Constraint-oriented biased quantum search for general constrained combinatorial optimization problems

TL;DR

This paper introduces a quantum algorithm for solving general constrained combinatorial optimization problems, extending previous methods to handle arbitrary constraints and potentially outperform classical solvers in runtime and solution quality.

Contribution

The paper generalizes quantum search algorithms to handle a broader class of constraints in combinatorial optimization, beyond linear constraints, and evaluates potential quantum advantages.

Findings

Potential runtime savings of up to 10^2-10^3 times over classical methods

Algorithm can handle arbitrary efficiently computable constraints

Quantum approach may outperform classical heuristics in solution quality

Abstract

We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously developed quantum methods that were primarily restricted to linear constraints, we generalize the approach to encompass a broader class of problems in discrete domains. To evaluate the potential of our algorithm, we assume the existence of sufficiently advanced logical quantum hardware. With this assumption, we demonstrate that our method has the potential to outperform state-of-the-art classical solvers and heuristics in terms of both runtime scaling and solution quality. The same may be true for more realistic implementations, as the logical quantum algorithm can achieve runtime savings of up to $10^2-10^3$.