Abstract: We start with reviews on quantum computation and braiding of Majorana fermions. Then, we show that only the braiding of Majorana fermions is not enough for universal quantum computation due to the embedding problem, where certain gates including the CNOT gate cannot be embedded in larger qubits. This problem is solved by introducing many-body Majorana operators [1]. We also derive analytic formula for short Kitaev chain describing low-energy theory [2], which will be useful for recent experimental realization of Majorana fermions in quantum dots [3]. Finally, we show that an N-connected honeycomb chain of the Kitaev spin liquid model acts as 3N+2 qubits [4] and discuss how to braid and execute fusion based on local spin correlation operators.
[1] M. Ezawa, Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
arXiv:2304.06260
[2] M. Ezawa, Robustness of Majorana edge states of short-length Kitaev chains coupled with environment, arXiv:2310.18083
[3] Tom Dvir, et. al. Realization of a minimal Kitaev chain in coupled quantum dots,
Nature 614, 445 (2023).
[4] M. Ezawa, Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with 5 qubits, arXiv:2401.01051