Efficient topological compilation for a weakly integral anyonic model

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(2n) log 1/epsilon) and entanglement cost that is exponential in n. Another flavor of the algorithm produces efficient circuits with upper complexity bound in O(n 3(2n) log 1/epsilon) and no additional entanglement cost.