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arxiv: 1302.5843 · v3 · submitted 2013-02-23 · ❄️ cond-mat.stat-mech · cs.CC· cs.DS· quant-ph

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Ising formulations of many NP problems

Andrew Lucas
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classification ❄️ cond-mat.stat-mech cs.CCcs.DSquant-ph
keywords isingproblemsformulationsmanynp-completeadiabaticalgorithmscase
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We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.

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