The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical Solvers

TL;DR

This paper benchmarks a hybrid quantum solver for combinatorial optimization on IBM quantum hardware, showing it can match or outperform classical solvers in speed and solution quality on specific instances.

Contribution

It provides the first end-to-end benchmark of a hybrid quantum solver on real hardware, demonstrating competitive performance with classical solvers.

Findings

HSQC achieves high-quality solutions in under one second.

On 20 instances, HSQC matches ground-state energy in 14 cases.

Quantum solver performance is comparable to classical solvers running on hundreds of CPUs or GPUs.

Abstract

We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline--from preprocessing to QPU execution and postprocessing--under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve.