Pre-asymptotic advantage for non-Sobol low-discrepancy sequences and uniform grids

Investigate whether a pre-asymptotic quantum query advantage can be obtained by combining quantum amplitude estimation with low-discrepancy sequences other than Sobol' sequences and with the vanilla Riemannian uniform grid.

Background

The paper develops and analyzes Quantum quasi-Monte Carlo using Sobol' sequences, showing a possible finite-query advantage window relative to classical quasi-Monte Carlo under an empirical model for the Sobol quality parameter. The analysis is therefore specific to the chosen point construction and does not establish whether the same phenomenon occurs for other deterministic point sets.

The authors explicitly leave open the exploration of this advantage for other low-discrepancy sequences and for the vanilla Riemannian uniform grid. Resolving this would clarify how broadly the proposed quantum quasi-Monte Carlo mechanism applies beyond Sobol' constructions.