---
title: Mapper Library (latest version)
description: API reference for Mapper Library in the latest version of qiskit-fermions-c
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-fermions-c/qf-mappers-library
---

# Mapper Library

The C API provides efficient implementations of commonly used operator representation mapper routines.

|                                                                                      |                                                                                                                                                                                                                       |
| ------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| [`qf_ferm_op_jordan_wigner()`](#qf_ferm_op_jordan_wigner "qf_ferm_op_jordan_wigner") | Map a [`QfFermionOperator`](/docs/api/qiskit-fermions-c/qf-ferm-op#qffermionoperator "QfFermionOperator") to a [QkObs](/docs/api/qiskit-c/qk-obs) under the Jordan-Wigner transformation.                             |
| [`qf_fermion_to_majorana()`](#qf_fermion_to_majorana "qf_fermion_to_majorana")       | Map a [`QfFermionOperator`](/docs/api/qiskit-fermions-c/qf-ferm-op#qffermionoperator "QfFermionOperator") to a [`QfMajoranaOperator`](/docs/api/qiskit-fermions-c/qf-maj-op#qfmajoranaoperator "QfMajoranaOperator"). |
| [`qf_majorana_to_fermion()`](#qf_majorana_to_fermion "qf_majorana_to_fermion")       | Map a [`QfMajoranaOperator`](/docs/api/qiskit-fermions-c/qf-maj-op#qfmajoranaoperator "QfMajoranaOperator") to a [`QfFermionOperator`](/docs/api/qiskit-fermions-c/qf-ferm-op#qffermionoperator "QfFermionOperator"). |

***

### qf\_ferm\_op\_jordan\_wigner

`QfExitCode qf_ferm_op_jordan_wigner(const QfFermionOperator *op, uint32_t num_qubits, QkObs **out)`

Applies the Jordan-Wigner transformation to an operator.

Map a [`QfFermionOperator`](/docs/api/qiskit-fermions-c/qf-ferm-op#qffermionoperator "QfFermionOperator") to a [QkObs](/docs/api/qiskit-c/qk-obs) under the Jordan-Wigner transformation.   [\[1\]](#id2)

#### Definition

The Jordan-Wigner transformation maps fermionic creation and annihilation operators to spin (or in this case, qubit) operators:

$$
a^\dagger_j \rightarrow \bigotimes_{k\lt j} \sigma^Z_k \otimes \sigma^-_j ~~\text{and}~~
a_j \rightarrow \bigotimes_{k\lt j} \sigma^Z_k \otimes \sigma^+_j \, ,
$$

where $a^\dagger_j$ ($a_j$) is the fermionic creation (annihilation) operator acting on the $j$-th spin-less fermionic mode, $\sigma^P$ with $P \in \{X,Y,Z\}$ are the spin-$\frac{1}{2}$ Pauli operators and $\sigma^\pm = (\sigma^X \pm \mathrm{i} \sigma^Y) / 2$.

This mapping preserves the fermionic anti-commutation relations by introducing a chain of $\sigma^Z$ operators on all qubits preceding the acted-upon index $j$.

\[[1](#id1)]

P. Jordan and E. Wigner, Über das Paulische Äquivalenzverbot, Zeitschrift für Physik 47, No. 9. (1928), pp. 631–651, [doi:10.1007/BF01331938](https://link.springer.com/article/10.1007/BF01331938).

#### Example

```c
1// define some kind of fermionic operator
2QfFermionOperator *hamil = qf_ferm_op_one();
3
4// and map it to a qubit operator
5QkObs *result;
6QfExitCode exit = qf_ferm_op_jordan_wigner(hamil, 4, &result);
7
8assert(exit == QfExitCode_Success);
```

**Parameters**

- **op** – A pointer to the fermionic operator to be mapped.
- **num\_qubits** – The number of qubits of the resulting operator. This must be strictly greater than the largest mode index acted upon by `op`.
- **out** – A pointer to where the created qubit operator will be written on success. It is left untouched if the transformation fails.

**Returns**

An exit code. This is `>0` if an error occurred. In particular, a `QfExitCode_ValueError` is returned if `num_qubits` is too small to hold the operator’s support.

### qf\_fermion\_to\_majorana

`QfMajoranaOperator *qf_fermion_to_majorana(const QfFermionOperator *fer_op)`

Map a `QfFermionOperator` to a `QfMajoranaOperator`.

#### 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 [`QfMajoranaOperator`](/docs/api/qiskit-fermions-c/qf-maj-op#qfmajoranaoperator "QfMajoranaOperator") these will be stored on the even and odd Majorana modes, respectively.

#### Example

```c
1// define some kind of fermionic operator
2QfFermionOperator *fer_op = qf_ferm_op_one();
3
4// and map it to a majorana operator
5QfMajoranaOperator *maj_op = qf_fermion_to_majorana(fer_op);
```

**Parameters**

- **fer\_op** – A pointer to the fermionic operator to be mapped.

**Returns**

A pointer to the mapped majorana operator.

### qf\_majorana\_to\_fermion

`QfFermionOperator *qf_majorana_to_fermion(const QfMajoranaOperator *maj_op)`

Map a `QfMajoranaOperator` to a `QfFermionOperator`.

#### 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.

#### Example

```c
1// define some kind of majorana operator
2QfMajoranaOperator *maj_op = qf_maj_op_one();
3
4// and map it to a fermion operator
5QfFermionOperator *fer_op = qf_majorana_to_fermion(maj_op);
```

**Parameters**

- **maj\_op** – A pointer to the majorana operator to be mapped.

**Returns**

A pointer to the mapped fermion operator.