Small-space quantum algorithm for exact optimization

Determine whether finding an optimal polynomial for the streaming Hermite optimal polynomial intersection problem requires more quantum memory, or construct a one-pass quantum algorithm that finds an optimal polynomial using small space with unrestricted postprocessing.

Background

The paper establishes approximate quantum advantages for streaming HOPI, including approximation ratios arbitrarily close to one at the cost of exponential postprocessing. Exact optimization is not resolved. The stated question concerns whether achieving the true optimum imposes an additional quantum-memory requirement, even when postprocessing time is unrestricted.

References

Exact optimization raises a separate question: does finding an optimal polynomial require more quantum memory, or can a one-pass algorithm achieve it in small space with unrestricted 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”