quantum volume reflects that where a qubit count would not.

How should I read a benchmark headline? Ask which axis it measures. Quantum volume and CLOPS judge NISQ-era capability and speed, and they are the right tools for comparing today’s machines. For cryptographic risk, switch to logical qubit count, gate fidelity below the threshold, and demonstrated error correction, and treat the two scorecards as separate (How to Tell Real Quantum Progress From Hype).

Last verified 2026-07-12 · Maintained by Addie LaMarr, LaMarr Labs.