Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling

We investigate the form required for the time-dependent Rabi frequencies involved in a procedure capable to protect the action of quantum gates on an atomic qutrit by means of external fields continuously decoupling the system from the environmental noise. Several simulations are considered to protect the action of quantum-gate models, including randomly chosen ones. We argue that the requirements for the Rabi frequencies could be nowadays experimentally met. We also investigate the transition from one gate operation to another, including protecting a qutrit memory state. We finally apply our methodology to protect from noise the application of an algorithm capable of distinguishing the parity of permutations of three elements.