Low-complexity approximations with least-squares formulation of the time-dependent Schr{ö}dinger equation

Abstract: We propose new methods designed to numerically approximate the solution to the time dependent Schr{\"o}dinger equation, based on two types of ansatz: tensors, and approximation by a linear combination of gaussian wave packets. In both cases, the method can be seen as a restricted optimization problem, which can be solved by adapting either the Alternating Least Square algorithm in the tensor case, or some greedy algorithm in the gaussian wavepacket case. We also discuss the efficiency of both approaches.