Q-score

Q-score is an application-level benchmark announced by Atos in December 2020 and specified by Martiel, Ayral & Allouche (Atos’s quantum business now operates as Eviden). It scores a full quantum system (hardware and software stack together) by the largest MaxCut problem it solves effectively, and it was among the first application-centric, hardware-agnostic single-number metrics.

How it works

For each candidate size n, the system solves MaxCut on 100 random Erdős–Rényi graphs G(n, 1/2) (n vertices, hence n qubits), and the average cut value C(n) is rescaled as β(n) = (C(n) − n²/8) / (λn^(3/2)): the improvement over random assignment (expected cut n²/8), in units of how an optimal solver’s improvement scales (λ = 0.178). A size passes if β(n) > β* = 0.2, and the Q-score is the largest passing n. Both reference values are analytic, so no classical simulation of the quantum run is needed and the test scales to arbitrary size. The original protocol runs QAOA with a COBYLA optimizer and 2048 shots; extensions drop that requirement to cover quantum annealers and photonic systems, and a generalized framework adds a Max-Clique variant.

Strengths and limitations

Q-score is end-to-end and genuinely cross-paradigm: gate-based, annealing, and photonic machines have all been scored. But results hinge on solver settings: under a 60-second limit, D-Wave’s 2000Q and Advantage annealers scored 70 and 140 while classical tabu-search, simulated-annealing, and hybrid solvers scored 2,300–12,500 (van der Schoot et al.), so a high Q-score alone is not evidence of quantum advantage. The threshold β* = 0.2 is explicitly arbitrary (ideal depth-1 QAOA passes at every size, giving an infinite Q-score), and since “Q-score” can denote either the original protocol or the broader framework, quoted values are comparable only under identical settings. It is unrelated to the marketing “Q Score”.

Notable results

The BACQ/MetriQs-France program (Thales, Eviden, CEA, CNRS, Teratec, LNE) uses Q-score MaxCut and Max-Clique as core KPIs in its Fast-Track QPU measurement campaign with IQM, Pasqal, Quandela, TNO, and AQT. TNO maintains a multi-backend implementation (v1.1.0, January 2024), while the original myQLM repository has been dormant since March 2023, and the annual Q-score ranking Atos announced never became a regular publication.