



@article {2515,
	title = {Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation},
	year = {2020},
	month = {1/16/2020},
	abstract = {<p>We study two-qubit circuits over the Clifford+CS gate set which consists of Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes with magic state distillation. However, since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is desirable to construct circuits that use few CS gates. In the present paper, we introduce an algorithm to construct optimal circuits for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and efficiently produces a Clifford+CS circuit for U using the least possible number of CS gates. Because our algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for the operator. We give a formal description of these normal forms as walks over certain graphs and use this description to derive an asymptotic lower bound of 5log(1/epsilon)+O(1) on the number CS gates required to epsilon-approximate any 4x4 unitary matrix.\&nbsp;</p>},
	url = {https://arxiv.org/abs/2001.05997},
	author = {Andrew N. Glaudell and Neil J. Ross and J. M. Taylor}
}
