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Illuminated by the Pulse Width Modulation (PWM) technology in classicalcontrol engineering, we propose the PWM approximation which transformscontinuous and bang-bang control into each other. This method works bysqueezing the approximation error into high-frequency components above aprescribed cutoff frequency $\Omega$, which can be tailored by modulating theswitch time of the bang-bang control. Because the quantum dynamics underbang-bang control can be efficiently calculated, PWM allows us to speed upquantum control design particularly in large dimensional systems with smallnumber of control variables. Moreover, PWM paves the way to implement variousbang-bang control protocols in the literature with an arbitrary waveform, whichis more desirable in laboratory.

Pulse Width Modulation method for quantum control design