TL;DR
This paper presents Ising model formulations for numerous NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems, facilitating potential quantum optimization approaches.
Contribution
It extends existing mappings to the Ising model for a wide range of NP problems, with efficient spin requirements, aiding quantum algorithm development.
Findings
All problems have at most cubic number of spins in their Ising formulations.
Provides unified mappings for Karp's NP-complete problems.
Potential applications in adiabatic quantum optimization.
Abstract
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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