Nonadiabatic holonomic one-qubit gates

Adiabatic quantum gate implementation generally takes longer time, which is disadvantageous in view of decoherence. In this report we implement several essential one-qubit quantum gates nonadiabatically by making use of a dynamical invariant associated with a Hamiltonian. Moreover we require that these gates be holonomic, that is, the dynamical phases associated with the gates vanish. Our implementation is based on our recent work [J. Phys. Soc. Jpn. 83, 034001 (2014)] and the gate parameters required for the implementations are found by numerical optimization.