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International Conference on Evaluation of Novel Approaches to Software Engineering

Domain-Driven Modeling of Combinatorial Constraint Satisfaction Problems for Quantum Solvers

Marc Uphues, Sebastian Thöne, Herbert Kuchen

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.5220/0014833500004015

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Over the last years, quantum computing has reached a level of technological maturity that enables the exploration of potential applications. One use case is solving combinatorial Constraint Satisfaction Problems. Yet, it seems challenging to utilize quantum computing for such problems in practice, as software developers must translate these problems to specialized models required by quantum solvers. A common candidate is the model of Quadratic Unconstrained Binary Optimization. It serves as an input format for both quantum annealing and gate-based quantum algorithms. With this paper, we present a software-based and domain-driven modeling approach that is compatible with such quantum solvers. It facilitates the inline-declaration of problems within domain model code through an annotation-based syntax. Our novel approach is driven by a framework-like engine that encapsulates and automates the process of problem instantiation, translation, solver invocation, and solution mapping. It ena bles software developers and domain experts to solely focus on the problem domain, rather than highly specialized models prescribed by quantum solvers. By incorporating principles of Domain-Driven Design, our approach employs a well-known modeling technique.

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Over the last years, quantum computing has reached a level of technological maturity that enables the exploration of potential applications. One use case is solving combinatorial Constraint Satisfaction Problems. Yet, it seems challenging to utilize quantum computing for such problems in practice, as software developers must translate these problems to specialized models required by quantum solvers. A common candidate is the model of Quadratic Unconstrained Binary Optimization. It serves as an input format for both quantum annealing and gate-based quantum algorithms. With this paper, we present a software-based and domain-driven modeling approach that is compatible with such quantum solvers. It facilitates the inline-declaration of problems within domain model code through an annotation-based syntax. Our novel approach is driven by a framework-like engine that encapsulates and automates the process of problem instantiation, translation, solver invocation, and solution mapping. It ena bles software developers and domain experts to solely focus on the problem domain, rather than highly specialized models prescribed by quantum solvers. By incorporating principles of Domain-Driven Design, our approach employs a well-known modeling technique.
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We present experiments in solving constrained optimization and constraint satisfaction problems by means of Quantum Annealing in terms of QUBO (Quadratic Unconstrained Binary Optimization). We investigate different QUBO formulations for the encoding of integers into Booleans and for the encoding of the At-Most-One constraint, which is used in combinatorial problems requiring capacity constraints. We compare four different QUBO models and report experiments done on the D-Wave annealing computer and the "quantum-inspired" Fixstars Amplify Annealing Engine. For this, we consider a simple example taken from the domain of Constraint Satisfaction Problems (CSP), the N-queens problem, as its formulation involves multiple instances of the At-Most-One constraints.