Diagonal gates in the Clifford hierarchy
Quantum Physics
2017-02-01 v1
Abstract
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for prime-dimensional qudits. They turn out to be -th roots of unity raised to polynomial functions of the basis state to which they are applied, and we determine which level of the Clifford hierarchy a given gate sits in based on and the degree of the polynomial.
Cite
@article{arxiv.1608.06596,
title = {Diagonal gates in the Clifford hierarchy},
author = {Shawn X. Cui and Daniel Gottesman and Anirudh Krishna},
journal= {arXiv preprint arXiv:1608.06596},
year = {2017}
}
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8 pages