Quantum Multiple Rotation Averaging

2026-02-10

AI Summary

This work addresses the problem of multiple rotation averaging (MRA) in 3D vision and robotics—recovering globally consistent absolute rotations from noisy relative measurements—and proposes IQARS, a novel algorithm that, for the first time, adapts MRA to quantum annealing architectures. By iteratively decomposing the problem into local quadratic non-convex subproblems and integrating binarization, manifold geometry preservation, and non-convex optimization, IQARS efficiently solves MRA on a D-Wave quantum annealer while circumventing the limitations of conventional convex relaxations. Experimental results demonstrate that IQARS achieves approximately 12% higher accuracy than Shonan Averaging, the current state-of-the-art classical method, on both synthetic and real-world datasets.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

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.

Problem

• Multiple Rotation Averaging
• Rotation Synchronization
• 3D Vision
• Non-convex Optimization
• Manifold Geometry

Innovation

• quantum annealing
• rotation synchronization
• non-convex optimization
• manifold geometry
• 3D vision