Simulating the exchange of Majorana zero modes with a photonic system

TL;DR

This paper demonstrates a photonic quantum simulation of Majorana zero modes, enabling the study of their exchange statistics and error immunity without direct physical manipulation.

Contribution

It introduces a photonic simulation approach for Majorana zero modes using the Jordan-Wigner transformation, bypassing experimental challenges in direct exchange operations.

Findings

Probed the geometric phase associated with Majorana exchange

Demonstrated error immunity of Majorana-encoded quantum information

Showed the feasibility of simulating Majorana modes in photonic systems

Abstract

The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. Unfortunately, their exchange that can reveal their exotic statistics needs manipulations that are still beyond our experimental capabilities. Here we take an alternative approach. Through the Jordan-Wigner transformation, the Kitaev's chain supporting two Majorana zero modes is mapped to the spin-1/2 chain. We experimentally simulated the spin system and its evolution with a photonic quantum simulator. This allows us to probe the geometric phase, which corresponds to the exchange of two Majorana zero modes positioned at the ends of a three-site chain. Finally, we demonstrate the immunity of quantum information encoded in the Majorana zero modes against local errors through the simulator. Our photonic simulator opens the way for the efficient realization and manipulation of Majorana zero modes in complex architectures.