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Phys Rev Lett. 2009 Aug 28;103(9):090501. Epub 2009 Aug 24.

Error threshold for color codes and random three-body Ising models.

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Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland.


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.

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