Photonic quantum walks with four-dimensional coins

TL;DR

This paper demonstrates an experimental realization of a four-dimensional coin quantum walk on a line and other graphs, revealing multiple propagation speeds and showcasing the platform's scalability and versatility for complex quantum walk dynamics.

Contribution

The work introduces a scalable experimental platform for four-dimensional coin quantum walks, enabling exploration of richer dynamics and boundary conditions beyond traditional two-dimensional coin systems.

Findings

Multiple ballistic propagation speeds observed

Successful implementation on various graph structures

Platform supports arbitrary 4x4 unitary coin operations

Abstract

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain range of dynamics on complex graphs, higher dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work we present an experimental realization of a discrete-time quantum walk on a line graph that, instead of two-dimensional, exhibits a four-dimensional coin space. Making use of the extra degree of freedom we observe multiple ballistic propagation speeds specific to higher dimensional coin operators. By implementing a scalable technique, we demonstrate quantum walks on circles of various sizes, as well as on an example of a Husimi cactus graph. The quantum walks are realized via time-multiplexing in a Michelson interferometer loop architecture, employing as the coin degrees of freedom the polarization and the traveling direction of the pulses in the loop. Our theoretical analysis shows that the platform supports implementations of quantum walks with arbitrary $4 \times 4$ unitary coin operations, and usual quantum walks on a line with various periodic and twisted boundary conditions.