Replica-Based Study of Noisy XEB for Quantum Advantage Benchmarking

Debate is ongoing over the most useful metrics for assessing quantum advantage (QA), the veracity of QA claims, and how classically “spoof-able” QA metrics are. One discussion centers on measures for random circuit sampling (RCS) tasks, where the goal is sample-efficient reproduction of the chaotic statistics of ensembles of randomly-constructed quantum circuits. While the cross-entropy benchmark (XEB) — a popular metric for recent RCS QA claims — provides some indication that quantum devices are capable of performing tasks beyond the reach of classical analogues, the task remains to develop sample-efficient tools to reliably distinguish clean quantum systems, noisy quantum systems, and classical spoofers. Clearly demarcating this hierarchy would advance quantum information processing as a near-term tool and help to error-bound future RCS tests. We present a comparative study over noisy linear XEB profiles and related measures by applying a replica treatment to recast into tractable saddle point evaluations and then codifying hierarchies of subspaces. We identify noise-induced symmetry breaking and compare profiles to examine distinguishability. This paves the way for extensions to other nonlinear XEB measures as well as noisy-case comparisons to spoofers.