2023/05/26 by Chang, Weng-Long, Wong, Renata, Chung, Wen-Yu +3
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2305.16644
Given an undirected, unweighted graph with n vertices and m edges, the maximum cut problem is to find a partition of the n vertices into disjoint subsets V1 and V2 such that the number of edges between them is as large as possible. Classically, it is an NP-complete problem, which has potential applications ranging from circuit layout design, statistical physics, computer vision, machine learning and network science to clustering. In this paper, we propose a quantum algorithm to solve the maximum cut problem for any graph G with a quadratic speedup over its classical counterparts, where the temporal and spatial complexities are reduced to, respectively, O(√(2n/r)) and O(m2). With respect to oracle-related quantum algorithms for NP-complete problems, we identify our algorithm as optimal. Furthermore, to justify the feasibility of the proposed algorithm, we successfully solve a typical maximum cut problem for a graph with three vertices and two edges by carrying out experiments on IBM's quantum computer.