fermion_to_majorana

fermion_to_majorana(fer_op)

Map a FermionOperator to a MajoranaOperator.

Parameters:

fer_op – the fermionic operator to map.

Returns:

The mapped majorana operator.

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Definition

This function implements the simple transformation:

\[a^\dagger_j \rightarrow \frac{1}{2} (\gamma_j - i \gamma'_j) ~~\text{and}~~ a_j \rightarrow \frac{1}{2} (\gamma_j + i \gamma'_j)\]

where \(a^\dagger_j\) (\(a_j\)) is the fermionic creation (annihilation) operator acting on the \(j\)-th spin-less fermionic mode, and \(\gamma_j\)/\(\gamma'_j\) are the two Majorana fermion operators. In the case of the MajoranaOperator these will be stored on the even and odd Majorana modes, respectively.

Usage

>>> from qiskit_fermions.mappers.library import fermion_to_majorana
>>> from qiskit_fermions.operators import FermionOperator
>>> fer_op = FermionOperator.from_dict({((True, 0), (False, 0)): 1})
>>> maj_op = fermion_to_majorana(fer_op)
>>> print(maj_op.normal_ordered().simplify())
 5.000000e-1 +0.000000e0j * ()
 0.000000e0+5.000000e-1j * (1 0)