  Non-adiabatic holonomic quantum computation is a method used to implement
high-speed quantum gates with non-Abelian geometric phases associated with
paths in state space. Due to their noise tolerance, these phases can be used to
construct error resilient quantum gates. We extend the holonomic dark path
qubit scheme in [M.-Z. Ai {\t et al.}, Fundam. Res. {\bf 2}, 661 (2022)] to
qudits. Specifically, we demonstrate one- and two-qudit universality by using
the dark path technique. Explicit qutrit ($d=3$) gates are demonstrated and the
scaling of the number of loops with the dimension $d$ is addressed. This
scaling is linear and we show how any diagonal qudit gate can be implemented
efficiently in any dimension.
