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arXiv · 2305.16644

Quantum Speedup for the Maximum Cut Problem

Weng-Long Chang·Renata Wong·Wen-Yu Chung·Yu-Hao Chen·Ju-Chin Chen·Athanasios V. Vasilakos
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Abstract

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 $V_1$ and $V_2$ 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, $O(\sqrt{2^n/r})$ and $O(m^2)$. 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.

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Weng-Long Chang, Renata Wong, Wen-Yu Chung, Yu-Hao Chen, Ju-Chin Chen, Athanasios V. Vasilakos. 2023-05-26. Quantum Speedup for the Maximum Cut Problem. https://arxiv.org/abs/2305.16644

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