8 problems

Gauging-booster conjecture. The gauging booster will allow native logical action in arbitrary Clifford hierarchies implemented via twisted (gauged) 2D product codes, including HGP…

Let $D(D_{4N})$ denote the stabilizer model based on the Drinfeld double of the dihedral group $D_{4N}$. When $4N=2^{n-1}$, realize the gates on a Hilbert space of $n$ physical qub…

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

Two-qudit semi-Clifford conjecture. Every $k$-th level gate of two qudits of prime dimension is semi-Clifford:

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.

For $m$ qubits, let ${\mathcal C}^{(3)}$ be the third level of the Clifford hierarchy, and call a unitary matrix semi-Clifford when it maps some maximal commuting subgroup of the H…

Let ${\mathcal C}^{(k)}$ denote the $k$th level of the Clifford hierarchy. A unitary is semi-Clifford if there exists a maximal commuting subgroup of the Heisenberg–Weyl group that…