Classical Coding Problem from Transversal $T$ Gates

Understand

Universal quantum computation requires the implementation of a logical non-Clifford gate.

• In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates.
• For example, this could enable magic state distillation with non-CSS codes and, thus, provide better parameters than CSS-based protocols.
• However, among non-degenerate stabilizer codes that support transversal $T$, we prove that CSS codes are optimal.