In a recent series of two research papers Cui, Wang and Hong proposed a class of anyonic models for universal quantum computation based on weakly-integral anyons. 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. From the mathematical standpoint the underlying unitary bases arising in various versions of the weakly-integral anyonic models are de\ufb01ned over a certain ring of Eisenstein rationals, that has useful number-theoretic properties. In this paper we develop a compilation algorithm to approximate arbitrary n-qutrit unitaries with asymptotically e\ufb03cient circuits over the metaplectic anyon model, the most recent instance of the weakly-integral anyonic class. One \ufb02avor of our algorithm produces e\ufb03cient circuits with upper complexity bound asymptotically in O(32 n log1\/\u03b5) and entanglement cost that is exponential in n. Another \ufb02avor of the algorithm produces e\ufb03cient circuits with upper complexity bound in O(n32 n log1\/\u03b5) and no additional entanglement cost.<\/p>\n","protected":false},"excerpt":{"rendered":"
In a recent series of two research papers Cui, Wang and Hong proposed a class of anyonic models for universal quantum computation based on weakly-integral anyons. 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. From the mathematical standpoint 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