Randomised benchmarking for universal qudit gates

Abstract

We aim to establish a scalable scheme for characterising 
diagonal non-Clifford gates
for single- and multi-qudit systems; d is a prime-power integer.
By employing cyclic operators and a qudit T gate,
we generalise the dihedral benchmarking scheme for single- and multi-qudit
circuits.
Our results establish a path for experimentally benchmarking qudit systems and
are of theoretical and experimental interest because 
our scheme is optimal insofar as it does not require preparation of the full qudit Clifford
gate set to characterise a non-Clifford gate.
Moreover, combined with Clifford randomised benchmarking, 
our scheme is useful to characterise the generators of a universal gate set.