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.

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(format(fer_op.normal_ordered().simplify()))
 0.000000e0 +1.000000e0j * ()
 0.000000e0 -2.000000e0j * (+0 -0)