Jordan-Wigner transformation and qubits with nontrivial exchange rule

Alexander Yu. Vlasov

Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Even in standard model with local fermionic modes formally only the 'occupied' state |1> is truly relevant for Fermi-Dirac statistics, but 'vacuum' state |0> is not. Introduction of exchange rule for such fermionic qubits indexed by some 'positions' may look questionable due to general super-selection principle. However, a consistent algebraic construction of such 'super-indexed' qubits is presented in this work. Considered method has some relation with construction of super-spaces, but it has some differences with standard definition of supersymmety sometimes used for generalizations of qubit model.

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