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On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction

  • Gilles Zémor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5557)

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 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.

Keywords

Minimum Distance Regular Graph Cayley Graph Dual Graph Quantum Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gilles Zémor
    • 1
  1. 1.Institut de Mathématiques de BordeauxUMR 5251, Université Bordeaux 1TalenceFrance

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