# majorana_to_fermion

### majorana_to_fermion(maj_op)

Map a [`MajoranaOperator`](qiskit_fermions.operators.MajoranaOperator.html.md#qiskit_fermions.operators.MajoranaOperator) to a [`FermionOperator`](qiskit_fermions.operators.FermionOperator.html.md#qiskit_fermions.operators.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

```pycon
>>> 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)
```