@article{bocharov2015efficient,
author = {Bocharov, Alex and Roetteler, Martin and Svore, Krysta M. and Svore, Krysta M.},
title = {Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits},
year = {2015},
month = {February},
abstract = {Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approximate any given single-qubit unitary to precision ϵ over the Clifford+T basis. Surprisingly, the T count of the synthesized RUS circuit surpasses the theoretical lower bound of 3 log2(1/ϵ) that holds for purely unitary single-qubit circuit decomposition. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected T count of 1.15 log2(1/ϵ) for single-qubit z rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher density in the space of all unitaries compared to the density of purely unitary implementations.},
publisher = {APS},
url = {http://approjects.co.za/?big=en-us/research/publication/efficient-synthesis-of-universal-repeat-until-success-circuits/},
pages = {80502},
journal = {Physical Review Letters},
volume = {114},
}