Ising formulations of many NP problems
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.
- Publication:
-
Frontiers in Physics
- Pub Date:
- February 2014
- DOI:
- 10.3389/fphy.2014.00005
- arXiv:
- arXiv:1302.5843
- Bibcode:
- 2014FrP.....2....5L
- Keywords:
-
- Algorithms;
- complexity theory;
- spin glasses;
- adiabatic quantum computation;
- NP;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Computational Complexity;
- Computer Science - Data Structures and Algorithms;
- Quantum Physics
- E-Print:
- 27 pages