Quantum walks are more than tools for building quantum algorithms. They have been used effectively to model and simulate quantum dynamics in many complex physical processes. Particularly, a variant of discrete-time quantum walk known as split-step quantum walk is closely related to Dirac cellular automata and topological insulators whose realizations rely on position-dependent control of evolution operators. Owing to the ease of manipulating multiple degrees of freedom of photons, we provide an optical setup of split-step operators which in combination with position-dependent coin (PDC) operation can accomplish a table-top setup of generalized split-step walks. Also, we propose an optical implementation for PDC operation that allows, for instance, to realize electric quantum walks, control localization dynamics, and emulate space-time curvature effects. In addition, we propose a setup to realize {\it any} t-step split-step quantum walk involving 2 J-plates, 2 variable waveplates, a half-waveplate, an optical switch, and an optical delay line.
@article{arxiv.2207.12341,
title = {Optical realization of one-dimensional generalized split-step quantum walks},
author = {P. A. Ameen Yasir and Abhaya S. Hegde and C. M. Chandrashekar},
journal= {arXiv preprint arXiv:2207.12341},
year = {2023}
}