TechRxiv

Bioinspired Quantum Oracle Circuits for Biomolecular Solutions of the Maximum Cut Problem

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posted on 2023-12-07, 03:44 authored by Weng-Long Chang, Renata WongRenata Wong, Yu-Hao Chen, Wen-Yu Chung, Ju-Chin Chen, Athanasios V. Vasilakos
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 biomolecular and a quantum algorithm to solve the maximum cut problem for any graph G. The quantum algorithm is inspired by the biomolecular algorithm and has a quadratic speedup over its classical counterparts, where the temporal and spatial complexities are reduced to, respectively, O((2n/r)1/2) 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 simulator.

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Email Address of Submitting Author

renata.wong.kei@gmail.com

ORCID of Submitting Author

0000-0001-5468-0716

Submitting Author's Institution

Chang Gung University

Submitting Author's Country

  • Taiwan

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