Équipe de Recherche en Physique de l'Information Quantique


Abstract = {Topological phases can be defined in terms of local equivalence:
two systems are in the same topological phase if it is possible to transform
one into the other by a local reorganization of its degrees of freedom. The
classification of topological phases therefore amounts to the classification of
long-range entanglement. Such local transformation could result, for instance,
from the adiabatic continuation of one system’s Hamiltonian to the other. Here,
we use this definition to study the topological phase of translationally invariant
stabilizer codes in two spatial dimensions, and show that they all belong to one
universal phase. We do this by constructing an explicit mapping from any such
code to a number of copies of Kitaev’s code. Some of our results extend to some
two-dimensional (2D) subsystem codes, including topological subsystem codes.
Error correction benefits from the corresponding local mappings. In particular, it
enables us to use decoding algorithm developed for Kitaev’s code to decode any
2D stabilizer code and subsystem code.},
Author = {Hector Bombin and Guillaume Duclos-Cianci and David Poulin},
Eprint = {arXiv:1103.4606},
Keywords = {Topological QC},
Title = {Universal topological phase of 2D stabilizer codes},
Year = {2012},
Journal = {New J. Phys.},
Volume = {14},
Pages = {073048},
local-url = {BDP12a1.pdf}}