Optical realization of one-dimensional generalized split-step quantum walks

TL;DR

This paper presents an optical setup for implementing generalized split-step quantum walks, enabling simulation of complex quantum phenomena like topological effects, localization, and space-time curvature in a controlled, tabletop environment.

Contribution

It introduces a novel optical configuration for realizing generalized split-step quantum walks with position-dependent operations and flexible control over quantum dynamics.

Findings

Demonstrates optical implementation of split-step operators

Enables simulation of electric quantum walks and localization

Proposes a versatile setup for any t-step split-step walk

Abstract

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.