5 problems

An impure $[[n,k,3]]$ stabilizer code is a quantum stabilizer code encoding $k$ logical qubits into $n$ physical qubits, with minimum distance $3$ and with nontrivial stabilizer el…

Let $\mathbf{TS}^*$ be a proposed categorical spectrum of topological stabilizer codes, with $\mathbf{TS}^n$ its degree-$n$ component, and let $\mathbf Q^*(\mathrm{pt})$ denote the…

Transversal Clifford impossibility conjecture. There exists no stabilizer code where transversal Clifford gates realize the logical C-QSK circuit for any non-trivial exponentiated…

An $\left[\!\left[n,k\!:\!m,d\!:\!c\right]\!\right]_{q}$ hybrid stabilizer code has length $n$, quantum dimension $k$, classical dimension $m$, quantum minimum distance $d$, and cl…

Asymptotic Hamming-bound conjecture. For any $d$ there exists $n(d)$ such that for $n\geq n(d)$ the Hamming bound in equation (HBnondeg) holds for unrestricted data-syndrome codes.