Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. In this paper, we show how quantum algorithms can accelerate CP, at both the levels of inference and search. Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the $\texttt{alldifferent}$ global constraint and discuss its applicability to a broader family of global constraints with similar structure. We propose frameworks for the integration of quantum filtering algorithms within both classical and quantum backtracking search schemes, including a novel hybrid classical-quantum backtracking search method. This work suggests that CP is a promising candidate application for early fault-tolerant quantum computers and beyond.

中文翻译：

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量子加速约束规划

约束规划 (CP) 是用于建模和解决约束满足和组合优化问题的范式。在 CP 中，问题使用描述可接受解决方案的约束进行建模，并通过逻辑推理增强的回溯树搜索来解决。在本文中，我们展示了量子算法如何在推理和搜索级别上加速 CP。利用现有的量子算法，我们为 $\texttt{alldifferent}$ 全局约束引入了一种量子加速过滤算法，并讨论了它对具有类似结构的更广泛的全局约束系列的适用性。我们提出了在经典和量子回溯搜索方案中集成量子滤波算法的框架，包括一种新颖的混合经典-量子回溯搜索方法。