Extending quantum annealing to continuous domains: a hybrid method for quadratic programming

We propose Quantum Enhanced Simulated Annealing (QESA), a novel hybrid optimization framework that integrates quantum annealing (QA) into simulated annealing (SA) to tackle continuous optimization problems. While QA has shown promise in solving binary problems such as those expressed in Ising or QUBO form, its direct applicability to real-valued domains remains limited. QESA bridges this gap by using QA to select discrete search directions that guide SA through the continuous solution space, enabling the use of quantum resources without requiring full problem discretization. We demonstrate QESA's effectiveness on box-constrained quadratic programming (QP) problems, a class of non-convex optimization tasks that frequently arise in practice. Experimental results show that QESA consistently outperforms classical baselines in solution quality, particularly on larger and more ill-conditioned problems, while maintaining competitive runtime. As quantum annealing hardware matures, QESA offers a scalable and flexible strategy for leveraging quantum capabilities in continuous optimization.