Classical multipass tradeoff for HOPI

Determine whether classical streaming algorithms can match the inverse dependence on the number of passes in the paper’s classical lower bound for Hermite optimal polynomial intersection, particularly when their memory is comparable to the quantum space budget.

Background

The paper proves a classical lower bound relating approximation quality, field and derivative parameters, memory, and the number of passes, and describes the resulting tradeoff as essentially optimal on the one-pass side. It leaves unresolved whether classical algorithms can attain the inverse-pass dependence suggested by the lower bound when allowed multiple passes and memory close to the quantum algorithm’s budget.

References

Can algorithms match the inverse dependence on the number of passes in \Cref{thm:classical-lower-summary}, particularly when their memory is comparable to the quantum budget?

— Exponential quantum advantages for decoded quantum interferometry in the streaming setting  (2610.01902 - Wu et al., 1 Oct 2026) in Section 1, subsection “Open problems and AI disclosure”

Can they achieve the approximation--space frontier without exponential-time postprocessing?

— Exponential quantum advantages for decoded quantum interferometry in the streaming setting  (2610.01902 - Wu et al., 1 Oct 2026) in Section 1, subsection “Open problems and AI disclosure”