  The application of high-dimensional quantum systems (qudits) in quantum
computing and communications seems to be a promising avenue due to the
possibility of increasing the amount of information encoded in one physical
carrier. In this work, we propose a method for implementing single-qudit gates
for qudits based on light modes with orbital angular momentum. Method for
logical qudits encoding, which ensures the quasi-cyclicity of operations, is
introduced. Based on the protocol for converting the orbital angular momentum
of light in the Raman quantum memory scheme [Vashukevich E.A. et. al. PRA, 101,
033830 (2020)], we show that the considered gates provide an extremely high
level of fidelity of single-qudit transformations. We also compare quantum
gates' properties for systems of different dimensions and find the optimal
conditions for carrying out transformations in the protocol under
consideration.
