Braiding Majorana fermions yields non-Clifford gates in the Z4 parafermion representation, and braiding Z4 parafermions yields non-Clifford gates in the Majorana representation, enabling a conceptual route to universal topological quantum computation.
This implies that : ic′ = c3 & −icc′ = 1 (C4) since c4 = 1 , this implies ic′c = 1 & −icc′ = 1 (C5) which is a contradiction
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Generating non-Clifford gate operations through exact mapping between Majorana fermions and $\mathbb{Z}_4$ parafermions
Braiding Majorana fermions yields non-Clifford gates in the Z4 parafermion representation, and braiding Z4 parafermions yields non-Clifford gates in the Majorana representation, enabling a conceptual route to universal topological quantum computation.