Non-adiabatic non-Abelian geometric phase of spin-3/2 system in the rotating magnetic field is considered. Explicit expression for the corresponding effective non-Abelian gauge potential is obtained. This formula can be used for construction of quantum gates in quantum computations.
@article{arxiv.quant-ph/0110015,
title = {On non-Adiabatic Holonomoic Quantum Computer},
author = {A. E. Margolin and V. I. Strazhev and A. Ya. Tregubovich},
journal= {arXiv preprint arXiv:quant-ph/0110015},
year = {2009}
}