Tricolored lattice gauge theory with randomness: fault tolerance in topological color codes Academic Article uri icon

abstract

  • We compute the error threshold of color codes - a class of topological quantum codes that allow a direct implementation of quantum Clifford gates - when both qubit and measurement errors are present. By mapping the problem onto a statistical - mechanical three - dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.8(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

author list (cited authors)

  • Andrist, R. S., Katzgraber, H. G., Bombin, H., & Martin-Delgado, M. A.

citation count

  • 25

publication date

  • August 2011