@article{paetznick2014repeat-until-success,
author = {Paetznick, Adam and Svore, Krysta M.},
title = {Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries},
year = {2014},
month = {November},
abstract = {We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance epsilon that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit Z-axis rotation to within distance epsilon, where the number of T gates scales as 1.3 log(1/epsilon) - 2.79, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of 2.4 log(1/epsilon) - 3.3 can be achieved for arbitrary unitaries and a small range of epsilon, which is roughly twice as good as optimal deterministic decomposition methods.},
publisher = {Rinton Press},
url = {http://approjects.co.za/?big=en-us/research/publication/repeat-until-success-non-deterministic-decomposition-of-single-qubit-unitaries/},
pages = {1277-1301},
journal = {Quantum Information and Computation},
volume = {14},
}