A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

Details A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

2001-04-26

arxiv.org/abs/quant-ph/0104129v1

Physics

Quantum Physics

15 pages, 6 figures, email correspondence to farhi@mit.edu ; a shorter version of this article appeared in the April 20, 2001

Scientific paper

10.1126/science.1057726

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

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