String-net liquid: Difference between revisions

Revision as of 05:18, 1 May 2016

Revision as of 07:46, 24 August 2016

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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 arXiv|last=Kitaev|first=Alexei, Y.|author2=Chris Laumann |title=Topological phases and quantum computation|date=2009|arxiv=0904.2771}}</ref> Such a ground state is an example of a string-net condensate,<ref>{{Cite journal|journal=Physical Review A|volume=85|page=062328|doi=10.1103/PhysRevA.85.062328|last=Morimae|first=Tomoyuki|title=Quantum computational tensor network on string-net condensate|date=2012|arxiv=1012.1000|bibcode = 2012PhRvA..85f2328M }}</ref> which has the same [[topological order]]

as the [[Z2 spin liquid]] above.