Using 1-Factorization from Graph Theory for Quantum Speedups on Clique Problems

• URL: http://arxiv.org/abs/2308.16827v1
• Date: Thu, 31 Aug 2023 15:59:35 GMT
• Title: Using 1-Factorization from Graph Theory for Quantum Speedups on Clique Problems
• Authors: Ali Hadizadeh Moghadam, Payman Kazemikhah, Hossein Aghababa
• Abstract summary: We provide new Quantum oracle designs based on the 1-factorization of complete graphs. We also discuss the usage of one of these oracles in bringing the Triangle Finding time complexity down to $O(n2.25 poly(log n))$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The clique problems, including $k$-CLIQUE and Triangle Finding, form an important class of computational problems; the former is an NP-complete problem, while the latter directly gives lower bounds for Matrix Multiplication. A number of previous efforts have approached these problems with Quantum Computing methods, such as Amplitude Amplification. In this paper, we provide new Quantum oracle designs based on the 1-factorization of complete graphs, all of which have depth $O(n)$ instead of the $O(n^2)$ presented in previous studies. Also, we discuss the usage of one of these oracles in bringing the Triangle Finding time complexity down to $O(n^{2.25} poly(log n))$, compared to the $O(n^{2.38})$ classical record. Finally, we benchmark the number of required Amplitude Amplification iterations for another presented oracle, for solving $k$-CLIQUE.

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