@techreport{kliuchnikov2015a,
author = {Kliuchnikov, V. and Bocharov, A. and Roetteler, M. and Yard, J. and Bocharov, Alex and Yard, Jon and Roetteler, Martin and Kliuchnikov, Vadym},
title = {A framework for approximating qubit unitaries},
year = {2015},
month = {October},
abstract = {We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves ε-approximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+π/12 [arXiv:1409.3552], running on average in time polynomial in O(log(1/ε)) (conditional on a number-theoretic conjecture). Ours is the first such algorithm that works for a wide range of gate sets and provides insight into what should constitute a “good” gate set for a fault-tolerant quantum computer.},
url = {http://approjects.co.za/?big=en-us/research/publication/a-framework-for-approximating-qubit-unitaries/},
number = {MSR-TR-2015-80},
note = {arXiv preprint arXiv:1510.03888},
}