Quantum Permutation Synchronization

TL;DR

This paper introduces QuantumSync, a quantum algorithm leveraging quantum annealing to solve permutation synchronization problems in computer vision, demonstrating the potential of quantum computers for complex discrete optimization tasks.

Contribution

It formulates permutation synchronization as a constrained QUBO problem and implements it on D-Wave quantum annealers, showing promising results for quantum optimization.

Findings

QuantumSync effectively solves permutation synchronization.

Quantum annealing guarantees high-probability global optimality.

Proof-of-concept on D-Wave demonstrates quantum advantage potential.

Abstract

We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (I) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proof-of-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems.