String-net liquid: Difference between revisions

Revision as of 16:07, 24 May 2014

Revision as of 15:42, 24 July 2014

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===The toric code===

The [[toric code]] is a two dimensional spin lattice, that acts as a quantum error-correcting code. It is defined on a two dimensional lattice with [[torus|toric]] [[boundary conditions]] with a spin-1/2 on each link. It can be shown that the ground state of the standard toric code Hamiltonian is an ''equal weight superposition'' of closed string states.<ref name=kitaevlaumann>{{cite journal|last=Kitaev|first=Alexei, Y.|coauthorsauthor2=Chris Laumann |title=Topological phases and quantum computation|journal=ArXiv|year=2009|url=http://arxiv.org/abs/0904.2771}}</ref> Such a ground state is an example of a string-net condensate,<ref>{{cite journal|last=Morimae|first=Tomoyuki|title=Quantum computational tensor network on string-net condensate|journal=ArXiv|year=2011|url=http://arxiv.org/pdf/1012.1000v2.pdf}}</ref> which has the same [[topological order]]

as the [[Z2 spin liquid]] above.