Title: Splitting methods for quantum dynamics and control
Advancements in quantum technologies are heavily dependent on the use of computational methods for the prediction of the dynamics of quantum systems, as well as automated techniques for their control and design. Of particular interest in this talk are quantum systems such as spins and electrons under the influence of external time-dependent controls such as lasers and magnetic fields.
The various ingredients required are: (i) numerical solvers for computing quantum dynamics (ii) procedures for computations of gradients and (iii) optimal control routines that are fast, accurate and conserve physical properties of the systems. The problem becomes particularly challenging in the presence of highly oscillatory external fields, unbounded potentials, long temporal windows of simulation, small quantum effects, need for high accuracy, and highly dimensionality.
In this talk I will present some recently developed Magnus expansion based exponential splitting methods for computing quantum dynamics under highly-oscillatory controls, efficient techniques for computing their exact derivatives, and an adaptive procedure for their optimal control called QOALA.