%0 Journal Article
%J Quantum Information and Computation
%D 2015
%T Optimal ancilla-free Clifford+V approximation of z-rotations
%A Neil J. Ross
%X 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.
%B Quantum Information and Computation
%V 15
%P 932-950
%8 2015/03/06
%G eng
%U http://arxiv.org/abs/1409.4355v2
%N 11-12