Closing the Quantum-Classical Scaling Gap in Approximate Optimization

TL;DR

This paper reevaluates claims of quantum advantage in approximate optimization by comparing quantum annealing to a classical nonlinear Hamiltonian dynamics approach, showing classical methods can match or outperform quantum scaling.

Contribution

It introduces the use of Simulated Bifurcation Machine as a classical benchmark, challenging previous quantum advantage claims and emphasizing the importance of larger problem sizes for accurate scaling assessment.

Findings

Classical SBM matches or exceeds quantum annealing performance.

Small problem sizes are insufficient for asymptotic scaling conclusions.

Quantum advantage is unlikely with current quantum annealer capabilities.

Abstract

In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical reference algorithm -- Parallel Tempering with Isoenergetic Cluster Moves (PT-ICM). Here, we reassess these findings with different classical paradigm -- Simulated Bifurcation Machine (SBM) -- that harnesses nonlinear Hamiltonian dynamics. By leveraging chaotic behavior rather than thermal fluctuations, SBM achieves comparable or superior scaling performance, effectively closing the previously reported quantum-classical gap. We show that small problem sizes analyzed in [1] are insufficient for inferring asymptotic scaling, due to sensitivity to runtime and hardware-specific factors. By extending the benchmark to larger instances -- beyond current quantum annealing capabilities -- we establish strong classical scaling behavior. And as a result, we conclude that it is unlikely that current generation of quantum annealers, can demonstrate supremacy in discrete approximate optimization under operationally meaningful conditions.