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.

翻译：约束性编程(CP)是用来模拟和解决约束性满意度和组合优化问题的范例。在CP,问题以描述可接受的解决办法的限制因素为模型,并通过以逻辑推理增强的回溯跟踪树搜索来解决。在本文中,我们展示了量子算法如何在推断和搜索两个层面加速CP。利用现有量子算法,我们为美元(textt{allcepet}$)的全球制约因素引入了量子加速过滤算法,并讨论了它是否适用于结构类似的更广泛的全球制约因素大家庭。我们提出了将量子过滤算法纳入古典和量子回溯跟踪搜索计划的框架,包括一种新型的混合古典量子回溯跟踪搜索方法。这项工作表明,CP是早期耐过错量计算机及以后的有希望的候选应用程序。