Auxiliary-Qubit-Free Quantum Approximate Optimization Algorithm for the Minimum Dominating Set Problem
Guanghui Li, Xiaohui Ni, Junjian Su, Sujuan Qin, Fenzhuo Guo, Bingjie Xu, Wei Huang, Fei Gao
Published: 2025/9/20
Abstract
Quantum Approximate Optimization Algorithm (QAOA) is a promising framework for solving combinatorial optimization problems on near-term quantum devices. One such problem is the Minimum Dominating Set (MDS), which is NP-hard in graph theory. Existing QAOA studies for the MDS problem typically require a large number of auxiliary qubits, which increases hardware demands and hinders scalability on Noisy Intermediate-Scale Quantum (NISQ) devices. In this paper, we propose an auxiliary-qubit-free QAOA for the MDS problem. Unlike previous studies that introduce auxiliary variables to convert inequality constraints into equalities, our algorithm utilizes Boolean algebra to perform this transformation, eliminating the need for auxiliary qubits. Numerical experiments demonstrate that our algorithm achieves comparable performance to the existing best QAOA for this problem while using fewer qubits. Additionally, an ablation study based on multi-angle QAOA reveals that the solution quality of the algorithm can be further improved by replacing shared circuit parameters with independent ones.