  We introduce a scheme to characterise a qudit T gate that has different noise
than a set of Clifford gates. We developed our scheme through representation
theory and ring theory to generalise non-Clifford interleaved benchmarking to
qudit systems. By restricting to the qubit case, we recover the dihedral
benchmarking scheme. Our characterisation scheme provides experimental
physicists a practical method for characterising universal qudit gate sets and
advances randomised benchmarking research by providing the characterisation of
a complete qudit library.
