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

TL;DR

This paper introduces Floquet engineering techniques to simulate complex and highly connected continuous-time quantum walks, expanding experimental control over quantum transport and algorithm development.

Contribution

It presents a method to use periodically-driven Hamiltonians for simulating complex and next-to-nearest neighbor couplings in quantum walks, enhancing experimental capabilities.

Findings

Protocols for simulating complex couplings with broken time-reversal symmetry

Methods to increase graph connectivity via next-to-nearest neighbor couplings

Potential applications in quantum transport and dispersion engineering

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 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.