High order non-unitary split-step decomposition of unitary operators

We propose a high order numerical decomposition of exponentials of Hermitian operators in terms of a product of exponentials of simple terms, following an idea which has been pioneered by M Suzuki, implementing it for complex coefficients. We outline a convenient fourth-order formula which can be written compactly for an arbitrary number of non-commuting terms in the Hamiltonian and which is superior to the optimal formula with real coefficients, both in complexity and accuracy. We show asymptotic stability of our method for a sufficiently small time step and demonstrate its efficiency and accuracy in different numerical models.