Quantum volume

Quantum volume addresses the inadequacy of using raw qubit count alone to gauge a quantum computer’s power. A device with many qubits but high error rates or short coherence times may be less capable than a smaller, more coherent system. The metric was proposed by IBM researchers in a 2018 paper to provide a holistic benchmark.² It is defined as the maximum depth d of a circuit with d qubits (i.e., a square circuit of width d and depth d) that can be executed with a success probability above a threshold (typically 2/3). The quantum volume is then reported as 2^d. This design weights the effects of gate errors, measurement errors, and crosstalk uniformly, making it a robust indicator of a device’s practical ability to run complex algorithms.

Quantum volume depends on several hardware parameters: number of qubits, gate fidelities, coherence times (T₁ and T₂), and connectivity (the ability to perform two-qubit gates between arbitrary pairs). The calculation uses randomized benchmarking of model circuits that are randomly generated but have a known ideal output. The largest square circuit that yields a statistically significant success probability determines the quantum volume.² For example, if a device can reliably execute a 7-qubit, 7-gate-deep circuit, its quantum volume is 2⁷ = 128. The metric is device-agnostic and can be applied to any quantum computing platform, including superconducting qubits, trapped ions, and photonic systems.

IBM has published a steady progression of quantum volume milestones on its roadmap. The first demonstration in 2018 achieved a quantum volume of 8 (2³). Subsequent generations reached 16 (2019), 32 (2020), 64 (2021), and 128 (2022) on the Eagle processor. In 2023, IBM announced plans to achieve quantum volume 256 and beyond. Other companies, such as Honeywell (now Quantinuum), have reported quantum volumes exceeding 256 for their trapped-ion systems, using a similar but not identical methodology.³ These milestones are often used as indicators of progress toward fault-tolerant quantum computing, though they remain subject to debate about comparability across different platforms.

Quantum volume has been criticized for not capturing all aspects of quantum computer performance. It does not account for the speed of gate operations, qubit readout times, or the ability to perform error correction. Some researchers argue that the metric is biased toward hardware with low gate error rates and high connectivity, while ignoring overheads such as compilation times and classical communication. Additionally, the square-circuit assumption may not reflect real-world algorithms, which often have asymmetric width and depth. The National Academies of Sciences have noted that no single metric is sufficient, and quantum volume must be complemented by other benchmarks such as circuit layer operations per second (CLOPS) and quantum error correction thresholds.

Alternative definitions: The term “quantum volume” has also been used informally earlier, but the rigorous definition was popularized by IBM. Noise robustness: The metric naturally incorporates the effect of noise because the success probability drops as circuit size increases. Edge case: A device with perfect qubits but poor connectivity may have a lower quantum volume than a smaller, fully connected chip. Open-source implementation: The qiskit-ignis library (now part of Qiskit) provides tools to estimate quantum volume experimentally. Cross-platform comparison: Quantum volume values from different hardware types are not directly comparable without standardizing the benchmarking protocol, a topic of active research in the quantum computing community.

Qubit

The basic unit of quantum information, analogous to a classical bit but capable of existing in a superposition of states.

Gate error rate

The probability that a quantum gate operation introduces an error, typically measured via randomized benchmarking.

Coherence time

The duration over which a qubit retains its quantum state before decoherence occurs, characterized by T1 and T2 times.

Circuit depth

The number of sequential layers of quantum gates in a circuit; a measure of the circuit's temporal length.

Quantum volume

A metric defined as 2^d where d is the maximum depth of a square circuit (width = depth) that a quantum computer can execute with high success probability.