Effects of imperfect pulses on dynamical decoupling using quantum trajectory method

The dynamical decoupling(DD) method is widely adopted to preserve coherence in different quantum systems. In the case of ideal pulses, its effects on the suppression of noise can be analytically described by the mathematical form of filter function. However, in practical experiments, the unavoidable pulse errors limit the efficiency of DD. In this paper,we study the effects of imperfect pulses on DD efficiency based on quantum trajectories. By directly generating a pseudo noise sequence correlated in time, we can explore the performance of DD with different pulse errors in the typical noise environment. It shows that, for the typical 1/f noise environment, the phase error of operational pulses severely affects the performance of noise suppression, while the detuning and intensity errors have less influence. Also, we get the thresholds of these errors for efficient DD under the given experimental conditions. Our method can be widely applied to guide practical DD experimental implementation.