Decomposition Algorithms for Solving NP-hard Problems on a Quantum Annealer

Djidjev, Hristo Nikolov; Pelofske, Elijah Autumn Rain; Hahn, Georg

doi:10.1007/s11265-020-01550-1

Decomposition Algorithms for Solving NP-hard Problems on a Quantum Annealer

Journal Article · Mon Jun 29 00:00:00 EDT 2020 · Journal of Signal Processing Systems

DOI:https://doi.org/10.1007/s11265-020-01550-1· OSTI ID:1822729

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp’s 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers can search for the optimum value of such NP-hard optimization problems, given the problem can be embedded on their hardware. However, this is often not possible due to certain limitations of the hardware connectivity structure of the annealer. This paper studies a general framework for a decomposition algorithm for NP-hard graph problems aiming to identify an optimal set of vertices. Our generic algorithm allows us to recursively divide an instance until the generated subproblems can be embedded on the quantum annealer hardware and subsequently solved. Furthermore, the framework is applied to the maximum clique and minimum vertex cover problems, and we propose several pruning and reduction techniques to speed up the recursive decomposition. The performance of both algorithms is assessed in a detailed simulation study.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1822729

Report Number(s):: LA-UR--19-30809

Journal Information:: Journal of Signal Processing Systems, Journal Name: Journal of Signal Processing Systems Journal Issue: 4 Vol. 93; ISSN 1939-8018

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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