  Illuminated by the Pulse Width Modulation (PWM) technology in classical
control engineering, we propose the PWM approximation which transforms
continuous and bang-bang control into each other. This method works by
squeezing the approximation error into high-frequency components above a
prescribed cutoff frequency $\Omega$, which can be tailored by modulating the
switch time of the bang-bang control. Because the quantum dynamics under
bang-bang control can be efficiently calculated, PWM allows us to speed up
quantum control design particularly in large dimensional systems with small
number of control variables. Moreover, PWM paves the way to implement various
bang-bang control protocols in the literature with an arbitrary waveform, which
is more desirable in laboratory.
