Operator quantum errorcorrecting subsystems for selfcorrecting quantum memories
Abstract
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum errorcorrecting codes, one requires the ability to apply a procedure which exactly reverses on the errorcorrecting subspace any correctable error. In contrast, for operator errorcorrecting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator errorcorrecting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is selfcorrecting. Such a system will be a natural hightemperature quantum memory, robust to noise without external intervening quantum errorcorrection procedures.
 Publication:

Physical Review A
 Pub Date:
 January 2006
 DOI:
 10.1103/PhysRevA.73.012340
 arXiv:
 arXiv:quantph/0506023
 Bibcode:
 2006PhRvA..73a2340B
 Keywords:

 03.67.Lx;
 75.10.Pq;
 Quantum computation;
 Spin chain models;
 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 17 pages, 3 figures, typos fixed, references added