Source code for pennylane.ops.functions.eigvals

# Copyright 2018-2022 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#     http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This module contains the qml.eigvals function.
"""
from typing import Sequence, Callable
import warnings

# pylint: disable=protected-access
from functools import reduce, partial
import scipy

import pennylane as qml
from pennylane.transforms import TransformError
from pennylane import transform
from pennylane.typing import TensorLike


[docs]def eigvals(op: qml.operation.Operator, k=1, which="SA") -> TensorLike: r"""The eigenvalues of one or more operations. .. note:: - For a :class:`~.SparseHamiltonian` object, the eigenvalues are computed with the efficient ``scipy.sparse.linalg.eigsh`` method which returns :math:`k` eigenvalues. The default value of :math:`k` is :math:`1`. For an :math:`N \times N` sparse matrix, :math:`k` must be smaller than :math:`N - 1`, otherwise ``scipy.sparse.linalg.eigsh`` fails. If the requested :math:`k` is equal or larger than :math:`N - 1`, the regular ``qml.math.linalg.eigvalsh`` is applied on the dense matrix. For more details see the ``scipy.sparse.linalg.eigsh`` `documentation <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html#scipy.sparse.linalg.eigsh>`_. - A second-quantized :mod:`molecular Hamiltonian <pennylane.qchem.molecular_hamiltonian>` is independent of the number of electrons and its eigenspectrum contains the energies of the neutral and charged molecules. Therefore, the `smallest` eigenvalue returned by ``qml.eigvals`` for a molecular Hamiltonian might not always correspond to the neutral molecule. Args: op (Operator or QNode or QuantumTape or Callable): A quantum operator or quantum circuit. k (int): The number of eigenvalues to be returned for a :class:`~.SparseHamiltonian`. which (str): Method for computing the eigenvalues of a :class:`~.SparseHamiltonian`. The possible methods are ``'LM'`` (largest in magnitude), ``'SM'`` (smallest in magnitude), ``'LA'`` (largest algebraic), ``'SA'`` (smallest algebraic) and ``'BE'`` (:math:`k/2` from each end of the spectrum). Returns: TensorLike or qnode (QNode) or quantum function (Callable) or tuple[List[QuantumTape], function]: If an operator is provided as input, the eigenvalues are returned directly in the form of a tensor. Otherwise, the transformed circuit is returned as described in :func:`qml.transform <pennylane.transform>`. Executing this circuit will provide the eigenvalues as a tensor. **Example** Given an operation, ``qml.eigvals`` returns the eigenvalues: >>> op = qml.Z(0) @ qml.X(1) - 0.5 * qml.Y(1) >>> qml.eigvals(op) array([-1.11803399, -1.11803399, 1.11803399, 1.11803399]) It can also be used in a functional form: >>> x = torch.tensor(0.6, requires_grad=True) >>> eigval_fn = qml.eigvals(qml.RX) >>> eigval_fn(x, wires=0) tensor([0.9553+0.2955j, 0.9553-0.2955j], grad_fn=<LinalgEigBackward>) In its functional form, it is fully differentiable with respect to gate arguments: >>> loss = torch.real(torch.sum(eigval_fn(x, wires=0))) >>> loss.backward() >>> x.grad tensor(-0.2955) This operator transform can also be applied to QNodes, tapes, and quantum functions that contain multiple operations; see Usage Details below for more details. .. details:: :title: Usage Details ``qml.eigvals`` can also be used with QNodes, tapes, or quantum functions that contain multiple operations. However, in this situation, **eigenvalues may be computed numerically**. This can lead to a large computational overhead for a large number of wires. Consider the following quantum function: .. code-block:: python3 def circuit(theta): qml.RX(theta, wires=1) qml.Z(0) We can use ``qml.eigvals`` to generate a new function that returns the eigenvalues corresponding to the function ``circuit``: >>> eigvals_fn = qml.eigvals(circuit) >>> theta = np.pi / 4 >>> eigvals_fn(theta) array([ 0.92387953+0.38268343j, 0.92387953-0.38268343j, -0.92387953+0.38268343j, -0.92387953-0.38268343j]) """ if not isinstance(op, qml.operation.Operator): if not isinstance(op, (qml.tape.QuantumScript, qml.QNode)) and not callable(op): raise TransformError("Input is not an Operator, tape, QNode, or quantum function") return _eigvals_tranform(op, k=k, which=which) if isinstance(op, qml.ops.Hamiltonian): warnings.warn( "For Hamiltonians, the eigenvalues will be computed numerically. " "This may be computationally intensive for a large number of wires. " "Consider using a sparse representation of the Hamiltonian with qml.SparseHamiltonian.", UserWarning, ) return qml.math.linalg.eigvalsh(qml.matrix(op)) if isinstance(op, qml.SparseHamiltonian): sparse_matrix = op.sparse_matrix() if k < sparse_matrix.shape[0] - 1: return scipy.sparse.linalg.eigsh(sparse_matrix, k=k, which=which)[0] return qml.math.linalg.eigvalsh(sparse_matrix.toarray()) # TODO: make `eigvals` take a `wire_order` argument to mimic `matrix` try: return op.eigvals() except qml.operation.EigvalsUndefinedError: return eigvals(op.expand(), k=k, which=which)
@partial(transform, is_informative=True) def _eigvals_tranform( tape: qml.tape.QuantumTape, k=1, which="SA" ) -> (Sequence[qml.tape.QuantumTape], Callable): def processing_fn(res): [qs] = res op_wires = [op.wires for op in qs.operations] all_wires = qml.wires.Wires.all_wires(op_wires).tolist() unique_wires = qml.wires.Wires.unique_wires(op_wires).tolist() if len(all_wires) != len(unique_wires): warnings.warn( "For multiple operations, the eigenvalues will be computed numerically. " "This may be computationally intensive for a large number of wires.", UserWarning, ) matrix = qml.matrix(qs, wire_order=qs.wires) return qml.math.linalg.eigvals(matrix) # TODO: take into account wire ordering, by reordering eigenvalues # as per operator wires/wire ordering, and by inserting implicit identity # matrices (eigenvalues [1, 1]) at missing locations. ev = [eigvals(op, k=k, which=which) for op in qs.operations] if len(ev) == 1: return ev[0] return reduce(qml.math.kron, ev) return [tape], processing_fn