majorana_to_fermion

majorana_to_fermion(maj_op)

Map a MajoranaOperator to a FermionOperator.

Parameters:

maj_op – the Majorana operator to map.

Returns:

The mapped fermion operator.

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Definition

This function implements the simple transformation:

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

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

Usage

>>> from qiskit_fermions.mappers.library import majorana_to_fermion
>>> from qiskit_fermions.operators import MajoranaOperator
>>> maj_op = MajoranaOperator.from_dict({(0, 1): 1})
>>> fer_op = majorana_to_fermion(maj_op)
>>> print(fer_op.normal_ordered().simplify())
 0.000000e0 -1.000000e0j * ()
 0.000000e0 +2.000000e0j * (+_0 -_0)