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…

Diagonalizing sequence conjecture. For every $U_0\in\operatorname{U}(2)$, the sequences satisfy

Let $q$ be prime, let $\mathcal{S}\subseteq \pauli{q}[*]$ be a set of generalized Pauli operators, let $sq\mathcal{C}$ denote the gate set of single-qudit Clifford operators, and l…

Let $d\geq 2$ be fixed, and let $\mathcal{G}\subset \mathrm{SU}(d)$ be a finite gate set that densely generates $\mathrm{SU}(d)$. An inverse-free Solovay–Kitaev theorem asserts tha…