# Code source de qiskit.opflow.gradients.derivative_base

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
""" DerivativeBase Class """
import warnings
from abc import abstractmethod
from typing import Callable, Iterable, List, Optional, Tuple, Union
import numpy as np
from qiskit.utils.quantum_instance import QuantumInstance
from qiskit.circuit import ParameterExpression, ParameterVector
from qiskit.providers import BaseBackend, Backend
from ..converters.converter_base import ConverterBase
from ..expectations import ExpectationBase, PauliExpectation
from ..list_ops.composed_op import ComposedOp
from ..list_ops.list_op import ListOp
from ..list_ops.tensored_op import TensoredOp
from ..operator_base import OperatorBase
from ..primitive_ops.primitive_op import PrimitiveOp
from ..state_fns import StateFn, OperatorStateFn
OperatorType = Union[StateFn, PrimitiveOp, ListOp]
[docs]class DerivativeBase(ConverterBase):
r"""Base class for differentiating opflow objects.
Converter for differentiating opflow objects and handling
things like properly differentiating combo_fn's and enforcing product rules
when operator coefficients are parameterized.
This is distinct from CircuitGradient converters which use quantum
techniques such as parameter shifts and linear combination of unitaries
to compute derivatives of circuits.
CircuitGradient - uses quantum techniques to get derivatives of circuits
DerivativeBase - uses classical techniques to differentiate opflow data structures
"""
# pylint: disable=arguments-differ
[docs] @abstractmethod
def convert(
self,
operator: OperatorBase,
params: Optional[
Union[ParameterVector, ParameterExpression, List[ParameterExpression]]
] = None,
) -> OperatorBase:
r"""
Args:
operator: The operator we are taking the gradient, Hessian or QFI of
params: The parameters we are taking the gradient, Hessian or QFI with respect to.
Returns:
An operator whose evaluation yields the gradient, Hessian or QFI.
Raises:
ValueError: If ``params`` contains a parameter not present in ``operator``.
"""
raise NotImplementedError
[docs] def gradient_wrapper(
self,
operator: OperatorBase,
bind_params: Union[ParameterExpression, ParameterVector, List[ParameterExpression]],
grad_params: Optional[
Union[
ParameterExpression,
ParameterVector,
List[ParameterExpression],
Tuple[ParameterExpression, ParameterExpression],
List[Tuple[ParameterExpression, ParameterExpression]],
]
] = None,
backend: Optional[Union[BaseBackend, Backend, QuantumInstance]] = None,
expectation: Optional[ExpectationBase] = None,
) -> Callable[[Iterable], np.ndarray]:
"""Get a callable function which provides the respective gradient, Hessian or QFI for given
parameter values. This callable can be used as gradient function for optimizers.
Args:
operator: The operator for which we want to get the gradient, Hessian or QFI.
bind_params: The operator parameters to which the parameter values are assigned.
grad_params: The parameters with respect to which we are taking the gradient, Hessian
or QFI. If grad_params = None, then grad_params = bind_params
backend: The quantum backend or QuantumInstance to use to evaluate the gradient,
Hessian or QFI.
expectation: The expectation converter to be used. If none is set then
`PauliExpectation()` is used.
Returns:
Function to compute a gradient, Hessian or QFI. The function
takes an iterable as argument which holds the parameter values.
"""
from ..converters import CircuitSampler
if not grad_params:
grad_params = bind_params
grad = self.convert(operator, grad_params)
if expectation is None:
expectation = PauliExpectation()
grad = expectation.convert(grad)
def gradient_fn(p_values):
p_values_dict = dict(zip(bind_params, p_values))
if not backend:
converter = grad.assign_parameters(p_values_dict)
return np.real(converter.eval())
else:
p_values_dict = {k: [v] for k, v in p_values_dict.items()}
converter = CircuitSampler(backend=backend).convert(grad, p_values_dict)
return np.real(converter.eval()[0])
return gradient_fn
[docs] @staticmethod
def parameter_expression_grad(
param_expr: ParameterExpression, param: ParameterExpression
) -> Union[ParameterExpression, float]:
"""Get the derivative of a parameter expression w.r.t. the given parameter.
Args:
param_expr: The Parameter Expression for which we compute the derivative
param: Parameter w.r.t. which we want to take the derivative
Returns:
ParameterExpression representing the gradient of param_expr w.r.t. param
"""
warnings.warn(
"The DerivativeBase.parameter_expression_grad method is deprecated as of "
"Qiskit Terra 0.18.0 and will be removed no earlier than 3 months after "
"the release date. Use the ParameterExpression.gradient method instead for "
"a direct replacement.",
DeprecationWarning,
stacklevel=2,
)
return _coeff_derivative(param_expr, param)
@classmethod
def _erase_operator_coeffs(cls, operator: OperatorBase) -> OperatorBase:
"""This method traverses an input operator and deletes all of the coefficients
Args:
operator: An operator type object.
Returns:
An operator which is equal to the input operator but whose coefficients
have all been set to 1.0
Raises:
TypeError: If unknown operator type is reached.
"""
if isinstance(operator, PrimitiveOp):
return operator / operator.coeff
op_coeff = operator.coeff # type: ignore
return (operator / op_coeff).traverse(cls._erase_operator_coeffs)
@classmethod
def _factor_coeffs_out_of_composed_op(cls, operator: OperatorBase) -> OperatorBase:
"""Factor all coefficients of ComposedOp out into a single global coefficient.
Part of the automatic differentiation logic inside of Gradient and Hessian
counts on the fact that no product or chain rules need to be computed between
operators or coefficients within a ComposedOp. To ensure this condition is met,
this function traverses an operator and replaces each ComposedOp with an equivalent
ComposedOp, but where all coefficients have been factored out and placed onto the
ComposedOp. Note that this cannot be done properly if an OperatorMeasurement contains
a SummedOp as it's primitive.
Args:
operator: The operator whose coefficients are being re-organized
Returns:
An operator equivalent to the input operator, but whose coefficients have been
reorganized
Raises:
ValueError: If an element within a ComposedOp has a primitive of type ListOp,
then it is not possible to factor all coefficients out of the ComposedOp.
"""
if isinstance(operator, ListOp) and not isinstance(operator, ComposedOp):
return operator.traverse(cls._factor_coeffs_out_of_composed_op)
if isinstance(operator, ComposedOp):
total_coeff = operator.coeff
take_norm_of_coeffs = False
for k, op in enumerate(operator.oplist):
if take_norm_of_coeffs:
total_coeff *= op.coeff * np.conj(op.coeff) # type: ignore
else:
total_coeff *= op.coeff # type: ignore
if hasattr(op, "primitive"):
prim = op.primitive # type: ignore
if isinstance(op, StateFn) and isinstance(prim, TensoredOp):
# Check if any of the coefficients in the TensoredOp is a
# ParameterExpression
for prim_op in prim.oplist:
# If a coefficient is a ParameterExpression make sure that the
# coefficients are pulled together correctly
if isinstance(prim_op.coeff, ParameterExpression):
prim_tensored = StateFn(
prim.reduce(), is_measurement=op.is_measurement, coeff=op.coeff
)
operator.oplist[k] = prim_tensored
return operator.traverse(cls._factor_coeffs_out_of_composed_op)
elif isinstance(prim, ListOp):
raise ValueError(
"This operator was not properly decomposed. "
"By this point, all operator measurements should "
"contain single operators, otherwise the coefficient "
"gradients will not be handled properly."
)
if hasattr(prim, "coeff"):
if take_norm_of_coeffs:
total_coeff *= prim._coeff * np.conj(prim._coeff)
else:
total_coeff *= prim._coeff
if isinstance(op, OperatorStateFn) and op.is_measurement:
take_norm_of_coeffs = True
return cls._erase_operator_coeffs(operator).mul(total_coeff)
else:
return operator
def _coeff_derivative(coeff, param):
if isinstance(coeff, ParameterExpression) and len(coeff.parameters) > 0:
return coeff.gradient(param)
return 0
```