On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction
Language
en
Communication dans un congrès
This item was published in
Coding and Cryptology, second international workshop IWCC 2009, Coding and Cryptology, second international workshop IWCC 2009, International Workshop on Coding and Cryptology, 2009-06-01, Zhangjiajie. 2009-06, vol. 5557, p. 259-273
Springer
English Abstract
We review constructions of quantum surface codes and give an alternative, algebraic, construction of the known classes of surface codes that have fixed rate and growing minimum distance. This construction borrows from ...Read more >
We review constructions of quantum surface codes and give an alternative, algebraic, construction of the known classes of surface codes that have fixed rate and growing minimum distance. This construction borrows from Margulis's family of Cayley graphs with large girths, and highlights the analogy between quantum surface codes and cycle codes of graphs in the classical case. We also attempt a brief foray into the class of quantum topological codes arising from higher dimensional manifolds and find these examples to have the same constraint on the rate and minimum distance as in the 2-dimensional case.Read less <
ANR Project
COdes Correcteurs Quantiques - ANR-08-EMER-0003
Origin
Hal imported