Efficient topological compilation for a weakly integral anyonic model
2016; American Physical Society; Volume: 93; Issue: 1 Linguagem: Inglês
10.1103/physreva.93.012313
ISSN2469-9942
AutoresAlex Bocharov, Shawn X. Cui, Vadym Kliuchnikov, Zhenghan Wang,
Tópico(s)Quantum many-body systems
ResumoA 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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