@article {1532, title = {Optimal ancilla-free Clifford+V approximation of z-rotations}, journal = {Quantum Information and Computation}, volume = {15}, year = {2015}, month = {2015/03/06}, pages = {932-950}, 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. }, url = {http://arxiv.org/abs/1409.4355v2}, author = {Neil J. Ross} }