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The formalism of continuous-time quantum walks on graphs has been widely usedin the study of quantum transport of energy and information, as well as in thedevelopment of quantum algorithms. In experimental settings, however, there islimited control over the coupling coefficients between the different nodes ofthe graph (which are usually considered to be real-valued), thereby restrictingthe types of quantum walks that can be implemented. In this work, we apply theidea of Floquet engineering in the context of continuous-time quantum walks,i.e., we define periodically-driven Hamiltonians which can be used to simulatethe dynamics of certain target continuous-time quantum walks. We focus on twomain applications: i) simulating quantum walks that break time-reversalsymmetry due to complex coupling coefficients; ii) increasing the connectivityof the graph by simulating the presence of next-to-nearest neighbor couplings.Our work provides explicit simulation protocols that may be used for directingquantum transport, engineering the dispersion relation of one-dimensionalquantum walks or investigating quantum dynamics in highly connected structures.

Floquet engineering of continuous-time quantum walks: towards the simulation of complex and next-to-nearest neighbor couplings