Constructing Functional Braids for Low-Leakage Topological Quantum Computing

Details Constructing Functional Braids for Low-Leakage Topological Quantum Computing Constructing Functional Braids for Low-Leakage Topological Quantum Computing

2008-02-28

arxiv.org/abs/0802.4213v2

Phys. Rev. A 78, 042325 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 4 figures, updated, accepeted by Phys. Rev. A

Scientific paper

10.1103/PhysRevA.78.042325

We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example. To be specific, we construct a functional braid in a six-anyon Hilbert space that exchanges two neighboring anyons while conserving the encoded quantum information. The leakage error is $\sim$$10^{-10}$ for a braid of $\sim$100 interchanges of anyons. Applying the braid greatly reduces the leakage error in the construction of generic controlled-rotation gates.

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