# Source code for pyquil.experiment._result

```
##############################################################################
# Copyright 2016-2019 Rigetti Computing
#
# 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.
##############################################################################
"""
Schema definition of an ExperimentResult, which encapsulates the outcome of a collection of
measurements that are aimed at estimating the expectation value of some observable.
"""
import logging
from dataclasses import dataclass
from typing import Any, Dict, List, Optional, Union
import numpy as np
from pyquil.experiment._setting import ExperimentSetting
log = logging.getLogger(__name__)
[docs]@dataclass(frozen=True)
class ExperimentResult:
"""An expectation and standard deviation for the measurement of one experiment setting
in a tomographic experiment.
In the case of readout error calibration, we also include
expectation, standard deviation and count for the calibration results, as well as the
expectation and standard deviation for the corrected results.
"""
setting: ExperimentSetting
expectation: Union[float, complex]
total_counts: int
std_err: Optional[Union[float, complex]] = None
raw_expectation: Optional[Union[float, complex]] = None
raw_std_err: Optional[float] = None
calibration_expectation: Optional[Union[float, complex]] = None
calibration_std_err: Optional[Union[float, complex]] = None
calibration_counts: Optional[int] = None
additional_results: Optional[List["ExperimentResult"]] = None
def __init__(
self,
setting: ExperimentSetting,
expectation: Union[float, complex],
total_counts: int,
std_err: Optional[Union[float, complex]] = None,
raw_expectation: Optional[Union[float, complex]] = None,
raw_std_err: Optional[Union[float, complex]] = None,
calibration_expectation: Optional[Union[float, complex]] = None,
calibration_std_err: Optional[Union[float, complex]] = None,
calibration_counts: Optional[int] = None,
additional_results: Optional[List["ExperimentResult"]] = None,
):
object.__setattr__(self, "setting", setting)
object.__setattr__(self, "expectation", expectation)
object.__setattr__(self, "total_counts", total_counts)
object.__setattr__(self, "raw_expectation", raw_expectation)
object.__setattr__(self, "calibration_expectation", calibration_expectation)
object.__setattr__(self, "calibration_counts", calibration_counts)
object.__setattr__(self, "additional_results", additional_results)
object.__setattr__(self, "std_err", std_err)
object.__setattr__(self, "raw_std_err", raw_std_err)
object.__setattr__(self, "calibration_std_err", calibration_std_err)
def __str__(self) -> str:
return f"{self.setting}: {self.expectation} +- {self.std_err}"
def __repr__(self) -> str:
return f"ExperimentResult[{self}]"
[docs] def serializable(self) -> Dict[str, Any]:
return {
"type": "ExperimentResult",
"setting": self.setting,
"expectation": self.expectation,
"std_err": self.std_err,
"total_counts": self.total_counts,
"raw_expectation": self.raw_expectation,
"raw_std_err": self.raw_std_err,
"calibration_expectation": self.calibration_expectation,
"calibration_std_err": self.calibration_std_err,
"calibration_counts": self.calibration_counts,
}
[docs]def bitstrings_to_expectations(
bitstrings: np.ndarray, joint_expectations: Optional[List[List[int]]] = None
) -> np.ndarray:
"""
Given an array of bitstrings (each of which is represented as an array of bits), map them to
expectation values and return the desired joint expectation values. If no joint expectations
are desired, then just the 1 -> -1, 0 -> 1 mapping is performed.
:param bitstrings: Array of bitstrings to map.
:param joint_expectations: Joint expectation values to calculate. Each entry is a list which
contains the qubits to use in calculating the joint expectation value. Entries of length
one just calculate single-qubit expectation values. Defaults to None, which is equivalent
to the list of single-qubit expectations [[0], [1], ..., [n-1]] for bitstrings of length n.
:return: An array of expectation values, of the same length as the array of bitstrings. The
"width" could be different than the length of an individual bitstring (n) depending on
the value of the ``joint_expectations`` parameter.
"""
expectations: np.ndarray = 1 - 2 * bitstrings
if joint_expectations is None:
return expectations
region_size = len(expectations[0])
e = []
for c in joint_expectations:
where = np.zeros(region_size, dtype=bool)
where[c] = True
e.append(np.prod(expectations[:, where], axis=1))
return np.stack(e, axis=-1)
[docs]def correct_experiment_result(
result: ExperimentResult,
calibration: ExperimentResult,
) -> ExperimentResult:
"""
Given a raw, unmitigated result and its associated readout calibration, produce the result
absent readout error.
:param result: An ``ExperimentResult`` object with unmitigated readout error.
:param calibration: An ``ExperimentResult`` object resulting from running readout calibration
on the ``ExperimentSetting`` associated with the ``result`` parameter.
:return: An ``ExperimentResult`` object corrected for symmetric readout error.
"""
corrected_expectation = result.expectation / calibration.expectation
# combine standard errors (are we assuming the counts are the same?)
assert result.std_err is not None and calibration.std_err is not None
corrected_variance = ratio_variance(
result.expectation, result.std_err ** 2, calibration.expectation, calibration.std_err ** 2 # type: ignore
)
# recursively apply to additional results
additional_results = None
if result.additional_results is not None and calibration.additional_results:
assert len(result.additional_results) == len(calibration.additional_results)
additional_results = [
correct_experiment_result(r, c) for r, c in zip(result.additional_results, calibration.additional_results)
]
return ExperimentResult(
setting=result.setting,
expectation=corrected_expectation,
std_err=np.sqrt(corrected_variance).item(),
total_counts=result.total_counts,
raw_expectation=result.expectation,
raw_std_err=result.std_err,
calibration_expectation=calibration.expectation,
calibration_std_err=calibration.std_err,
calibration_counts=calibration.total_counts,
additional_results=additional_results,
)
[docs]def ratio_variance(
a: Union[float, np.ndarray],
var_a: Union[float, np.ndarray],
b: Union[float, np.ndarray],
var_b: Union[float, np.ndarray],
) -> Union[float, np.ndarray]:
r"""
Given random variables 'A' and 'B', compute the variance on the ratio Y = A/B. Denote the
mean of the random variables as a = E[A] and b = E[B] while the variances are var_a = Var[A]
and var_b = Var[B] and the covariance as Cov[A,B]. The following expression approximates the
variance of Y
Var[Y] \approx (a/b) ^2 * ( var_a /a^2 + var_b / b^2 - 2 * Cov[A,B]/(a*b) )
We assume the covariance of A and B is negligible, resting on the assumption that A and B
are independently measured. The expression above rests on the assumption that B is non-zero,
an assumption which we expect to hold true in most cases, but makes no such assumptions
about A. If we allow E[A] = 0, then calculating the expression above via numpy would complain
about dividing by zero. Instead, we can re-write the above expression as
Var[Y] \approx var_a /b^2 + (a^2 * var_b) / b^4
where we have dropped the covariance term as noted above.
See the following for more details:
- https://doi.org/10.1002/(SICI)1097-0320(20000401)39:4<300::AID-CYTO8>3.0.CO;2-O
- http://www.stat.cmu.edu/~hseltman/files/ratio.pdf
- https://w.wiki/EMh
:param a: Mean of 'A', to be used as the numerator in a ratio.
:param var_a: Variance in 'A'
:param b: Mean of 'B', to be used as the numerator in a ratio.
:param var_b: Variance in 'B'
"""
return var_a / b ** 2 + (a ** 2 * var_b) / b ** 4
```