Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures

Journal Article (Journal Article)

We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature. © 2009 The American Physical Society.

Full Text

Duke Authors

Cited Authors

  • Viteri, CR; Tomita, Y; Brown, KR

Published Date

  • October 19, 2009

Published In

Volume / Issue

  • 80 / 4

Electronic International Standard Serial Number (EISSN)

  • 1094-1622

International Standard Serial Number (ISSN)

  • 1050-2947

Digital Object Identifier (DOI)

  • 10.1103/PhysRevA.80.042313

Citation Source

  • Scopus