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Demonstrating non-Abelian statistics of Majorana fermions using twist defects
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We study the twist defects in the toric code model introduced by Bombin [Phys. Rev. Lett. 105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner transformation, we show explicitly the twist defects carry unpaired Majorana zero modes. We also draw the same conclusion using two alternative approaches of a perturbation theory and a projective construction. We propose a quantum non-demolition measurement scheme of the parity of Majorana modes. Such a scheme provides an alternative avenue to demonstrate the non-Abelian statistics of Majorana fermions with measurement-based braidings.
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Practical gates by Majorana fermion motion
Majorana fermion motion serves as a primitive for braiding-based logical gates in stabilizer codes, enabling denser packing and numerical outperformance of lattice surgery for 2-qubit Clifford gates under near-term noise.
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