A Quantum Computational Approach to Correspondence Problems on Point Sets

TL;DR

This paper introduces a new quantum algorithm for solving correspondence problems on point sets, leveraging adiabatic quantum computing to achieve efficient state preparation and demonstrate practical applications in computer vision.

Contribution

The paper develops a novel quantum algorithm tailored for correspondence problems, with subquadratic complexity and experimental validation on simulated sampling.

Findings

Successful point set alignment using the quantum algorithm

Subquadratic complexity in state preparation

Analysis of solution differences and energy values

Abstract

Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review AQC and derive a new algorithm for correspondence problems on point sets suitable for execution on AQC. Our algorithm has a subquadratic computational complexity of the state preparation. Examples of successful transformation estimation and point set alignment by simulated sampling are shown in the systematic experimental evaluation. Finally, we analyse the differences in the solutions and the corresponding energy values.