Improved Accreditation of Analogue Quantum Simulation and Establishing Quantum Advantage

We improve on the results of [A. Jackson et al. Proc. Natl. Acad. Sci. U.S.A 121 (6). 2024] on the verification of analogue quantum simulators by eliminating the use of universal Hamiltonians, removing the need for two-qubit gates, and no longer assuming error is represented by identical maps across simulations. This new protocol better reflects the reality of extant analogue simulators. It integrates well with recent complexity theoretic results, leading to a near-term feasible simulation-based route to establishing quantum advantage.