# A synthetic gauge field for two-dimensional time-multiplexed quantum random walks

## TL;DR

This paper demonstrates a 2D topological quantum random walk using synthetic gauge fields, leading to multiple bandgaps, spatial confinement, and topological edge states, expanding the simulation capabilities of photonic systems.

## Contribution

It introduces a novel 2D quantum random walk with synthetic gauge fields, showcasing topological features not previously realized in time-multiplexed photonic systems.

## Key findings

- Synthetic gauge fields induce multiple bandgaps.
- Spatial confinement observed in the random walk distribution.
- Topological edge states appear at domain interfaces.

## Abstract

Temporal multiplexing provides an efficient and scalable approach to realize a quantum random walk with photons that can exhibit topological properties. But two dimensional time-multiplexed topological quantum walks studied so far have relied on generalizations of the Su-Shreiffer-Heeger (SSH) model with no synthetic gauge field. In this work, we demonstrate a 2D topological quantum random walk where the non-trivial topology is due to the presence of a synthetic gauge field. We show that the synthetic gauge field leads to the appearance of multiple bandgaps and consequently, a spatial confinement of the random walk distribution. Moreover, we demonstrate topological edge states at an interface between domains with opposite synthetic fields. Our results expand the range of Hamiltonians that can be simulated using photonic random walks.