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Pré-Publication, Document De Travail Année : 2023

(Quantum) complexity of testing signed graph clusterability

Résumé

This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which yields a polynomial speedup over the best classical clusterability tester known [arXiv:2102.07587]. Second, we prove an $\tilde{\Omega}(\sqrt{N})$ classical query lower bound for testing clusterability, which nearly matches the upper bound from [arXiv:2102.07587]. This settles the classical query complexity of clusterability testing, and it shows that our quantum algorithm has an advantage over any classical algorithm.
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hal-04516220 , version 1 (22-03-2024)

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Kuo-Chin Chen, Simon Apers, Min-Hsiu Hsieh. (Quantum) complexity of testing signed graph clusterability. 2024. ⟨hal-04516220⟩
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