Practical Pulse Engineering: Gradient Ascent Without Matrix Exponentiation

Abstract: 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.