Floquet engineering of continuous-time quantum walks: Toward the simulation of complex and next-nearest-neighbor couplings
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Abstract
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 paper, 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 and (ii) increasing the connectivity of the graph by simulating the presence of next-nearest-neighbor couplings. Our paper 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.