Optimality of hidden-rotation learning for the rotated square well

Determine whether learning the hidden rotation is an optimal classical strategy for solving the Rotated Square Well problem.

Background

The paper analyzes two classical approaches to the Rotated Square Well (RSW) problem: random-ray tomography, which reconstructs the hidden slab arrangement in Θ(d² log d) queries, and an adaptive random walk that does not explicitly learn the hidden rotation and has a modeled Θ(d³/log d) query complexity. The authors observe that rotation learning is the more efficient of the two strategies considered.

The information-theoretic lower bound established in the paper applies to classical algorithms that reconstruct the hidden rotation, rather than to every possible classical optimization algorithm. Consequently, whether every asymptotically optimal classical strategy must learn the hidden rotation remains unresolved and is stated as a conjecture.

References

Hence, this suggests that learning the rotation may indeed be the optimal strategy for this problem, which we leave open as a conjecture.

— CV-QAOA: Efficient Low-Depth Quantum Optimization of Continuous Variables  (2610.06815 - Bharadwaj et al., 5 Oct 2026) in Section 1, Introduction; paragraph beginning “On the classical side, we give an information-theoretic lower bound”