TL;DR
- Qubit count is the headline number, but it does not tell you how much real computation a quantum machine can finish before noise wins.
- Quantum Volume (QV) is a single whole-system score that folds together qubit number, gate fidelity, connectivity, and measurement quality into one figure.
- QV is measured, not claimed: you run random square circuits, compare the output against an ideal classical simulation, and check whether the heavy output probability clears a fixed statistical bar.
- A higher QV means the machine can run deeper and wider circuits that still carry signal, which is what actually matters for algorithms.
- Quantinuum has led this benchmark for years and recently reported a QV of 2^25 (about 33.5 million) on its 56-qubit System Model H2, a figure you can verify from its own disclosures and third-party coverage.
If you only remember one thing: a 56-qubit machine with high QV can out-compute a 100-qubit machine with low QV, because volume measures usable work, not inventory.
Why is qubit count a misleading headline?
Ask most people how to compare two quantum computers and they will reach for qubit count. It is concrete, it fits in a headline, and it goes up over time. The problem is that a qubit is only useful for as long as it holds its state and interacts cleanly with its neighbors.
Three things quietly erode that usefulness:
- Gate error. Every one-qubit and two-qubit operation has a small probability of corrupting the state. Errors compound as circuits get deeper.
- Connectivity. If qubit A cannot talk directly to qubit D, the compiler inserts extra swap operations to move information around, and each swap is more error exposure.
- Readout and preparation error. Measuring and initializing qubits is itself imperfect.
A machine can have many qubits and still be unable to run a circuit of meaningful depth, because the error budget is spent long before the computation finishes. Counting qubits is like rating a warehouse by the number of shelves while ignoring whether anything stays on them. This is exactly the gap that a measurement-first benchmark is designed to close.
What is Quantum Volume in one sentence?
Quantum Volume is the size of the largest random square circuit that a quantum computer can run and still produce an output that is statistically closer to the ideal result than to noise.
"Square" is the key word. A square circuit uses the same number of qubits and layers of gates. If a machine can reliably run a circuit on m qubits with m layers of random two-qubit gates, then its Quantum Volume is 2 raised to the power of m. The exponent m is sometimes called the achievable circuit width and depth.
Because QV scales as a power of two, the numbers get large fast. A QV of 2^10 is 1,024. A QV of 2^20 is about one million. A QV of 2^25 is about 33.5 million. The jumps look dramatic, but each extra power of two represents one more qubit successfully folded into a reliable square circuit, which is genuinely hard to win.
How is the quantum volume formula actually computed?
Here is the worked logic, step by step, without hiding the statistics.
Step 1: Build random square circuits
For a candidate width m, you generate many random circuits on m qubits with m layers. Each layer pairs qubits at random and applies random two-qubit unitaries. These circuits have no structure to exploit, which is the point: they stress the whole system evenly.
Step 2: Simulate the ideal output
For each random circuit, you compute the ideal output distribution on a classical computer. For every possible output bitstring you get an ideal probability. You then sort these probabilities and find the median. Any bitstring whose ideal probability is above the median is called a heavy output.
Step 3: Run the circuit on real hardware and measure heavy outputs
You run the same circuit many times on the actual quantum machine and record how often it returns a heavy output. That fraction is the heavy output probability, or HOP.
Step 4: Apply the pass or fail test
For a perfect machine, random square circuits produce heavy outputs with probability near 0.85. For pure noise, the HOP falls toward 0.5. The accepted bar is that the average HOP across the circuit set must exceed 2/3, and it must clear that bar with two-sigma statistical confidence, meaning the result is not a lucky fluctuation.
Step 5: Find the largest passing width
You find the largest m for which the machine passes. The Quantum Volume is then:
QV = 2 ** m_max
# worked example
m_max = 25 # largest square-circuit width that passes HOP > 2/3 at 2-sigma
QV = 2 ** m_max # 33,554,432 (reported as 2^25)
print(QV) # 33554432
A short illustration of the pass check itself:
import statistics
def passes_qv(hops, threshold=2/3):
# hops: list of per-circuit heavy output probabilities
mean = statistics.mean(hops)
sigma = statistics.pstdev(hops) / (len(hops) ** 0.5) # standard error of the mean
lower_2sigma = mean - 2 * sigma
return lower_2sigma > threshold, mean, lower_2sigma
ok, mean, bound = passes_qv([0.71, 0.69, 0.70, 0.72, 0.68])
print(ok, round(mean, 3), round(bound, 3))
The elegance is that a single scalar now reflects qubit count, two-qubit fidelity, connectivity overhead, and readout quality at the same time. You cannot fake it by adding idle qubits, because idle qubits that cannot join a reliable square circuit do not raise m.
Why does Quantum Volume matter more than qubit count?
QV answers the question an algorithm designer actually cares about: how deep and wide can I go before my results dissolve into noise? That is the operational ceiling.
Consider two machines:
- Machine A: 100 qubits, modest fidelity, limited connectivity. It may only pass square circuits up to width 10, so QV is about 1,024.
- Machine B: 56 qubits, high fidelity, all-to-all connectivity. It may pass square circuits up to width 25, so QV is about 33.5 million.
Machine B can run far larger reliable computations despite having fewer qubits. For near-term algorithms, where every extra layer of depth is precious, Machine B is the more capable device by a wide margin. This is why serious buyers and researchers read QV, error rates, and clock speed together rather than fixating on a single qubit tally.
What did Quantinuum actually report, and can you verify it?
Quantinuum has led the Quantum Volume benchmark for several years, roughly doubling its score on a regular cadence. According to the company's own disclosures and independent coverage, its 56-qubit trapped-ion System Model H2 reached a Quantum Volume of 2^25, which is 33,554,432. Reports describe this as a step up from an earlier 2^23 (about 8 million) figure the same year, and note that the H2 system uses all-to-all connectivity, which reduces the swap overhead that hurts fixed-layout hardware.
Two measurement notes keep this honest:
- The score is a system-level claim validated by the HOP test above, not a marketing abstraction.
- Independent outlets reported the same 2^25 figure, which is the kind of corroboration a measurement-first reader should look for before repeating a number.
Where a specific secondary detail could not be independently pinned down, treat it as approximate. The core figure to anchor on is QV equals 2^25 on a 56-qubit H2 system, which is well documented.
How should you read any quantum benchmark claim?
A short measurement checklist:
- Is the metric whole-system or component-level? QV is whole-system. A single two-qubit fidelity number is component-level and tells you less on its own.
- Was it validated against an ideal reference? QV compares to classical simulation. That is why QV itself stops being measurable once machines pass the size that classical computers can still simulate, which pushes the field toward newer benchmarks.
- Is there a statistical bar? QV requires two-sigma confidence over the 2/3 threshold. Claims without error bars deserve caution.
- Is it reproducible or corroborated? Prefer numbers that appear in primary disclosures and independent coverage.
FAQ
Is Quantum Volume the only benchmark that matters?
No. QV is an excellent single-number summary for near-term machines, but it saturates once circuits grow beyond classical simulation. The field now also tracks metrics like circuit layer operations per second (CLOPS) for speed, algorithmic qubit counts, and application-level benchmarks. Read them together.
Does a higher Quantum Volume always mean a better computer for my problem?
Usually it means more usable computational room, but the right machine depends on your workload. Some problems care more about speed or specific gate sets. QV is a strong general indicator, not a guarantee for every algorithm.
Why is Quantum Volume expressed as a power of two?
Because it reports the size of the state space of the largest reliable square circuit. A circuit on m qubits spans 2^m possible outcomes, so QV equals 2^m. Each extra reliable qubit doubles the score, which is why progress looks like a staircase of powers of two.
What is the heavy output probability threshold and why 2/3?
The 2/3 bar sits between the noise floor near 0.5 and the ideal value near 0.85. Passing it with two-sigma confidence shows the machine is meaningfully closer to ideal behavior than to random noise, which is the minimum evidence that the circuit carried real signal.
Can a vendor inflate Quantum Volume by adding qubits?
Not easily. Idle or low-fidelity qubits that cannot participate in a reliable square circuit do not increase the achievable width m, so they do not raise QV. That resistance to padding is a big part of why the benchmark earned trust.
Where can I find the raw data behind a QV claim?
Start with the vendor's technical disclosure, then look for independent reporting and any published circuit sets or HOP distributions. Corroboration across primary and secondary sources is the measurement-first standard.
Closing note
Quantum Volume is a reminder that in computing, as in science, the number that fits on a slide is rarely the number that governs real capability. Measure the whole system, hold it to a statistical bar, and prefer scores you can verify. That discipline is exactly how you separate a machine that looks impressive from one that can actually finish the job.
Disclosure: QuantID is a technology alliance partner of VIDRAFT, which was recently selected to use Quantinuum's platform. This article is written from a neutral, measurement-first perspective and relies on publicly reported figures.
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