Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

Details Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

2009-10-03

arxiv.org/abs/0910.0573v2

Phys. Rev. A 81, 012319 (2010)

Physics

Quantum Physics

8 pages, 4 figures, 1 table

Scientific paper

10.1103/PhysRevA.81.012319

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 3-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 similar error stability than color codes on triangular lattices, as well as 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 demonstrate the inherent robustness of this implementation.

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