Error threshold for color codes and random three-body Ising models.
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.
Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland.
Helmut G
HG
Katzgraber
H
H
Bombin
M A
MA
Martin-Delgado