Quantum Multiple Rotation Averaging

TL;DR

This paper introduces IQARS, a quantum annealing-based algorithm for multiple rotation averaging that improves accuracy over classical methods by reformulating the problem to leverage quantum hardware advantages.

Contribution

IQARS is the first method to reformulate MRA as a sequence of quantum-executable non-convex sub-problems, removing reliance on convex relaxations and better preserving rotation manifold geometry.

Findings

IQARS achieves approximately 12% higher accuracy than classical methods on D-Wave annealers.

Current quantum annealers support limited problem scales but show promising improvements.

IQARS demonstrates the potential of quantum annealing for complex 3D vision problems.

Abstract

Multiple rotation averaging (MRA) is a fundamental optimization problem in 3D vision and robotics that aims to recover globally consistent absolute rotations from noisy relative measurements. Established classical methods, such as L1-IRLS and Shonan, face limitations including local minima susceptibility and reliance on convex relaxations that fail to preserve the exact manifold geometry, leading to reduced accuracy in high-noise scenarios. We introduce IQARS (Iterative Quantum Annealing for Rotation Synchronization), the first algorithm that reformulates MRA as a sequence of local quadratic non-convex sub-problems executable on quantum annealers after binarization, to leverage inherent hardware advantages. IQARS removes convex relaxation dependence and better preserves non-Euclidean rotation manifold geometry while leveraging quantum tunneling and parallelism for efficient solution space exploration. We evaluate IQARS's performance on synthetic and real-world datasets. While current annealers remain in their nascent phase and only support solving problems of limited scale with constrained performance, we observed that IQARS on D-Wave annealers can already achieve ca. 12% higher accuracy than Shonan, i.e., the best-performing classical method evaluated empirically.