  Since 2005 there has been a huge growth in the use of engineered control
pulses to perform desired quantum operations in systems such as NMR quantum
information processors. These approaches, which build on the original gradient
ascent pulse engineering (GRAPE) algorithm, remain computationally intensive
because of the need to calculate matrix exponentials for each time step in the
control pulse. Here we discuss how the propagators for each time step can be
approximated using the Trotter--Suzuki formula, and a further speed up achieved
by avoiding unnecessary operations. The resulting procedure can give a
substantial speed gain with negligible cost in propagator error, providing a
more practical approach to pulse engineering.
