@article { WOS:000665821600002,
title = {Optimal two-qubit circuits for universal fault-tolerant quantum computation},
journal = {npj Quantum Inform.},
volume = {7},
number = {1},
year = {2021},
month = {JUN 22},
publisher = {NATURE RESEARCH},
type = {Article},
abstract = {We study two-qubit circuits over the Clifford+CS gate set, which consists of the 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 through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of 5log(2)(1/epsilon)+O(1) on the number of CS gates required to epsilon-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.},
doi = {10.1038/s41534-021-00424-z},
author = {Glaudell, Andrew N. and Ross, Neil J. and Taylor, Jacob M.}
}