Benchmarking quantum simulation at scale

Establishing a rigorous quantum advantage remains difficult because verifying the correctness of classically intractable quantum simulations is often as computationally expensive as the simulation itself. This paper addresses the challenge of verifying large-scale quantum simulations of non-equilibrium dynamics by identifying a specific class of quantum states that are both classically simulable and representative of typical, non-simulable dynamics.

The researchers utilize stabilizer scars—a subset of quantum many-body scars (QMBS)—which possess a structure that enables efficient classical computation and direct fidelity estimation (DFE). By embedding these scar states within a larger Hilbert space, the authors show that the fidelity of quantum-simulated scar states can be measured efficiently using a polynomial number of observables and shots. They then argue, through both analytical bounds and numerical simulations, that under local depolarizing noise, the fidelity of these scar states serves as a proxy for the fidelity of typical, classically intractable states.

The study establishes that for models hosting stabilizer scars, the fidelity of non-classically simulable states is approximately equal to that of the scar states under local noise. Numerical simulations using Markov Chain Monte Carlo (MCMC) sampling demonstrate that the fidelity estimation protocol is efficient, with costs scaling polynomially with the system size. The authors show that the difference in fidelity between scar and non-scar states vanishes asymptotically as the system size increases or as the noise level decreases, providing a scalable benchmark for quantum advantage experiments.