Quantum Approximate Optimization Algorithm for Graph Partitioning

Quantum approximate optimization algorithm (QAOA) is an algorithm framework for solving combinatorial optimization problems. It is regarded as one of the promising candidates to demonstrate the advantages of quantum computing in the near future. Within the QAOA framework, the symmetries of quantum states induced by the binary encoding scheme restrain the performance of QAOA. Inspired by the Dicke state preparation algorithm, we proposed a new encoding scheme that eliminated the symmetry of quantum states representing solutions. Beyond that, we also proposed a novel evolution operator, star graph (SG) mixer, and its corresponding SG algorithm. The quantum circuit implementation of the SG algorithm on IBM Q showed the SG algorithm has an average performance improvement of about 25.3% over the standard QAOA algorithm in solving the graph partitioning problem. © 2024 Chinese Institute of Electronics. All rights reserved.