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arXiv · 1504.03383

Efficient Topological Compilation for Weakly-Integral Anyon Model

Alex Bocharov·Shawn X. Cui·Vadym Kliuchnikov·Zhenghan Wang
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Abstract

A class of anyonic models for universal quantum computation based on weakly-integral anyons has been recently proposed. While universal set of gates cannot be obtained in this context by anyon braiding alone, designing a certain type of sector charge measurement provides universality. In this paper we develop a compilation algorithm to approximate arbitrary $n$-qutrit unitaries with asymptotically efficient circuits over the metaplectic anyon model. One flavor of our algorithm produces efficient circuits with upper complexity bound asymptotically in $O(3^{2\,n} \, \log{1/\varepsilon})$ and entanglement cost that is exponential in $n$. Another flavor of the algorithm produces efficient circuits with upper complexity bound in $O(n\,3^{2\,n} \, \log{1/\varepsilon})$ and no additional entanglement cost.

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Alex Bocharov, Shawn X. Cui, Vadym Kliuchnikov, Zhenghan Wang. 2016-06-09. Efficient Topological Compilation for Weakly-Integral Anyon Model. https://doi.org/10.1103/physreva.93.012313

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