Typicality of superpolynomial quantum advantages beyond known cases

Establish whether superpolynomial quantum advantages, beyond random circuit sampling and factoring-based tasks, hold for typical instances under natural input distributions rather than only in worst-case scenarios.

Background

The authors stress the practical importance of average‑case (typical) performance over worst‑case separations. While some problems, such as random circuit sampling and discrete logarithm/factoring, have compelling evidence for typical hardness, many other proposed superpolynomial quantum advantages lack established average‑case hardness.

They explicitly note that, at present, most superpolynomial quantum advantages have not been shown to be typical, motivating the need to identify further problems and tools that demonstrate average‑case quantum advantages relevant to real‑world instances.