Generating topological order: No speedup by dissipation

Robert König, Fernando Pastawski

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We consider the problem of converting a product state to a ground state of a topologically ordered system through a locally generated open-system dynamic. Employing quantum-information tools, we show that such a conversion takes an amount of time proportional to the diameter of the system. Our result applies to typical two-dimensional topologically ordered systems as well as, for example, the three-dimensional and four-dimensional toric codes. It is tight for the toric code, giving a scaling with the linear system size. Our results have immediate operational implications for the preparation of topologically ordered states, a crucial ingredient for topological quantum computation: Dissipation cannot provide any significant speedup compared to unitary evolution.

Original languageEnglish
Article number045101
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume90
Issue number4
DOIs
StatePublished - 1 Jul 2014
Externally publishedYes

Fingerprint

Dive into the research topics of 'Generating topological order: No speedup by dissipation'. Together they form a unique fingerprint.

Cite this