Résumé
Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for several combinatorial optimization problems. Specifically, the combination of Quantum Minimum Finding (obtained from Grover Search) with dynamic programming has proved particularly efficient in improving the complexity of NP-hard problems currently solved by classical dynamic programming. For these problems, the classical dynamic programming complexity (ignoring the polynomial factors) in O*(c^n) can be reduced by a hybrid algorithm to O*(c_quant^n), with c_quant < c. In this paper, we provide a bounded-error hybrid algorithm that achieves such an improvement on NP-hard minimization problems for which we give a generic description. We illustrate our approach on a variety of scheduling problems. Our algorithm reduces the exponential-part complexity compared to the best-known classical algorithm, sometimes at the cost of an additional pseudopolynomial factor.