Fig. 1: The 15 elements of \(\boldsymbol{\mathcal{S}}\).
From: Optimal two-qubit circuits for universal fault-tolerant quantum computation

These operators are one suitable choice for 15 \({\mathcal{R(P, Q)}}\) gates which are not equivalent to each other up to right-multiplication by Cliffords. All other choices are equivalent to this one up to right-multiplication by Cliffords. The ordering of \({\mathcal{S}}\) is given by reading left-to-right and row-by-row.