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T. Wu1 A. Kazakov1 G. Simion1 Z. Wan1 Y. Wang1 J. Liang1 K.W. West2 K.W. Baldwin2 L.N. Pfeiffer2 Y. Lyanda-Geller1 L.P. Rokhinson1 3

1, Purdue University, West Lafayette, Indiana, United States
2, Princeton University, Princeton, New Jersey, United States
3, Purdue University, West Lafayette, Indiana, United States

We introduce a new platform based on spin transitions in the fractional quantum Hall effect regime where parafermions - higher order non-abelian excitations - can be realized. Local (gate) control of spin transition allows formation of isolated domain walls, which consist of counter-propagating edge states of opposite polarization with fractional charge excitations. When superconductivity is induced into such a domain wall from superconducting contacts via proximity effect, arafermions are expected to be formed at the domain wall boundaries. In a multi-gate device a re-configurable network of domain walls can be formed allowing creation, braiding, manipulation and fusion of parafermions. In respect to the quantum computing application parafermons are more computationally intense han Majoranas and are a building block for Fibonacci fermions, even high order non-Abelian particles that can perform universal gate operations within the opologically protected subspace.

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