Abstract
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 thealldifferentglobal 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.
Highlights
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems [1]
In the context of inference, we explore the use of quantum algorithms for graph problems, especially that for finding maximum matchings in graphs [13], to accelerate classical inference algorithms in CP
While we argue that our proposals are suitable for early generations of such devices because their hybrid nature allows for putting smaller parts of the problem on the device, we do not expect that the quantum algorithms we discuss will be successfully implementable using NISQ devices
Summary
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems [1]. The encapsulation of combinatorial substructure within CP models provides an elegant mechanism for carving off portions of complex problems into inference subproblems that can be solved by a quantum co-processor. These smaller subproblems require fewer resources, making them promising candidates for the early faulttolerant quantum computers of the future. Our initial explorations indicate the potential for symbiosis between the two paradigms: quantum algorithms can accelerate both inference and search in CP, and CP offers an attractive, modular formalism for tackling hard problems that makes it a promising candidate application for early fault-tolerant quantum computers, and beyond.
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