Emergent Quantum Walk Dynamics from Classical Interacting Particles

TL;DR

This paper demonstrates how discrete-time quantum walk dynamics can emerge from a classical system of interacting particles, providing a new minimal lattice model that mimics quantum behavior without wavefunctions.

Contribution

It introduces a classical particle system that reproduces quantum walk dynamics, bridging classical active matter models with quantum phenomena.

Findings

Classical particle system reproduces quantum walk behavior

Framework connects active matter with quantum dynamics

Provides a minimal lattice-based microscopic model

Abstract

The dynamics of a discrete-time quantum walk (DTQW) can be realized within a purely classical interacting particle system composed of some boxes and a large but finite number of balls, and can, in principle, be implemented in a tabletop experimental setting. The distribution of the balls evolves under stochastic, occupation-dependent update rules at each lattice site, producing quantum-walk dynamics without invoking a wavefunction. The update parameters are fixed by the parameters of coin and shift operations of the DTQW. This framework naturally yields a generalized active spin model and provides a minimal lattice-based microscopic understanding of the emergence of quantum-like dynamics in active matter systems. This interdisciplinary approach connects the classical models to the broad range of applications where DTQWs are successfully employed.