Optimal ancilla-free Clifford+V approximation of z-rotations
Abstract
We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+V circuit solving the given problem instance. In the absence of such an oracle, our algorithm is still near-optimal, producing circuits of V-count m + O(log(log(1/epsilon))), where m is the V-count of the third-to-optimal solution. A restricted version of the algorithm approximates z-rotations in the Pauli+V gate set. Our method is based on previous work by the author and Selinger on the optimal ancilla-free approximation of z-rotations using Clifford+T gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of z-rotations using Clifford+V gates.
Keywords
Cite
@article{arxiv.1409.4355,
title = {Optimal ancilla-free Clifford+V approximation of z-rotations},
author = {Neil J. Ross},
journal= {arXiv preprint arXiv:1409.4355},
year = {2015}
}
Comments
14 pages. Extends previous version from Pauli+V to Clifford+V. arXiv admin note: text overlap with arXiv:1403.2975