David L. Goodwin

TL;DR: In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.

TL;DR: In this article, the authors applied gradient ascent pulse engineering (grape) to optimize the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when averaged over atoms with an experimentally relevant range of velocities, beam intensities, and Zeeman states.

TL;DR: In this paper, the authors demonstrate that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself, leading to the possibility of using very efficient numerical optimization techniques.

TL;DR: Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory as mentioned in this paper.