The Symmetry‐Based Expressive QAOA for the MaxCut Problem
Zhao Xiumei, Yongmei Li, Guanghui Li, Yijie Shi, Su‐Juan Qin, Fei Gao · Advanced Quantum Technologies · 2025
Abstract The eXpressive Quantum Approximate Optimization Algorithm (XQAOA), a recently developed variant of QAOA for the MaxCut problem, can enhance approximation ratios at low circuit depths by assigning more classical parameters to the ansatz. Although XQAOA improves the performance of the circuit model, the introduction of a large number of additional parameters increases the cost of parameter optimization. Whether it is possible to reduce the number of parameters while maintaining the performance of the quantum circuit remains an intriguing research topic. Building spatial symmetry into parameterized quantum circuits is an effective approach to addressing parameter redundancy. In this study, the direct application of the symmetry in XQAOA is investigated and it was found that this application leads to a decrease in the approximation ratio. To address this issue, an improved symmetry‐based XQAOA is proposed, where two‐qubit gates for edges in the same orbit share parameters, while single‐qubit gates have independent parameters. Numerical simulations demonstrate that this approach maintains a comparable approximation ratio while decreasing the number of function evaluations, thereby reducing the cost of training XQAOA. In addition, observations reveal that the smaller the number of edge orbits, the more significant the acceleration in training.