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.
Highlights
The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations
In this study we experimentally investigated the physics of Majorana zero modes (MZMs) emerging in the Kitaev Chain Model (KCM) by simulating it with an equivalent photonic system
We were able to transport two MZMs at the endpoints of a chain and measure the geometric phases resulting from their exchange
Summary
The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. 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. We demonstrate the immunity of quantum information encoded in the Majorana zero modes against local errors through the simulator. The simulated system has only two Majoranas (separated by a gap from all other excitations), any adiabatic manipulation can only result in a U(1) Â U(1) transformation that carries the hallmark of their anyonic statistics In this way, we are able to demonstrate the exchange of two MZMs in a three-site Kitaev chain encoded in the spatial modes of photons.
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