Effects of imperfect pulses on dynamical decoupling using quantum trajectory method<xref rid="cpb_27_12_120303fn1" ref-type="fn">*</xref><fn id="cpb_27_12_120303fn1"><label>*</label><p>Project supported by the National Basic Research Program of China (Grant No. 2016YFA0301903), the National Natural Science Foundation of China (Grant Nos. 11174370, 11304387, 61632021, 11305262, and 61205108), and the Research Plan Project of the National University of Defense Technology (Grant No. ZK16-03-04).</p></fn>

Effects of imperfect pulses on dynamical decoupling using quantum trajectory method**

Project supported by the National Basic Research Program of China (Grant No. 2016YFA0301903), the National Natural Science Foundation of China (Grant Nos. 11174370, 11304387, 61632021, 11305262, and 61205108), and the Research Plan Project of the National University of Defense Technology (Grant No. ZK16-03-04).

He Lin-Ze^{1, 2, 3}, Zhang Man-Chao^{1, 2, 3}, Wu Chun-Wang^{1, 2, 3}, Xie Yi^{1, 2, 3}, Wu Wei^{1, 2, 3}, Chen Ping-Xing^{1, 2, 3, †}

(color online) (a) CPMG sequence involves N π pulses evenly spaced at the time t between two π/2 pulses. The time interval between two π pulses is t/N. Each π pulse rotates the quantum state around the x-axis of the Bloch sphere, and the π/2 pulse rotates the state around the y-axis. (b) During the free-precession period, N π pulses change the phase accumulation direction alternately. It is described by a time-domain jump function s(t), with values indicating the phase accumulation direction. When a π pulse is operated, the value of the function is assumed to be zero.