Closing the Quantum-Classical Scaling Gap in Approximate Optimization

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.