Limits of quantum run-time advantage
Phys. Rev. Applied 25, 044084 – Published 29 April, 2026
DOI: https://doi.org/10.1103/gpsf-pn1x
Abstract
A robust definition of quantum run time is essential for assessing the performance of quantum algorithms and claims of quantum advantage. While for most classical hardware the total run time is well approximated by computation plus a weakly varying constant, on current quantum hardware a clean experimental separation between “pure computation” and “overhead” is often not justified. Consequently, conventional quantum run-time analyses that exclude substantial system-level overheads (e.g., readout, transpilation, thermalization) can lead to biased performance assessments. In this work we introduce experimentally grounded, end-to-end definitions of quantum run-time for both digital and analog quantum computers, together with a methodology for selecting strong classical baselines for quantum-classical run-time comparisons. Within this framework, we evaluate recent claims of quantum advantage in annealing- and gate-based algorithms. We examine three representative case studies. First, we revisit quantum annealing for approximate quadratic unconstrained binary optimization problems [Phys. Rev. Lett. 134, 160601 (2025)], which employs a well-motivated time-to-epsilon metric but effectively uses annealing time as a proxy for run time. Second, we analyze a restricted implementation of Simon’s problem [Phys. Rev. X 15, 021082 (2025)], where the favorable scaling in oracle calls is undisputed; however, we show that the estimated wall-clock run time of the quantum demonstration is approximately two orders of magnitude slower than a tuned classical baseline at the tested sizes. Finally, we find that the recently reported run-time advantage of the bias-field digitized counterdiabatic quantum optimization hybrid algorithm (arXiv:2505.08663) is not observed under more comprehensive benchmarking. Therefore, on current NISQ hardware, run-time-based quantum advantage has not yet been demonstrated under experimentally grounded performance metrics, and credible claims require careful time accounting, appropriate performance measures, and properly chosen classical reference implementations, as discussed in this work.
