# majorana_ternary_tree

### majorana_ternary_tree(op, encoding, num_qubits)

Map a [`MajoranaOperator`](qiskit_fermions.operators.MajoranaOperator.html.md#qiskit_fermions.operators.MajoranaOperator) to a [`SparseObservable`](https://quantum.cloud.ibm.com/docs/api/qiskit/qiskit.quantum_info.SparseObservable) under a
ternary-tree encoding.

Each Majorana operator’s image is a single Pauli string, whatever the tree, so a term that is a
product of several of them composes those strings rather than inflating into a sum.

* **Parameters:**
  * **op** – the Majorana operator to map.
  * **encoding** – the compiled encoding to map through.
  * **num_qubits** – the number of qubits for the resulting qubit operator. Must be at least the
    encoding’s mode count; a larger value pads with the identity.
* **Returns:**
  The mapped qubit operator, subject to the same simplification and grouping caveats as
  [`fermion_ternary_tree()`](qiskit_fermions.mappers.library.fermion_ternary_tree.html.md#qiskit_fermions.mappers.library.fermion_ternary_tree).
* **Raises:**
  * [**ValueError**](https://docs.python.org/3/builtins/exceptions.html#ValueError) – if `op` acts on a mode the encoding does not cover, or `num_qubits` is
        smaller than the encoding’s mode count. Note that Majorana index $m$ acts on mode
        $\lfloor m/2 \rfloor$.
  * [**OverflowError**](https://docs.python.org/3/builtins/exceptions.html#OverflowError) – if `num_qubits` is negative or does not fit in 32 bits.

## Usage

```pycon
>>> from qiskit_fermions.mappers import TernaryTree, TernaryTreeEncoding
>>> from qiskit_fermions.mappers.library import majorana_ternary_tree
>>> from qiskit_fermions.operators import MajoranaOperator
>>> mop = MajoranaOperator.from_dict({(0, 1): 1.0})
>>> enc = TernaryTreeEncoding(TernaryTree.breadth_first(2, 3))
>>> majorana_ternary_tree(mop, enc, 2).simplify()
<SparseObservable with 1 term on 2 qubits: (0+1j)(Z_1 Z_0)>
```

Note that the product of two Majorana strings carries a phase that depends on how their paths
overlap, and so on the tree.