Hybrid Sequential Quantum Computing

We introduce hybrid sequential quantum computing (HSQC), a paradigm for combinatorial optimization that systematically integrates classical and quantum methods within a structured, stage-wise workflow. HSQC may involve an arbitrary sequence of classical and quantum processes, as long as the global result outperforms the standalone components. Our testbed begins with classical optimizers to explore the solution landscape, followed by quantum optimization to refine candidate solutions, and concludes with classical solvers to recover nearby or exact-optimal states. We demonstrate two instantiations: (i) a pipeline combining simulated annealing (SA), bias-field digitized counterdiabatic quantum optimization (BF-DCQO), and memetic tabu search (MTS); and (ii) a variant combining SA, BF-DCQO, and a second round of SA. This workflow design is motivated by the complementary strengths of each component. Classical heuristics efficiently find low-energy configurations, but often get trapped in local minima. BF-DCQO exploits quantum resources to tunnel through these barriers and improve solution quality. Due to decoherence and approximations, BF-DCQO may not always yield optimal results. Thus, the best quantum-enhanced state is used to continue with a final classical refinement stage. Applied to challenging higher-order unconstrained binary optimization (HUBO) problems on a 156-qubit heavy-hexagonal superconducting quantum processor, we show that HSQC consistently recovers ground-state solutions in just a few seconds. Compared to standalone classical solvers, HSQC achieves a speedup of up to 700 times over SA and up to 9 times over MTS in estimated runtimes. These results demonstrate that HSQC provides a flexible and scalable framework capable of delivering up to two orders of magnitude improvement at runtime quantum-advantage level on advanced commercial quantum processors.