Hybrid Sequential Quantum Computing

We present Hybrid Sequential Quantum Computing (HSQC), a new paradigm for combinatorial optimization that systematically integrates classical and quantum algorithms in a structured, stage-wise workflow. HSQC enables an arbitrary sequence of classical and quantum processes, provided the overall performance exceeds that of the individual components. In our demonstration, classical optimizers first explore the energy landscape, followed by a quantum refinement stage using Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO), and concluded by a classical recovery phase to refine solutions near the optimum. We implement two variants: (i) SA → BF-DCQO → MTS, and (ii) SA → BF-DCQO → SA, combining simulated annealing (SA), memetic tabu search (MTS), and quantum tunneling effects from BF-DCQO. Benchmarking on higher-order unconstrained binary optimization (HUBO) instances mapped to a 156-qubit heavy-hex superconducting quantum processor, HSQC consistently recovers ground-state solutions within seconds. Compared to standalone methods, HSQC achieves up to 700× speedup over SA and 9× over MTS in estimated runtime. These results establish HSQC as a flexible and scalable framework capable of delivering near–quantum-advantage performance on current-generation quantum hardware.