# Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques

## TL;DR

This paper presents a massively parallel computational framework utilizing Krylov subspace techniques and high-performance libraries to simulate quantum dynamics of extremely large systems, enabling new insights into thermalization.

## Contribution

It introduces a scalable parallel implementation for quantum dynamics simulation using Krylov subspace methods, capable of handling Hilbert spaces over 9 billion states.

## Key findings

- Studied quantum system evolution with large Hilbert spaces.
- Analyzed thermalization properties of many-body systems.
- Provided a scalable framework for quantum dynamics simulations.

## Abstract

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions on the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We employ our setup to study the evolution of quasidisordered and clean many-body systems, focussing on the return probability and related dynamical exponents: the large system sizes accessible provide novel insights into their thermalization properties.