paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
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Abstract
An efficient method of computing the dynamics of a pure quantum state under the time-dependent Schrödinger equation is described: At each timestep, a restricted subspace of the potentially infinite-dimensional total Hilbert space is systematically and naturally constructed via the image of repeated applications of the Hamiltonian operator, and the time evolution is computed exactly within said subspace. The subspace is dynamically recomputed at each timestep such that it co-evolves with the state vector. We benchmark the method using the Holstein model and compare the formal information content of its representation to the matrix-product state formalism. The method is built from the ground up as a parallel algorithm for graphics processing units and is applicable to arbitrary Hamiltonians that are sparse in a given basis. It can be extended to open quantum system dynamics and/or time-dependent generators.