We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum 'solver' solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.

翻译：我们提出一种利用量子计算机解决二元线性规划问题的新方法，该方法可推广至一般整数线性规划。当前量子优化算法（混合型或纯量子型）作为通用独立求解器处理整数线性规划问题。然而，要使其具备实际应用价值，人们期望其性能超越现有经典求解器。这种期望对量子算法并不公平：经过数十年发展，经典整数线性规划求解器已形成多种算法协同工作的稳健体系以获得最优解。这正是我们当前希望量子"求解器"方案遵循的路径。本研究将任何适用的量子优化算法嵌入量子启发的经典约束生成框架。首先通过移除所有约束松弛原问题，并将其编码为伊辛哈密顿量供量子优化子程序处理。随后通过对子程序解态的采样，获取原始问题中约束违反信息，据此决定需向哈密顿量引入哪些耦合项。这些耦合项对应原始二元线性规划的约束条件。接着对新哈密顿量重新优化，直至获得可行解或满足其他停止条件。由于可控制单步添加至哈密顿量的约束数量，本算法效率至少不低于其所封装的（混合型）量子优化算法。我们通过小规模最小成本精确覆盖问题实例的求解结果验证了该主张。