Feasibility of selfcorrecting quantum memory and thermal stability of topological order
Abstract
Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of selfcorrecting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that the model does not work as selfcorrecting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions.
 Publication:

Annals of Physics
 Pub Date:
 October 2011
 DOI:
 10.1016/j.aop.2011.06.001
 arXiv:
 arXiv:1103.1885
 Bibcode:
 2011AnPhy.326.2566Y
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 72 pages, 37 figures