majorana_ternary_tree

majorana_ternary_tree(op, encoding, num_qubits)

Map a MajoranaOperator to a 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().

Raises:

ValueError – if op acts on a mode the encoding does not cover. Note that Majorana index \(m\) acts on mode \(\lfloor m/2 \rfloor\).

Usage

>>> 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.