A Hybrid Quantum-Classical Algorithm for Robust Fitting

TL;DR

This paper introduces a hybrid quantum-classical algorithm for robust geometric model fitting that provides error bounds and improves over heuristics, demonstrating practical quantum computing applications in computer vision.

Contribution

It proposes a novel formulation for robust fitting that combines integer programming with quantum annealing to achieve global solutions or error bounds.

Findings

Successfully tested on actual quantum hardware (D-Wave Advantage)

Provides tighter error bounds compared to classical heuristics

Demonstrates practical quantum computing application in computer vision

Abstract

Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is therefore critical to develop novel approaches that can bridge the gap between exact solutions that are costly, and fast heuristics that offer no quality assurances. In this paper, we propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs and terminates with a global solution or an error bound. The combinatorial subproblems are amenable to a quantum annealer, which helps to tighten the bound efficiently. While our usage of quantum computing does not surmount the fundamental intractability of robust fitting, by providing error bounds our algorithm is a practical improvement over randomised heuristics. Moreover, our work represents a concrete application of quantum computing in computer vision. We present results obtained using an actual quantum computer (D-Wave Advantage) and via simulation. Source code: https://github.com/dadung/HQC-robust-fitting