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quant-ph2025
Affine Equivalence in the Clifford Hierarchy
Jonas T. Anderson, Andrew Connelly
In this paper we prove a collection of results on the structure of permutations in the Clifford Hierarchy. First, we leverage results from the cryptography literature on affine equ…
quant-ph2025
Controlled Gates in the Clifford Hierarchy
Jonas T. Anderson, Matthew Weippert
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 y…
quant-ph2024
On Groups in the Qubit Clifford Hierarchy
Jonas T. Anderson
Here we study the unitary groups that can be constructed using elements from the qubit Clifford Hierarchy. We first provide a necessary and sufficient canonical form that semi-Clif…