map_edge_vertex_generators

map_edge_vertex_generators(operator, map_action, identity, compose=None)

Map a EdgeVertexOperator to another operator type.

This is a generic function to aid in implementing new mappers for EdgeVertexOperator instances. At its core, it simply iterates over the terms of the operator, mapping each encountered EdgeAction with the user-provided map_action function. In combination with the user-provided identity generator, this allows mapping to arbitrary output types.

Note

The output type T must support multiplication by a scalar via __mul__. If compose=None it must also support composition of two instances via __and__. SparseObservable does not, which is why the example below names compose() explicitly; a type with an __and__ (such as SparsePauliOp) can rely on the default.

Note

The mapping written out below is a deliberately minimal illustration of this function, not a replacement for edge_vertex_jordan_wigner(): it covers only nearest-neighbor interactions, and it is neither parallelized nor memory-bounded. Reach for the library function rather than copying this one.

>>> from qiskit_fermions.mappers import map_edge_vertex_generators
>>> from qiskit_fermions.operators import EdgeAction, EdgeVertexOperator
>>> from qiskit.quantum_info import SparseObservable
>>>
>>> def jordan_wigner_nearest_neighbor(mode: EdgeAction) -> SparseObservable:
...     left, right = mode
...     if left == right:
...         return SparseObservable.from_sparse_list(
...             [("Z", [left], 1.0)], num_qubits=num_qubits
...         )
...     if abs(left - right) != 1:
...         raise NotImplementedError(
...             "This mapping only handles nearest neighbor interactions"
...         )
...     # The orientation must be compared rather than differenced: an edge operator is
...     # antisymmetric, so the sign depends on the index order while the string does not.
...     lo, hi = min(left, right), max(left, right)
...     coeff = -1.0 if left < right else 1.0
...     return SparseObservable.from_sparse_list(
...         [("YX", [lo, hi], coeff)], num_qubits=num_qubits
...     )
>>>
>>> num_qubits = 4
>>> def identity() -> SparseObservable:
...     return SparseObservable.identity(num_qubits)
>>>
>>> op = EdgeVertexOperator.from_dict({
...     ((0, 0),): 2.0,
...     ((0, 1),): 0.5,
...     ((1, 1), (1, 2)): 1.0,
... })
>>> qop = map_edge_vertex_generators(
...     op, jordan_wigner_nearest_neighbor, identity, compose=SparseObservable.compose
... )
>>> print(sorted(qop.simplify().to_sparse_list()))
[('XX', [1, 2], 1j), ('YX', [0, 1], (-0.5+0j)), ('Z', [0], (2+0j))]
Parameters:

  • operator (EdgeVertexOperator) – the operator to be mapped.

  • map_action (Callable[[tuple[int, int]], T]) – the function to map a single EdgeAction to the desired output type.

  • identity (Callable[[], T]) – the function to generate the multiplicative identity instance of the output type.

  • compose (Callable[[T, T], T] | None) – an optional function to implement the compositiion logic of two output type instances. If this is not provided, it will default to using operator.and_().

Returns:

The mapped operator.

Return type:

T