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