Exploiting Geometric Degrees of Freedom in Topological Quantum Computing

Abstract

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)].

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

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Cited by in corpus (8)

• A Short Introduction to Topological Quantum Computation
• Introduction to topological quantum computation with non-Abelian anyons
• Topological Quantum Computing with Read-Rezayi States
• Quantum hashing with the icosahedral group
• Engineering Yang-Lee anyons via Majorana bound states
• Systematically generated two-qubit anyon braids
• Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing