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.op_transforms import OperationTransformError
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 OperationTransformError(
"Input is not an Operator, tape, QNode, or quantum function"
)
return _eigvals_tranform(op, k=k, which=which)
if isinstance(op, qml.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
_modules/pennylane/ops/functions/eigvals
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