Proposed companion to Clifford Volume that scores a device by the largest random free-fermion circuit it executes faithfully, verified scalably through Majorana-mode expectation values.
Free Fermion Volume (FFV) is the proposed companion of Clifford Volume: the same volumetric, classically verifiable scoring idea applied to random free-fermion (matchgate) circuits instead of Clifford circuits. Both were introduced in the same December 2025 paper by Portik, Kálmán, Monz and Zimborás within the EU Quantum Flagship’s benchmarking work. FFV remains a proposal: the protocol is fully specified and implemented, but no hardware-measured FFV score had been published as of July 2026, and unlike Clifford Volume it is not among the four core EU Quantum Flagship KPIs.
How it works
Random free-fermion circuits (random SO(2n) rotations of the device’s Majorana modes, compiled into Givens rotations under the Jordan–Wigner mapping) are run at width n. Free-fermion dynamics are efficiently classically simulable, so the ideal transformation of every Majorana operator is known exactly; the test checks that measured Majorana-operator expectation values match it, requiring parallel combinations to stay above a 1/e-style threshold while orthogonal combinations stay near zero. The score is the largest n passed, reported as the raw qubit count rather than 2^n.
Strengths and limitations
Like Clifford Volume, FFV keeps verification scalable to any width, and the pair are complementary: at fixed width, free-fermion circuits probe shallower depths and different connectivity sensitivity than Clifford circuits. Because matchgate circuits are classically simulable, a high FFV certifies faithful execution rather than quantum advantage. Watch the details: the authors write both “Free Fermion Volume” and “Free-Fermion Volume”; the score of 34 reported on Quantinuum’s H2-1 is a Clifford Volume, sometimes misattributed to both benchmarks; and FFV is a whole-device test, distinct from component-level matchgate benchmarking protocols.
Notable results
Simulation-only so far: the introducing paper validates FFV with noise-model simulations on a virtual backend, and an open-source implementation (freefermion_volume_benchmark) ships in the Apache-2.0 EQCB suite.