Quantum Volume and Device Benchmarks

Understand how quantum processors are benchmarked and compared.

Quantum Volume and Device Benchmarks

Comparing quantum computers is non-trivial. A device with more qubits is not necessarily better: gate fidelity, connectivity, and coherence all matter. IBM introduced Quantum Volume (QV) as a holistic benchmark that captures all these factors.

Quantum Volume Definition

QV is the largest random square circuit of depth n and width n that a quantum computer can execute with > 2/3 success probability (heavy output generation). A device achieves $Q V = 2^{n}$ if it can run n-qubit, n-depth random circuits reliably.

The QV test:

1.Generate 100+ random n-qubit circuits with random SU(4) gates
2.Classically compute the ideal output distribution
3.Run each circuit on hardware
4.Measure heavy output generation probability: P(heavy outputs) > 2/3
5.If yes: $Q V \geq 2^{n}$ . Try larger n.

Why this matters: Random circuits stress-test everything simultaneously:

•Gate fidelity (errors in each gate)
•Qubit connectivity (routing overhead from random gates)
•Crosstalk (errors induced by neighboring qubits)
•Measurement fidelity (readout errors)

Quantum Volume Progress

Year	Device	Quantum Volume
2019	IBM Q 5-qubit	8 ( $Q V = 2^{3}$ )
2020	IBM Falcon r4	64 ( $Q V = 2^{6}$ )
2021	IBM Falcon (later revision)	128 ( $Q V = 2^{7}$ )
2022	Quantinuum H1	8192 ( $Q V = 2^{13}$ )
2023	Quantinuum H2	65536 ( $Q V = 2^{16}$ )

Note: Quantinuum's trapped ion systems have dramatically higher QV than IBM's superconducting systems, despite having fewer total qubits. This is because QV measures quality, not quantity.

Limitations of Quantum Volume

QV has important limitations as a benchmark:

1.Application-specific performance may differ. A device with high QV is generally good, but the best device for your specific algorithm depends on connectivity, gate set, and circuit structure.

2.Logarithmic scaling. Going from QV=128 to QV=256 requires doubling all performance metrics simultaneously, making progress hard to see linearly.

This is the opening of the lesson. The full walkthrough, the interactive circuit, and the graded challenge continue inside myqubit.

How this lesson works

A guided reading lesson with interactive knowledge checks. Concepts are explained step by step with circuit diagrams and runnable examples, and you confirm understanding before moving on.

Part of: Quantum Hardware & NISQ

Explore the physics of real quantum computers, understand noise, and learn near-term algorithms designed for today's noisy hardware.

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