What Is Quantum Volume? A Clear Explanation of the Quantum Computing Benchmark

What Does Quantum Volume Actually Measure?

Quantum Volume is a whole-system benchmark for gate-based quantum computers. It was introduced to provide a more informative measure than physical qubit count alone.

A processor may contain many qubits but still be unable to perform large computations if its operations are inaccurate, its qubits have limited connectivity, measurements are unreliable or errors accumulate rapidly. Conversely, a smaller processor with high-quality operations may successfully run more demanding circuits.

Quantum Volume tests several parts of the system together:

The benchmark therefore evaluates the combined hardware-and-software system rather than an isolated component. The original Quantum Volume paper describes it as the largest random circuit with equal width and depth that a machine can implement successfully.

How Is the Quantum Volume Test Performed?

The benchmark uses randomly generated model circuits. For a test size of m, the circuit contains:

m active qubits m layers of operations Random pairings of the qubits in each layer Random two-qubit operations drawn from the mathematical group SU(4)

The benchmark is therefore described as a square circuit because its width and depth are equal.

1. 1

   Step 1: Generate random circuits

   Many random circuits are produced for a chosen width and depth. These circuits are intentionally generic rather than designed to solve one useful commercial problem.

2. 2

   Step 2: Calculate the ideal results

   Each circuit is simulated classically to determine its ideal output probability distribution. The possible output bit strings are then divided using the median ideal probability. Outputs whose ideal probabilities are above the median are called heavy outputs.

3. 3

   Step 3: Compile the circuit

   The abstract benchmark circuit must be translated into operations supported by the physical machine. The compiler may: Select the strongest available qubits Choose an efficient qubit layout Rewrite gates into native hardware operations Reduce routing operations Optimise the circuit for the device’s connectivity Compiler performance is intentionally part of the benchmark.

4. 4

   Step 4: Run the circuit repeatedly

   The compiled circuit is executed on the quantum processor, producing measured bit strings.

5. 5

   Step 5: Measure heavy-output probability

   The benchmark checks how often the processor produces outputs belonging to the ideal circuit’s heavy-output set. A test passes when the average heavy-output probability is greater than two-thirds with the required statistical confidence. The process is repeated at increasing circuit sizes until the system can no longer pass.

How Is a Quantum Volume Score Calculated?

Quantum Volume is normally expressed as:

Quantum Volume = 2ᵐ

Here, m is the largest square circuit size that successfully passes the benchmark.

What does Quantum Volume 1,024 mean?

It means that the tested system successfully completed the Quantum Volume protocol at m = 10 under the reported benchmark conditions.

It does not mean:

The processor contains 1,024 qubits It performed 1,024 quantum operations It is 1,024 times more powerful than another machine It can run every circuit involving 10 qubits It has demonstrated commercial quantum advantage It possesses fault-tolerant logical qubits

The score should always be read together with the device, test date, selected qubit subset, compilation method, number of circuits, confidence method and any optimisation or error-suppression techniques used.

What Makes Quantum Volume Increase?

Quantum Volume improves when a system can execute wider and deeper random circuits while keeping the output distribution sufficiently close to the ideal result.

Higher gate fidelity

Every imperfect operation introduces some error. Because Quantum Volume circuits contain repeated layers of two-qubit operations, even relatively small errors can accumulate quickly.

Improving two-qubit gate fidelity is therefore particularly important.

Better connectivity

If two qubits that need to interact are not physically connected, the compiler may need to move quantum information using additional operations.

These routing operations increase circuit depth and create more opportunities for errors.

Systems with flexible or all-to-all connectivity may therefore require fewer routing operations for the benchmark, although architecture-specific gate speed and fidelity still matter.

Lower crosstalk

Quantum operations should affect only their intended qubits. Crosstalk occurs when control operations unintentionally disturb neighbouring or inactive qubits.

Because Quantum Volume runs operations across multiple qubits and layers, it can expose system-level errors that may not be apparent from testing one gate at a time.

Better compilation

The same abstract random circuit can produce very different physical circuits depending on how it is compiled.

A good compiler may:

Select a higher-quality group of qubits Reduce SWAP operations Use more efficient native-gate decompositions Avoid weaker hardware connections Schedule operations to reduce unwanted interactions

This is why Quantum Volume measures the complete execution stack—not hardware quality alone. [1]

Reliable preparation and readout

The system must prepare the intended starting state and correctly measure the final state. Readout errors can reduce the observed heavy-output probability even when the circuit operations themselves are accurate.

What Quantum Volume Does—and Does Not—Tell Us

Quantum Volume is useful because it provides a standardised test that is more holistic than quoting physical qubit count or the error rate of a single gate.

It is particularly helpful for answering:

How large a demanding, generic square circuit can this hardware-and-software system execute successfully?

It does not answer every important question about quantum-computer performance.

It may test only the best qubits

It may test only the best qubits

Implementations can select the strongest connected subset of qubits available on a larger processor. A high score may therefore describe the best-performing region rather than the average quality of the entire chip.

It is a pass-or-fail benchmark

A circuit size either passes or does not pass the specified statistical threshold. This makes Quantum Volume easy to communicate, but it may hide gradual improvements that have not yet produced the next doubling of the score.

It uses one circuit shape

Quantum Volume uses square, random, highly entangling circuits. Real algorithms can have very different structures, depths, connectivity requirements and measurement patterns.

Performance on chemistry simulation, optimisation, error correction or dynamic circuits may therefore differ substantially.

Classical verification becomes difficult at scale

Identifying heavy outputs requires calculating the ideal circuit distribution classically. This becomes increasingly expensive as the number of qubits and circuit depth grow.

It should be one metric within a benchmark suite

Later benchmarking research recommends combining measures of quality, speed and scale rather than using one number as a universal ranking. Metrics such as layer fidelity were introduced partly because Quantum Volume focuses on a high-quality subset, produces a discrete result and does not directly describe performance across a large processor. [2][3]

The correct interpretation is therefore:

A higher Quantum Volume is evidence that a system successfully executed a more demanding version of this specific whole-system benchmark. It is not proof that the system is universally more powerful or more commercially useful.

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