Efficiency of dynamical decoupling sequences in the presence of pulse errors

For a generic dynamical decoupling sequence employing a single-axis control, we study its efficiency in the presence of small errors in the direction of the controlling pulses. In the case that the corresponding ideal dynamical decoupling sequence produces sufficiently good results, the impact of the errors is found to scale as ξ2, with negligible first-order effect, where ξ is the dispersion of the random errors. This analytical prediction is numerically tested in a model in which the environment is modeled by one qubit coupled to a quantum kicked rotator in chaotic motion. In this model, with periodic pulses applied to the qubit in the environment, it is found numerically that periodic bang-bang control may outperform Uhrig dynamical decoupling.