@article{blass2015optimal,
author = {Blass, Andreas and Bocharov, Alex and Gurevich, Yuri},
title = {Optimal Ancilla-free Pauli+V Circuits for Axial Rotations},
year = {2015},
month = {November},
abstract = {We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL2(ℤ) geometry is almost elementary.},
publisher = {AIP},
url = {http://approjects.co.za/?big=en-us/research/publication/optimal-ancilla-free-pauliv-circuits-for-axial-rotations/},
journal = {Journal of Mathematical Physics},
volume = {56},
number = {12},
}