Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense graphs, our quantum algorit...

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Bibliographic Details
Published inarXiv.org
Main Authors Yu, Hongye, Wilczek, Frank, Wu, Biao
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.02.2021
Subjects
Algorithms
Approximation
Hilbert space
Mathematical analysis
Physics - Quantum Physics
Polynomials
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Summary:We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense graphs, our quantum algorithm on average can find an independent set of size very close to \(\alpha(G)\), which is the size of the maximum independent set of a given graph \(G\). Numerical results indicate that an \(O(n^2)\) time complexity quantum algorithm is sufficient for finding an independent set of size \((1-\epsilon)\alpha(G)\). The best classical approximation algorithm can produce in polynomial time an independent set of size about half of \(\alpha(G)\).
ISSN:2331-8422
DOI:10.48550/arxiv.2005.13089