  A novel optical method for distinguishing chiral molecules is proposed and
validated within a quantum simulator employing a trapped-ion qudit. This
approach correlates the sign disparity of the dipole moment of chiral molecules
with distinct cyclic evolution trajectories, yielding the unity population
contrast induced by the different non-Abelian holonomies corresponding to the
chirality. Harnessing the principles of holonomic quantum computation (HQC),
our method achieves highly efficient, non-adiabatic, and robust detection and
separation of chiral molecules. Demonstrated in a trapped ion quantum
simulator, this scheme achieves nearly 100% contrast between the two
enantiomers in the population of a specific state, showcasing its resilience to
the noise inherent in the driving field.
