Practical quantum speedup in optimization

Establish whether contemporary quantum computers—whether quantum annealers or gate-based devices—can optimize combinatorial objective functions faster in practice than classical computers.

Background

The authors discuss fundamental questions about quantum optimization, noting uncertainty over practical speedups compared to classical methods. They reference work showing that certain aspects of QAOA, such as evaluating the expected objective value for low-depth circuits, can be performed efficiently on classical machines.

They further cite evidence that current gate-based quantum computers struggle to compete with GPUs and that known quadratic speedups (e.g., Grover’s algorithm) are insufficient for practical advantage under prevailing hardware constraints, motivating new algorithmic approaches.

References

Finally, if we focus on more fundamental aspects of quantum optimization, it is not yet clear if quantum computers can optimize functions faster in practice than classical computers.

— Combinatorial Optimization with Quantum Computers  (2412.15778 - Chicano et al., 2024) in Section 7 (Discussion and Future Directions)

The most immediate open problem is to design a quantum analogue of the event-management tool in PQSearch.

— A Quantum Scaling Algorithm for Maximum-Weight Perfect Matching in General Graphs  (2609.39457 - Mirsohi et al., 30 Sep 2026) in Section 6, Discussion and Open Problems

Although the perceived superiority of quantum computing for optimisation and simulation problems may be an enabler for adoption of hybrid computing, as the above list shows, the extent to which available commercial quantum solutions (most of which are cloud-based) offer sufficient performance gains over scaled-up classical computing hardware is unclear at this stage.

— Hybrid Classical-Quantum Solutions to Accelerate the Adoption of Quantum Computing  (2610.06638 - Deshpande et al., 5 Oct 2026) in Section 2, Hybrid Classical-Quantum Computing/Systems