Quantum Complexity of Multidimensional-Herringbone Instances

Determine the quantum query complexity of the multidimensional-herringbone instances introduced by Brânzei et al., and establish whether their Ω(k log² n / log k) classical lower-bound construction admits a quantum speedup.

Background

The multidimensional-herringbone family gives a classical lower bound of Ω(k log² n / log k) for Tarski fixed-point finding. The paper does not determine the corresponding quantum query complexity.

The authors identify a possible route toward a quantum improvement: a result used in the classical analysis allows a spine vertex of a prescribed ℓ₁-norm to be found using O(k log n) queries, suggesting that a method analogous to the wildcard-search approach developed in the appendix might yield a quadratic quantum speedup.