Quantum gates by periodic driving

Topological quantum computation has been extensively studied due to its robustness against decoherence. A conventional way to realize it is by adiabatic operations---it requires relatively long time to accomplish so that the speed of quantum computation slows down. In this work, we present a method to realize topological quantum computation by periodic driving. Compared to the adiabatic evolution, the total operation time can be regulated arbitrarily by the amplitude and frequency of the periodic driving. For the sinusoidal driving, we give an expression for the total operation time in the high-frequency limit. For the square wave driving, we derive an exact analytical expression for the evolution operator without any approximations, and show that the amplitude and frequency of driving field depend on its period and total operation time. This could provide a new direction in regulations of the operation time in topological quantum computation.