qml.liealg.op_to_adjvec

op_to_adjvec(ops, basis, is_orthogonal=True)

Decompose a batch of operators into a given operator basis.

The adjoint vector representation is provided by the coefficients $c_j$ in a given operator basis of the operator $\hat{b}_j$ such that the input operator can be written as $\hat{O} = \sum_j c_j \hat{b}_j$.

See also

adjvec_to_op()

Parameters

• ops (Iterable[Union[PauliSentence, Operator, TensorLike]]) – List of operators to decompose.

• basis (Iterable[Union[PauliSentence, Operator, TensorLike]]) – Operator basis.

• is_orthogonal (bool) – Whether the basis is orthogonal with respect to the trace inner product. Defaults to True, which allows to skip some computations.

Returns

The batch of coefficient vectors of the operators’ ops expressed in basis. The shape is (len(ops), len(basis).

Return type

TensorLike

The format of the resulting operators is determined by the type in basis. If is_orthogonal=True (the default), only normalization is taken into account in the projection. For is_orthogonal=False, orthogonalization also is considered.

Example

The basis can be numerical or operators.

>>> from pennylane.liealg import op_to_adjvec
>>> op = qml.X(0) + 0.5 * qml.Y(0)
>>> basis = [qml.X(0), qml.Y(0), qml.Z(0)]
>>> op_to_adjvec([op], basis)
array([[1. , 0.5, 0. ]])
>>> op_to_adjvec([op], [op.matrix() for op in basis])
array([[1. , 0.5, 0. ]])

Note how the function always expects an Iterable of operators as input.

The ops can also be numerical, but then basis has to be numerical as well.

>>> op = op.matrix()
>>> op_to_adjvec([op], [op.matrix() for op in basis])
array([[1. , 0.5, 0. ]])

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