Quantum Gates with Different Robust Merits

A protocol for implementing a universal set of quantum gates, which are safeguarded from noise through geometric, dephasing-free, and dynamical-decoupling approaches is proposed. With properly designed Hamiltonians, the desired interactions are realized directly within the Schr & ouml;dinger picture rather than relying on the interaction picture. This design confers two advantages. One is that the system's evolution remains continuously protected by the noise-mitigation strategies at every stage, eliminating the need to revert to the Schr & ouml;dinger picture. The other one is that the dynamical decoupling technique effectively averages out small residual free terms in the system's Hamiltonian, thus reducing the stringent requirements for precise control of system parameters to avoid errors. Furthermore, numerical results are presented to support our protocol by finding gate fidelities in the absence (presence) of noises or errors, without or with dynamical decoupling technique.