paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs

TL;DR

This paper introduces paces, a GPU-optimized method for solving the time-dependent Schrödinger equation by dynamically constructing co-evolving subspaces, enabling efficient quantum dynamics simulations.

Contribution

The paper presents a novel parallel algorithm that constructs and updates subspaces for quantum dynamics on GPUs, improving efficiency for sparse Hamiltonians.

Findings

Benchmarking against multiset-MPS shows accurate results for 1D Holstein model.

Successfully applied to compute optical spectra of 1D, 2D, and 3D chromophore aggregates.

Method achieves efficient parallel computation of quantum dynamics on GPUs.

Abstract

An efficient method of solving the time-dependent Schr\"odinger equation for pure states is described: At each timestep, a restricted subspace of the 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 such that it co-evolves with the state vector. The method is built from the ground up as a parallel algorithm for graphics processing units and suited to Hamiltonians that are sparse in a given basis. We benchmark the method by comparing its results for a 1D Holstein model to previously published multiset-MPS results, and then apply the method to compute optical spectra and non-equilibrium dynamics of one-, two- and three-dimensional model chromophore nanoaggregates.