Efficient Topological Compilation for Weakly-Integral Anyon Model

TL;DR

This paper presents a new compilation algorithm for the metaplectic anyon model, enabling efficient approximation of arbitrary multi-qutrit unitaries with asymptotic complexity bounds, advancing quantum computation with weakly-integral anyons.

Contribution

It introduces two novel algorithms for compiling unitaries in the metaplectic anyon model, improving efficiency and entanglement cost analysis for quantum circuit synthesis.

Findings

One algorithm achieves complexity in O(3^{2n} log(1/ε)) with exponential entanglement cost.

Another algorithm achieves complexity in O(n 3^{2n} log(1/ε)) with no additional entanglement cost.

Both algorithms enable asymptotically efficient quantum circuit approximations.

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.