Quantum advantage for optimization problems

Determine whether hybrid quantum-classical algorithms or purely quantum algorithms can solve optimization problems more efficiently than state-of-the-art classical solvers.

Background

The paper introduces QHyper, a software library designed to facilitate experimentation with quantum and hybrid solvers for combinatorial optimization. The motivation highlights the broader goal of establishing quantum advantage—demonstrating tasks where quantum methods surpass classical approaches. Despite significant interest, whether hybrid or purely quantum algorithms can outperform state-of-the-art classical solvers on optimization problems remains unresolved. QHyper aims to support systematic investigation of this question by providing a unified interface for problem formulation, solver execution, and (hyper)parameter optimization across quantum annealers, variational algorithms, and classical methods.

References

Therefore, determining whether hybrid or purely quantum algorithms could solve optimization problems more efficiently than state-of-the-art classical solvers would bring a major advancement and still remains an open question.

— QHyper: an integration library for hybrid quantum-classical optimization  (2409.15926 - Lamża et al., 2024) in Section 1 (Motivation and significance)

An important open question is whether such limited constraint information is sufficient to optimize quantum algorithms when exact solutions are unavailable.

— Reinforcement LearningtoHarness Approximation Errors for Long-Time QuantumSimulation  (2608.20139 - Shi et al., 20 Aug 2026) in Discussion and outlook section, final paragraph before Acknowledgments