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arXiv · 1803.11356

Quantum speed-up in solving the maximal clique problem

Weng-Long Chang·Qi Yu·Zhaokai Li·Jiahui Chen·Xinhua Peng·Mang Feng
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Abstract

The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal clique problem for any graph $G$ with $n$ vertices with quadratic speed-up over its classical counterparts, where the time and spatial complexities are reduced to, respectively, $O(\sqrt{2^{n}})$ and $O(n^{2})$. With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm to be optimal. To justify the feasibility of the proposed quantum algorithm, we have successfully solved an exemplified clique problem for a graph $G$ with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

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Weng-Long Chang, Qi Yu, Zhaokai Li, Jiahui Chen, Xinhua Peng, Mang Feng. 2018-03-30. Quantum speed-up in solving the maximal clique problem. https://doi.org/10.1103/physreva.97.032344

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