Emergent nonlinear phenomena in discrete-time quantum walks

Abstract

Quantum walks are important tools for the development of quantum algorithms and carrying out quantum simulations. Recent interest in nonlinear discrete-time quantum walks aims to use it as a shortcut through dynamical regimes hard to obtain using current methods. We introduce a model featuring a modified conditional shift operator to carry dependence on the local occupation probability with a given strength we are able to control. It accounts for a third-order nonlinear contribution which is found in many physical contexts. We find a rich set of dynamical profiles, including solitonlike propagation, self-trapping, and chaos, all these arising from rather simple rules. Our tool set goes beyond unitary transformations, thus broadening the possibilities for controlling quantum dynamics.