Hybrid Sequential Quantum Computing

TL;DR

The paper introduces Hybrid Sequential Quantum Computing (HSQC), a modular framework that interleaves classical optimization with quantum subroutines to tackle dense HUBO problems. By combining SA, BF-DCQO, and MTS (or SA) in a stage-wise pipeline, HSQC leverages classical search, quantum tunneling via counterdiabatic evolution, and quantum-informed initial states to accelerate convergence toward ground states. Across 156-qubit HUBO instances on IBM hardware, HSQC achieves ground-state recovery with substantial runtime advantages—up to about 700× faster than SA and up to 9× faster than MTS—demonstrating a practical route to runtime quantum advantage on near-term devices. The work also analyzes an SA→BF-DCQO→SA variant and discusses hardware-aware instance generation, circuit decomposition, and comparative results with D-Wave systems, highlighting HSQC’s robustness, scalability, and potential applicability to industrial optimization tasks as quantum hardware evolves.

Abstract

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.

Figures (8)

• Figure 1: Schematic of the hybrid sequential quantum computing (HSQC) framework. The optimization begins by formulating the target problem as a higher-order unconstrained binary optimization (HUBO) problem. A classical optimization routine first explores the energy landscape to identify promising low-energy configurations, continuing until further improvements become computationally expensive. The best configuration is then used to initialize the BF-DCQO protocol. The QPU then executes a controlled counterdiabatic evolution that guides the system through the energy landscape by exploiting quantum superposition and tunneling to escape local minima and converge toward lower-energy states. The resulting output is passed to a final classical optimization stage, which may employ heuristic or exact methods, to reach the ground state or obtain high-quality approximations. The runtime allocation across the stages is chosen adaptively based on the problem characteristics.
• Figure 2: Performance comparison between MTS and HSQC. For different number of generations $G_{\max}$, optimality gaps $\mathcal{G}$ obtained across the eight instances tested in Table \ref{['tab:mts_bfdcqo']}. Data points lying in the lower part of the plot mean that HSQC approach performed better than MTS.
• Figure 3: Minimum $\tau$ values for various standalone optimization routines for Instance 8. Comparing minimum $\tau$ values for MTS, HSQC and SA obtained from Table \ref{['tab:mts_shc_tau']} and Table. \ref{['tab:sa_tau']} with $T_{\rm{CPLEX}} = 22.896s$ value as a reference.
• Figure 4: Performance comparison between SA and HSQC. For different number of sweeps, optimality gaps obtained across the eight instances tested in Table \ref{['tab:sa_bfdcqo']}. Data points lying in the lower part of the plot mean that the HSQC approach performed better than SA.
• Figure 5: Estimating per-flip runtime for MTS. Total runtime of the Memetic tabu Search (MTS) algorithm as a function of the number of bit-flips (function evaluations). A linear fit is applied to extract the average time per flip, which is subsequently used to estimate MTS runtimes throughout the manuscript.