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

Marlon Brenes, Vipin Kerala Varma, Antonello Scardicchio, Ivan Girotto

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.

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