Controlled Gates in the Clifford Hierarchy
arXiv:2410.04711
Abstract
In this note we prove a necessary set of conditions which must be satisfied by any controlled gate in the qubit Clifford Hierarchy. These conditions are straightforward to derive yet quite restricting. We also extend our proofs to gates composed of certain direct sums of unitaries. Finally, we provide some evidence that these conditions are also sufficient.
9 pages, comments welcome