Exploiting Geometric Degrees of Freedom in Topological Quantum Computing

Details Exploiting Geometric Degrees of Freedom in Topological Quantum Computing Exploiting Geometric Degrees of Freedom in Topological Quantum Computing

2008-12-12

arxiv.org/abs/0812.2414v2

Phys. Rev. A 80, 012306 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 2 figures, accepted for publication in Phys. Rev. A

Scientific paper

In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [Phys. Rev. A 78, 042325 (2008)].

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