Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions
Qing Yan(闫青)1,2 and Qing-Feng Sun(孙庆丰)1,3,4,†
1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; 2 CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China; 3 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; 4 Beijing Academy of Quantum Information Sciences, Beijing 100193, China
Abstract Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can. Realizing the quantum computation requires the universal quantum gate set {T, H, CNOT} so as to perform any unitary transformation with arbitrary accuracy. Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions. Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures, which enable the braiding operation and the partial exchange operation. After defining a qubit by four chiral Majorana fermions, the single-qubit T and H quantum gates are realized via one partial exchange operation and three braiding operations, respectively. The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions. Besides, we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device. Thus, our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.
Fund: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303301), the National Natural Science Foundation of China (Grant No. 11921005), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and Beijing Municipal Science & Technology Commission, China (Grant No. Z191100007219013).
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