TimeEvolver: A Program for Time Evolution With Improved Error Bound
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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 i H, 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 (R. Sidje, ACM Trans. Math. Softw. 24 (1) 1998). On a standard notebook, TimeEvolver allows to compute time evolution with adjustable precision in Hilbert spaces of dimension greater than 10^6. Additionally, we provide routines for deriving the matrix H from a more abstract representation of the Hamiltonian operator.
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