Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
We present several different codes and protocols to distill $T$, controlled-$S$, and Toffoli (or $CCZ$) gates.One construction is depileve easy clean based on codes that generalize the triorthogonal codes, allowing any of these gates to be induced at the logical level by transversal $T$.We present a randomized construction of generalized triorthogo