Simulating the exchange of Majorana zero modes with a photonic system

Jin-Shi Xu, Kai Sun, Yong-Jian Han (), Chuan-Feng Li (), Jiannis K. Pachos and Guang-Can Guo
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Jin-Shi Xu: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS
Kai Sun: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS
Yong-Jian Han: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS
Chuan-Feng Li: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS
Jiannis K. Pachos: School of Physics and Astronomy, University of Leeds
Guang-Can Guo: Key Laboratory of Quantum Information, University of Science and Technology of China, CAS

Nature Communications, 2016, vol. 7, issue 1, 1-8

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms13194

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