Error Threshold for Color Codes and Random Three-Body Ising Models
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We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation, and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random three-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p(c) = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities do not necessarily imply lower resistance to noise.
author list (cited authors)
Katzgraber, H. G., Bombin, H., & Martin-Delgado, M. A.