TimeEvolver: A program for time evolution with improved error bound

Published: 3 May 2022| Version 1 | DOI: 10.17632/vvwvng9w36.1


We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where H is the Hamiltonian, with an initial vector v. The fact that H is Hermitian makes it possible to provide an easily computable bound on the accuracy of the Krylov approximation. Apart from effects of numerical roundoff, the resulting a posteriori error bound is rigorous, which represents a crucial novelty as compared to existing software packages such as Expokit [1]. On a standard notebook, TimeEvolver allows to compute time evolution with adjustable precision in Hilbert spaces of dimension greater than 106. Additionally, we provide routines for deriving the matrix H from a more abstract representation of the Hamiltonian operator.



Condensed Matter Physics, Computational Physics, Quantum Mechanics, Schrödinger Equation