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Bioinspired Quantum Oracle Circuits for Biomolecular Solutions of the Maximum Cut Problem
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  • Weng-Long Chang ,
  • Renata Wong ,
  • Yu-Hao Chen ,
  • Wen-Yu Chung ,
  • Ju-Chin Chen ,
  • Athanasios V. Vasilakos
Weng-Long Chang
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Renata Wong
Chang Gung University

Corresponding Author:[email protected]

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Yu-Hao Chen
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Wen-Yu Chung
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Ju-Chin Chen
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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 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 IBMâ\euro™s quantum simulator.