Abstract

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of “typical” instances. We find that, at large sizes , the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm, the harder it is also for the quantum adiabatic algorithm.

Date

2011

Authors

Itay Hen, A Peter Young

Journal

Physical Review E—Statistical, Nonlinear, and Soft Matter Physics

Volume

84

Issue

6

Pages

061152

Publisher

American Physical Society