# Source code for pennylane._grad

```
# Copyright 2018-2021 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 autograd wrappers :class:`grad` and :func:`jacobian`
"""
import warnings
from autograd import jacobian as _jacobian
from autograd.core import make_vjp as _make_vjp
from autograd.numpy.numpy_boxes import ArrayBox
from autograd.extend import vspace
from autograd.wrap_util import unary_to_nary
make_vjp = unary_to_nary(_make_vjp)
[docs]class grad:
"""Returns the gradient as a callable function of (functions of) QNodes.
By default, gradients are computed for arguments which contain the property
``requires_grad=True``. Alternatively, the ``argnum`` keyword argument can
be specified to compute gradients for function arguments without this property,
such as scalars, lists, tuples, dicts, or vanilla NumPy arrays. Setting
``argnum`` to the index of an argument with ``requires_grad=False`` will raise
a ``NonDifferentiableError``.
When the output gradient function is executed, both the forward pass
*and* the backward pass will be performed in order to
compute the gradient. The value of the forward pass is available via the
:attr:`~.forward` property.
.. warning::
``grad`` is intended to be used with the Autograd interface only.
Args:
func (function): a plain QNode, or a Python function that contains
a combination of quantum and classical nodes
argnum (int, list(int), None): Which argument(s) to take the gradient
with respect to. By default, the arguments themselves are used
to determine differentiability, by examining the ``requires_grad``
property.
Returns:
function: The function that returns the gradient of the input
function with respect to the differentiable arguments, or, if specified,
the arguments in ``argnum``.
"""
def __init__(self, fun, argnum=None):
self._forward = None
self._grad_fn = None
self._fun = fun
self._argnum = argnum
if self._argnum is not None:
# If the differentiable argnum is provided, we can construct
# the gradient function at once during initialization.
# Known pylint issue with function signatures and decorators:
# pylint:disable=unexpected-keyword-arg,no-value-for-parameter
self._grad_fn = self._grad_with_forward(fun, argnum=argnum)
def _get_grad_fn(self, args):
"""Get the required gradient function.
* If the differentiable argnum was provided on initialization,
this has been pre-computed and is available via self._grad_fn
* Otherwise, we must dynamically construct the gradient function by
inspecting as to which of the parameter arguments are marked
as differentiable.
"""
if self._grad_fn is not None:
return self._grad_fn, self._argnum
# Inspect the arguments for differentiability, and
# compute the autograd gradient function with required argnums
# dynamically.
argnum = []
for idx, arg in enumerate(args):
trainable = getattr(arg, "requires_grad", None) or isinstance(arg, ArrayBox)
if trainable:
argnum.append(idx)
if len(argnum) == 1:
argnum = argnum[0]
# Known pylint issue with function signatures and decorators:
# pylint:disable=unexpected-keyword-arg,no-value-for-parameter
return self._grad_with_forward(self._fun, argnum=argnum), argnum
[docs] def __call__(self, *args, **kwargs):
"""Evaluates the gradient function, and saves the function value
calculated during the forward pass in :attr:`.forward`."""
grad_fn, argnum = self._get_grad_fn(args)
if not isinstance(argnum, int) and not argnum:
warnings.warn(
"Attempted to differentiate a function with no trainable parameters. "
"If this is unintended, please add trainable parameters via the "
"'requires_grad' attribute or 'argnum' keyword."
)
self._forward = self._fun(*args, **kwargs)
return ()
grad_value, ans = grad_fn(*args, **kwargs) # pylint: disable=not-callable
self._forward = ans
return grad_value
@property
def forward(self):
"""float: The result of the forward pass calculated while performing
backpropagation. Will return ``None`` if the backpropagation has not yet
been performed."""
return self._forward
@staticmethod
@unary_to_nary
def _grad_with_forward(fun, x):
"""This function is a replica of ``autograd.grad``, with the only
difference being that it returns both the gradient *and* the forward pass
value."""
vjp, ans = _make_vjp(fun, x)
if not vspace(ans).size == 1:
raise TypeError(
"Grad only applies to real scalar-output functions. "
"Try jacobian, elementwise_grad or holomorphic_grad."
)
grad_value = vjp(vspace(ans).ones())
return grad_value, ans
[docs]def jacobian(func, argnum=None):
"""Returns the Jacobian as a callable function of vector-valued
(functions of) QNodes.
This is a wrapper around the :mod:`autograd.jacobian` function.
Args:
func (function): A vector-valued Python function or QNode that contains
a combination of quantum and classical nodes. The output of the computation
must consist of a single NumPy array (if classical) or a tuple of
expectation values (if a quantum node)
argnum (int or Sequence[int]): Which argument to take the gradient
with respect to. If a sequence is given, the Jacobian corresponding
to all marked inputs and all output elements is returned.
Returns:
function: the function that returns the Jacobian of the input
function with respect to the arguments in argnum
.. note::
Due to a limitation in Autograd, this function can only differentiate built-in scalar
or NumPy array arguments.
For ``argnum=None``, the trainable arguments are inferred dynamically from the arguments
passed to the function. The returned function takes the same arguments as the original
function and outputs a ``tuple``. The ``i`` th entry of the ``tuple`` has shape
``(*output shape, *shape of args[argnum[i]])``.
If a single trainable argument is inferred, or if a single integer
is provided as ``argnum``, the tuple is unpacked and its only entry is returned instead.
**Example**
Consider the QNode
.. code-block::
dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(weights):
qml.RX(weights[0, 0, 0], wires=0)
qml.RY(weights[0, 0, 1], wires=1)
qml.RZ(weights[1, 0, 2], wires=0)
return qml.probs()
weights = np.array(
[[[0.2, 0.9, -1.4]], [[0.5, 0.2, 0.1]]], requires_grad=True
)
It has a single array-valued QNode argument with shape ``(2, 1, 3)`` and outputs
the probability of each 2-wire basis state, of which there are ``2**num_wires`` = 4.
Therefore, the Jacobian of this QNode will be a single array with shape ``(2, 2, 1, 3)``:
>>> qml.jacobian(circuit)(weights).shape
(4, 2, 1, 3)
On the other hand, consider the following QNode for the same circuit
structure:
.. code-block::
dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(x, y, z):
qml.RX(x, wires=0)
qml.RY(y, wires=1)
qml.RZ(z, wires=0)
return tuple(qml.expval(qml.PauliZ(w)) for w in dev.wires)
x = np.array(0.2, requires_grad=True)
y = np.array(0.9, requires_grad=True)
z = np.array(-1.4, requires_grad=True)
It has three scalar QNode arguments and outputs the probability for each of
the 4 basis states. Consequently, its Jacobian will be a three-tuple of
arrays with the shape ``(4,)``:
>>> jac = qml.jacobian(circuit)(x, y, z)
>>> type(jac)
tuple
>>> for sub_jac in jac:
... print(sub_jac.shape)
(4,)
(4,)
(4,)
For a more advanced setting of QNode arguments, consider the QNode
.. code-block::
dev = qml.device("default.qubit", wires=3)
@qml.qnode(dev)
def circuit(x, y):
qml.RX(x[0], wires=0)
qml.RY(y[0, 3], wires=1)
qml.RX(x[1], wires=2)
return [qml.expval(qml.PauliZ(w)) for w in [0, 1, 2]]
x = np.array([0.1, 0.5], requires_grad=True)
y = np.array([[-0.3, 1.2, 0.1, 0.9], [-0.2, -3.1, 0.5, -0.7]], requires_grad=True)
If we do not provide ``argnum``, ``qml.jacobian`` will correctly identify both,
``x`` and ``y``, as trainable function arguments:
>>> jac = qml.jacobian(circuit)(x, y)
>>> print(type(jac), len(jac))
<class 'tuple'> 2
>>> qml.math.shape(jac[0])
(8, 2)
>>> qml.math.shape(jac[1])
(8, 2, 4)
As we can see, there are two entries in the output, one Jacobian for each
QNode argument. The shape ``(8, 2)`` of the first Jacobian is the combination
of the QNode output shape (``(8,)``) and the shape of ``x`` (``(2,)``).
Similarly, the shape ``(2, 4)`` of ``y`` leads to a Jacobian shape ``(8, 2, 4)``.
Instead we may choose the output to contain only one of the two
entries by providing an iterable as ``argnum``:
>>> jac = qml.jacobian(circuit, argnum=[1])(x, y)
>>> print(type(jac), len(jac))
<class 'tuple'> 1
>>> qml.math.shape(jac)
(1, 8, 2, 4)
Here we included the size of the tuple in the shape analysis, corresponding to the
first dimension of size ``1``.
Finally, we may want to receive the single entry above directly, not as a tuple
with a single entry. This is done by providing a single integer as ``argnum``
>>> jac = qml.jacobian(circuit, argnum=1)(x, y)
>>> print(type(jac), len(jac))
<class 'numpy.ndarray'> 8
>>> qml.math.shape(jac)
(8, 2, 4)
As expected, the tuple was unpacked and we directly received the Jacobian of the
QNode with respect to ``y``.
"""
# pylint: disable=no-value-for-parameter
def _get_argnum(args):
"""Inspect the arguments for differentiability and return the
corresponding indices."""
argnum = []
for idx, arg in enumerate(args):
trainable = getattr(arg, "requires_grad", None) or isinstance(arg, ArrayBox)
if trainable:
argnum.append(idx)
return argnum
def _jacobian_function(*args, **kwargs):
"""Compute the autograd Jacobian.
This wrapper function is returned to the user instead of autograd.jacobian,
so that we can take into account cases where the user computes the
jacobian function once, but then calls it with arguments that change
in differentiability.
"""
if argnum is None:
# Infer which arguments to consider trainable
_argnum = _get_argnum(args)
# Infer whether to unpack from the inferred argnum
unpack = len(_argnum) == 1
else:
# For a single integer as argnum, unpack the Jacobian tuple
unpack = isinstance(argnum, int)
_argnum = [argnum] if unpack else argnum
if not _argnum:
warnings.warn(
"Attempted to differentiate a function with no trainable parameters. "
"If this is unintended, please add trainable parameters via the "
"'requires_grad' attribute or 'argnum' keyword."
)
jac = tuple(_jacobian(func, arg)(*args, **kwargs) for arg in _argnum)
return jac[0] if unpack else jac
return _jacobian_function
```

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