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arXiv · 0902.4845

Error Threshold for Color Codes and Random 3-Body Ising Models

Helmut G. Katzgraber·H. Bombin·M. A. Martin-Delgado
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Abstract

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 3-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 does not necessarily imply lower resistance to noise.

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Helmut G. Katzgraber, H. Bombin, M. A. Martin-Delgado. 2009-08-24. Error Threshold for Color Codes and Random 3-Body Ising Models. https://doi.org/10.1103/physrevlett.103.090501

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