TY - JOUR
T1 - Generating topological order
T2 - No speedup by dissipation
AU - König, Robert
AU - Pastawski, Fernando
PY - 2014/7/1
Y1 - 2014/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84903833273&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.90.045101
DO - 10.1103/PhysRevB.90.045101
M3 - Article
AN - SCOPUS:84903833273
SN - 1098-0121
VL - 90
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 4
M1 - 045101
ER -