Practical pulse engineering: Gradient ascent without matrix exponentiation

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