Spin glass reflection of the decoding transition for quantum error correcting codes
Abstract
We study the decoding transition for quantum error correcting codes with the help of a mapping to randombond Wegner spin models. Families of quantum low density paritycheck (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette $\Z2$ gauge models) as well as unexplored earlier generally nonlocal disordered spin models with nontrivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of extended defects which generalize the notion of domain walls to nonlocal spin models. In recently discovered quantum LDPC code families with finite rates the number of distinct classes of such extended defects is exponentially large, corresponding to extensive ground state entropy of these codes. Here, the transition can be driven by the entropy of the extended defects, a mechanism distinct from that in the local spin models where the number of defect types (domain walls) is always finite.
 Publication:

arXiv eprints
 Pub Date:
 November 2013
 DOI:
 10.48550/arXiv.1311.7688
 arXiv:
 arXiv:1311.7688
 Bibcode:
 2013arXiv1311.7688K
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 2 figures