# Source code for qiskit.aqua.operators.expectations.expectation_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.
""" ExpectationBase Class """
import logging
from typing import Union
from abc import abstractmethod
import numpy as np
from ..operator_base import OperatorBase
from ..converters import ConverterBase
logger = logging.getLogger(__name__)
[docs]class ExpectationBase(ConverterBase):
r"""
A base for Expectation value converters. Expectations are converters which enable the
computation of the expectation value of an Observable with respect to some state function.
They traverse an Operator tree, replacing OperatorStateFn measurements with equivalent
measurements which are more amenable to computation on quantum or classical hardware. For
example, if one would like to measure the expectation value of an Operator ``o`` expressed
as a sum of Paulis with respect to some state function, but only has access to diagonal
measurements on Quantum hardware, we can create a measurement ~StateFn(o),
use a ``PauliExpectation`` to convert it to a diagonal measurement and circuit
pre-rotations to a append to the state, and sample this circuit on Quantum hardware with
a CircuitSampler. All in all, this would be:
``my_sampler.convert(my_expect.convert(~StateFn(o)) @ my_state).eval()``.
"""
[docs] @abstractmethod
def convert(self, operator: OperatorBase) -> OperatorBase:
""" Accept an Operator and return a new Operator with the measurements replaced by
alternate methods to compute the expectation value.
Args:
operator: The operator to convert.
Returns:
The converted operator.
"""
raise NotImplementedError
[docs] @abstractmethod
def compute_variance(self, exp_op: OperatorBase) -> Union[list, float, complex, np.ndarray]:
""" Compute the variance of the expectation estimator.
Args:
exp_op: The full expectation value Operator after sampling.
Returns:
The variances or lists thereof (if exp_op contains ListOps) of the expectation value
estimation.
"""
raise NotImplementedError
```