6 problems

Let $\mathcal{CH}_k$ denote the $k$th level of the qubit Clifford hierarchy, and let $\pi$ be a permutation gate on the computational-basis states. The inverse-closure conjecture.…

Let $\mathcal{CH}_k$ denote the $k$th level of the qubit Clifford hierarchy, and let a permutation gate be a unitary that permutes the computational-basis states. A Clifford permut…

A gate in $U(2^n)$ is generalized semi-Clifford if it can be expressed as … where $C_1,C_2$ are $n$-qubit Clifford gates, $P$ is a permutation matrix in $U(2^n)$, and the $Z_j$ are…

Let $U$ be an $n$-qudit unitary, and let $\left|\left|U\right|\right|_{Q^k}$ and $\left|\left|U\right|\right|_{q^k}$ denote its quantum uniformity norm and hierarchy-overlap measur…

Classification of two-qudit Clifford hierarchy gates. Every hierarchy gate of two qudits is either a Clifford gate or can be uniquely expressed as

Conjugate-tuple conjecture. Gates of the $k+1$-th level of the Clifford hierarchy, up to phase, are in bijective correspondence with conjugate tuples of $k$-th level gates.