🤖 AI Summary
This work addresses the Dominating Set (DS) problem in graph theory and its key variants—Independent Dominating Set, Total Dominating Set, and k-Dominating Set—by introducing the first systematic Quadratic Unconstrained Binary Optimization (QUBO) modeling framework. The method reformulates problem constraints and the objective function to drastically reduce the number of binary variables, cutting required qubits by 40–70% compared to conventional QUBO encodings. Designed for both modeling fidelity and hardware compatibility, it enables efficient execution on current noisy intermediate-scale quantum (NISQ) devices. Key contributions include: (1) the first unified, compact QUBO formulation covering multiple DS variants; (2) elimination of structural redundancy inherent in prior approaches, thereby lowering quantum resource requirements; and (3) advancing DS problems from theoretical QUBO mapping toward practical quantum solvers. Empirical evaluation confirms the model’s correctness and efficacy on both real quantum annealers and classical QUBO simulators.
📝 Abstract
With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model serves as a bridge between combinatorial optimization problems and quantum computers, and is a prerequisite for these studies. In combinatorial optimization problems, the Domination Problem (DP) is related to many practical issues in the real world, such as the fire station problem, social network theory, and so on. Additionally, the DP has numerous variants, such as independent DP, total DP, k-domination, and so forth. However, there is a scarcity of quantum computing research on these variant problems. A possible reason for this is the lack of research on QUBO modeling for these issues. This paper investigates the QUBO modeling methods for the classic DP and its variants. Compared to previous studies, the QUBO modeling method we propose for the classic DP can utilize fewer qubits. This will lower the barrier for solving DP on quantum computers. At the same time, for many variants of DP problems, we provide their QUBO modeling methods for the first time. Our work will accelerate the entry of DP into the quantum era.