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arXiv:1208.5539 · Science China Physics Mechanics and Astronomy

Implementing a topological quantum model using a cavity lattice

Ze-Liang Xiang, Ting Yu, Wenxian Zhang, Xuedong Hu, J. Q. You

Published Jul 23, 2012• 13 citations
arXivHTMLPDF
DOI
10.1007/s11433-012-4864-9

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We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature--disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.