Feedback-based quantum optimization and its classical counterpart: quantum advantage and the power of classical algorithms

TL;DR

This paper compares feedback-based quantum optimization with its classical counterpart, demonstrating potential quantum advantages in solution quality and classical algorithms' scalability for large problems.

Contribution

It introduces the classical counterpart of feedback-based quantum optimization, enabling analysis of quantum advantage and development of higher-order classical algorithms.

Findings

Quantum algorithms can outperform classical ones in solution quality.

Classical algorithms show faster convergence than quantum algorithms.

A classical algorithm demonstrates significant scalability for large problems.

Abstract

Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin systems to discuss the possibility of quantum advantage. It also enables us to develop higher-order theory of a previously proposed classical approach to feedback-based quantum optimization. First, we compare the feedback-based algorithm for quantum optimization (FALQON) and its variant with their classical counterparts. Then, we perform benchmark tests of various quantum and classical algorithms with small-scale instances, and of classical algorithms with large-scale instances. Main findings are that (i) quantum algorithms can be advantageous to classical algorithms in terms of the quality of solutions, while classical algorithms tend to show faster convergence than quantum ones, and (ii) one of the classical algorithms discussed in this paper shows significant scalability for higher-order unconstrained binary optimization problems. These findings highlight the importance of quantumness and the usefulness of classical approaches.