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

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 $10^2-10^3$.