Claudius Hubig - Time Evolution with a Krylov Variant for MPS Time Evolution with a Krylov Variant for MPS

I will briefly motivate the need for time-evolution methods on matrix-product states and provide an overview over the available methods. Focus will then be placed on the Krylov subspace method to evaluate exp(-tH)|ψ❭, starting from a naive translation of the standard method suitable for dense matrix-vector arithmetic to matrix-product arithmetic. Key improvements that can be made to the algorithm when applied to matrix-product arithmetics will then be illustrated, resulting in increased precision and reduced computational effort.