  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.
