Clifford Volume and Free Fermion Volume: Complementary Scalable Benchmarks for Quantum Computers

TL;DR

This paper introduces two scalable, platform-independent volumetric benchmarks, Clifford Volume and Free Fermion Volume, for quantifying quantum computational capacity in a verifiable manner, applicable across different hardware platforms.

Contribution

It proposes two novel, classically verifiable volumetric benchmarks based on Clifford and free fermion operations, suitable for cross-platform quantum hardware comparison.

Findings

Benchmarks are efficient to simulate classically for verification.

Experimental validation achieved a Clifford Volume of 34 on Quantinuum's H2-1.

Framework enables fair, scalable comparison of quantum devices.

Abstract

As quantum computing advances toward the late-NISQ and early fault-tolerant eras, scalable and platform-independent benchmarks are essential for quantifying computational capacity in a classically verifiable manner. We introduce two volumetric benchmarks, Clifford Volume and Free Fermion Volume, that assess quantum hardware by testing the execution of random Clifford and free fermion operations. These two groups of unitaries possess a combination of properties that make them ideal for benchmarking: (i) each is individually efficient to simulate classically, enabling verification at scale; (ii) together they form a universal gate set; (iii) they serve as essential algorithmic primitives in practical applications (including shadow tomography and quantum chemistry); and (iv) their definitions are formulated abstractly, without explicit reference to hardware-specific features such as qubit connectivity or native gate sets. This framework thus enables scalable and fair cross-platform comparisons and tracks meaningful computational advancement. We demonstrate the practical feasibility of these benchmarks through extensive numerical simulations across realistic noise parameters and through experimental validation on Quantinuum's H2-1 trapped-ion quantum computer, which achieves a Clifford Volume of 34.