Making classical ground-state spin computing fault-tolerant.

Journal Article

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error-free manner when working at nonzero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error-free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error-free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.

Full Text

Duke Authors

Cited Authors

  • Crosson, IJ; Bacon, D; Brown, KR

Published Date

  • September 3, 2010

Published In

Volume / Issue

  • 82 / 3 Pt 1

Start / End Page

  • 031106 -

PubMed ID

  • 21230024

Pubmed Central ID

  • 21230024

Electronic International Standard Serial Number (EISSN)

  • 1550-2376

International Standard Serial Number (ISSN)

  • 1539-3755

Digital Object Identifier (DOI)

  • 10.1103/physreve.82.031106

Language

  • eng