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.