@article{kliuchnikov2014asymptotically,
author = {Kliuchnikov, Vadym and Bocharov, Alex and Svore, Krysta M.},
title = {Asymptotically Optimal Topological Quantum Compiling},
year = {2014},
month = {April},
abstract = {We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between 10−10 and 10−30.},
publisher = {APS},
url = {http://approjects.co.za/?big=en-us/research/publication/asymptotically-optimal-topological-quantum-compiling/},
journal = {Physical Review Letters},
volume = {112},
}