# Source code for pennylane.measurements.measurements

```
# 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 functions for computing different types of measurement
outcomes from quantum observables - expectation values, variances of expectations,
and measurement samples using AnnotatedQueues.
"""
import contextlib
import copy
import functools
from abc import ABC, abstractmethod
from enum import Enum
from typing import Sequence, Tuple, Optional
import numpy as np
import pennylane as qml
from pennylane.operation import Operator
from pennylane.wires import Wires
from .shots import Shots
# =============================================================================
# ObservableReturnTypes types
# =============================================================================
class ObservableReturnTypes(Enum):
"""Enumeration class to represent the return types of an observable."""
Sample = "sample"
Counts = "counts"
AllCounts = "allcounts"
Variance = "var"
Expectation = "expval"
Probability = "probs"
State = "state"
MidMeasure = "measure"
VnEntropy = "vnentropy"
MutualInfo = "mutualinfo"
Shadow = "shadow"
ShadowExpval = "shadowexpval"
Purity = "purity"
def __repr__(self):
"""String representation of the return types."""
return str(self.value)
Sample = ObservableReturnTypes.Sample
"""Enum: An enumeration which represents sampling an observable."""
Counts = ObservableReturnTypes.Counts
"""Enum: An enumeration which represents returning the number of times
each of the observed outcomes occurred in sampling."""
AllCounts = ObservableReturnTypes.AllCounts
"""Enum: An enumeration which represents returning the number of times
each of the possible outcomes occurred in sampling, including 0 counts
for unobserved outcomes."""
Variance = ObservableReturnTypes.Variance
"""Enum: An enumeration which represents returning the variance of
an observable on specified wires."""
Expectation = ObservableReturnTypes.Expectation
"""Enum: An enumeration which represents returning the expectation
value of an observable on specified wires."""
Probability = ObservableReturnTypes.Probability
"""Enum: An enumeration which represents returning probabilities
of all computational basis states."""
State = ObservableReturnTypes.State
"""Enum: An enumeration which represents returning the state in the computational basis."""
MidMeasure = ObservableReturnTypes.MidMeasure
"""Enum: An enumeration which represents returning sampling the computational
basis in the middle of the circuit."""
VnEntropy = ObservableReturnTypes.VnEntropy
"""Enum: An enumeration which represents returning Von Neumann entropy before measurements."""
MutualInfo = ObservableReturnTypes.MutualInfo
"""Enum: An enumeration which represents returning the mutual information before measurements."""
Shadow = ObservableReturnTypes.Shadow
"""Enum: An enumeration which represents returning the bitstrings and recipes from
the classical shadow protocol"""
ShadowExpval = ObservableReturnTypes.ShadowExpval
"""Enum: An enumeration which represents returning the estimated expectation value
from a classical shadow measurement"""
Purity = ObservableReturnTypes.Purity
"""Enum: An enumeration which represents returning the purity of the system prior ot measurement."""
class MeasurementShapeError(ValueError):
"""An error raised when an unsupported operation is attempted with a
quantum tape."""
[docs]class MeasurementProcess(ABC):
"""Represents a measurement process occurring at the end of a
quantum variational circuit.
Args:
obs (.Operator): The observable that is to be measured as part of the
measurement process. Not all measurement processes require observables (for
example ``Probability``); this argument is optional.
wires (.Wires): The wires the measurement process applies to.
This can only be specified if an observable was not provided.
eigvals (array): A flat array representing the eigenvalues of the measurement.
This can only be specified if an observable was not provided.
id (str): custom label given to a measurement instance, can be useful for some applications
where the instance has to be identified
"""
# pylint: disable=too-many-arguments
def __init__(
self,
obs: Optional[Operator] = None,
wires: Optional[Wires] = None,
eigvals=None,
id: Optional[str] = None,
):
self.obs = obs
self.id = id
if wires is not None:
if len(wires) == 0:
raise ValueError("Cannot set an empty list of wires.")
if obs is not None:
raise ValueError("Cannot set the wires if an observable is provided.")
# _wires = None indicates broadcasting across all available wires.
# It translates to the public property wires = Wires([])
self._wires = wires
self._eigvals = None
if eigvals is not None:
if obs is not None:
raise ValueError("Cannot set the eigenvalues if an observable is provided.")
self._eigvals = np.array(eigvals)
# TODO: remove the following lines once devices
# have been refactored to accept and understand receiving
# measurement processes rather than specific observables.
# The following lines are only applicable for measurement processes
# that do not have corresponding observables (e.g., Probability). We use
# them to 'trick' the device into thinking it has received an observable.
# Below, we imitate an identity observable, so that the
# device undertakes no action upon receiving this observable.
self.name = "Identity"
self.data = []
# Queue the measurement process
self.queue()
@property
def return_type(self) -> Optional[ObservableReturnTypes]:
"""Measurement return type."""
return None
@property
def numeric_type(self) -> type:
"""The Python numeric type of the measurement result.
Returns:
type: The output numeric type; ``int``, ``float`` or ``complex``.
Raises:
QuantumFunctionError: the return type of the measurement process is
unrecognized and cannot deduce the numeric type
"""
raise qml.QuantumFunctionError(
f"The numeric type of the measurement {self.__class__.__name__} is not defined."
)
def _shape_legacy(self, device, shots: Shots) -> Tuple: # pylint: disable=unused-arguments
"""The expected output shape of the MeasurementProcess.
Note that the output shape is dependent on the shots and device when:
* The measurement type is either ``ProbabilityMP``, ``StateMP`` (from :func:`.state`) or
``SampleMP``;
* The shot vector was defined.
For example, assuming a circuit with ``shots=None``, expectation values
and variances define ``shape=(1,)``, whereas probabilities in the qubit
model define ``shape=(1, 2**num_wires)`` where ``num_wires`` is the
number of wires the measurement acts on.
Note that the shapes for vector-valued measurements such as
``ProbabilityMP`` and ``StateMP`` are adjusted to the output of
``qml.execute`` and may have an extra first element that is squeezed
when using QNodes.
Args:
device (pennylane.Device): a PennyLane device to use for determining the shape
shots (~.Shots): object defining the number and batches of shots
Returns:
Tuple: the output shape
Raises:
QuantumFunctionError: the return type of the measurement process is
unrecognized and cannot deduce the numeric type
"""
raise qml.QuantumFunctionError(
f"The shape of the measurement {self.__class__.__name__} is not defined"
)
[docs] def shape(self, device, shots: Shots) -> Tuple:
"""The expected output shape of the MeasurementProcess.
Note that the output shape is dependent on the shots or device when:
* The measurement type is either ``_Probability``, ``_State`` (from :func:`.state`) or
``_Sample``;
* The shot vector was defined.
For example, assuming a device with ``shots=None``, expectation values
and variances define ``shape=(,)``, whereas probabilities in the qubit
model define ``shape=(2**num_wires)`` where ``num_wires`` is the
number of wires the measurement acts on.
Args:
device (pennylane.Device): a PennyLane device to use for determining the shape
shots (~.Shots): object defining the number and batches of shots
Returns:
tuple: the output shape
Raises:
QuantumFunctionError: the return type of the measurement process is
unrecognized and cannot deduce the numeric type
"""
if not qml.active_return():
return self._shape_legacy(device, shots)
raise qml.QuantumFunctionError(
f"The shape of the measurement {self.__class__.__name__} is not defined"
)
@staticmethod
@functools.lru_cache()
def _get_num_basis_states(num_wires, device):
"""Auxiliary function to determine the number of basis states given the
number of systems and a quantum device.
This function is meant to be used with the Probability measurement to
determine how many outcomes there will be. With qubit based devices
we'll have two outcomes for each subsystem. With continuous variable
devices that impose a Fock cutoff the number of basis states per
subsystem equals the cutoff value.
Args:
num_wires (int): the number of qubits/qumodes
device (pennylane.Device): a PennyLane device
Returns:
int: the number of basis states
"""
cutoff = getattr(device, "cutoff", None)
base = 2 if cutoff is None else cutoff
return base**num_wires
[docs] def diagonalizing_gates(self):
"""Returns the gates that diagonalize the measured wires such that they
are in the eigenbasis of the circuit observables.
Returns:
List[.Operation]: the operations that diagonalize the observables
"""
try:
# pylint: disable=no-member
return self.expand().operations
except qml.operation.DecompositionUndefinedError:
return []
def __repr__(self):
"""Representation of this class."""
if self.obs is None:
if self._eigvals is None:
return f"{self.return_type.value}(wires={self.wires.tolist()})"
return f"{self.return_type.value}(eigvals={self._eigvals}, wires={self.wires.tolist()})"
# Todo: when tape is core the return type will always be taken from the MeasurementProcess
if getattr(self.obs, "return_type", None) is None:
return f"{self.return_type.value}({self.obs})"
return f"{self.obs}"
def __copy__(self):
cls = self.__class__
copied_m = cls.__new__(cls)
for attr, value in vars(self).items():
setattr(copied_m, attr, value)
if self.obs is not None:
copied_m.obs = copy.copy(self.obs)
return copied_m
@property
def wires(self):
r"""The wires the measurement process acts on.
This is the union of all the Wires objects of the measurement.
"""
if self.obs is not None:
return self.obs.wires
return (
Wires.all_wires(self._wires)
if isinstance(self._wires, list)
else self._wires or Wires([])
)
@property
def raw_wires(self):
r"""The wires the measurement process acts on.
For measurements involving more than one set of wires (such as
mutual information), this is a list of the Wires objects. Otherwise,
this is the same as :func:`~.MeasurementProcess.wires`
"""
return self._wires
[docs] def eigvals(self):
r"""Eigenvalues associated with the measurement process.
If the measurement process has an associated observable,
the eigenvalues will correspond to this observable. Otherwise,
they will be the eigenvalues provided when the measurement
process was instantiated.
Note that the eigenvalues are not guaranteed to be in any
particular order.
**Example:**
>>> m = MeasurementProcess(Expectation, obs=qml.PauliX(wires=1))
>>> m.eigvals()
array([1, -1])
Returns:
array: eigvals representation
"""
if self.obs is not None:
with contextlib.suppress(qml.operation.EigvalsUndefinedError):
return self.obs.eigvals()
return self._eigvals
@property
def has_decomposition(self):
r"""Bool: Whether or not the MeasurementProcess returns a defined decomposition
when calling ``expand``.
"""
# If self.obs is not None, `expand` queues the diagonalizing gates of self.obs,
# which we have to check to be defined. The subsequent creation of the new
# `MeasurementProcess` within `expand` should never fail with the given parameters.
return False if self.obs is None else self.obs.has_diagonalizing_gates
@property
def samples_computational_basis(self):
r"""Bool: Whether or not the MeasurementProcess measures in the computational basis."""
return self.obs is None
[docs] def expand(self):
"""Expand the measurement of an observable to a unitary
rotation and a measurement in the computational basis.
Returns:
.QuantumTape: a quantum tape containing the operations
required to diagonalize the observable
**Example:**
Consider a measurement process consisting of the expectation
value of an Hermitian observable:
>>> H = np.array([[1, 2], [2, 4]])
>>> obs = qml.Hermitian(H, wires=['a'])
>>> m = MeasurementProcess(Expectation, obs=obs)
Expanding this out:
>>> tape = m.expand()
We can see that the resulting tape has the qubit unitary applied,
and a measurement process with no observable, but the eigenvalues
specified:
>>> print(tape.operations)
[QubitUnitary(array([[-0.89442719, 0.4472136 ],
[ 0.4472136 , 0.89442719]]), wires=['a'])]
>>> print(tape.measurements[0].eigvals())
[0. 5.]
>>> print(tape.measurements[0].obs)
None
"""
if self.obs is None:
raise qml.operation.DecompositionUndefinedError
with qml.queuing.AnnotatedQueue() as q:
self.obs.diagonalizing_gates()
self.__class__(wires=self.obs.wires, eigvals=self.obs.eigvals())
return qml.tape.QuantumScript.from_queue(q)
[docs] def queue(self, context=qml.QueuingManager):
"""Append the measurement process to an annotated queue."""
if self.obs is not None:
context.remove(self.obs)
context.append(self)
return self
@property
def _queue_category(self):
"""Denotes that `MeasurementProcess` objects should be processed into the `_measurements` list
in `QuantumTape` objects.
This property is a temporary solution that should not exist long-term and should not be
used outside of ``QuantumTape._process_queue``.
"""
return "_measurements"
@property
def hash(self):
"""int: returns an integer hash uniquely representing the measurement process"""
fingerprint = (
self.__class__.__name__,
getattr(self.obs, "hash", "None"),
str(self._eigvals), # eigvals() could be expensive to compute for large observables
tuple(self.wires.tolist()),
)
return hash(fingerprint)
[docs] def simplify(self):
"""Reduce the depth of the observable to the minimum.
Returns:
.MeasurementProcess: A measurement process with a simplified observable.
"""
return self if self.obs is None else self.__class__(obs=self.obs.simplify())
# pylint: disable=protected-access
[docs] def map_wires(self, wire_map: dict):
"""Returns a copy of the current measurement process with its wires changed according to
the given wire map.
Args:
wire_map (dict): dictionary containing the old wires as keys and the new wires as values
Returns:
.MeasurementProcess: new measurement process
"""
new_measurement = copy.copy(self)
if self.obs is not None:
new_measurement.obs = self.obs.map_wires(wire_map=wire_map)
else:
new_measurement._wires = Wires([wire_map.get(wire, wire) for wire in self.wires])
return new_measurement
[docs]class SampleMeasurement(MeasurementProcess):
"""Sample-based measurement process.
Any class inheriting from ``SampleMeasurement`` should define its own ``process_samples`` method,
which should have the following arguments:
* samples (Sequence[complex]): computational basis samples generated for all wires
* wire_order (Wires): wires determining the subspace that ``samples`` acts on
* shot_range (tuple[int]): 2-tuple of integers specifying the range of samples
to use. If not specified, all samples are used.
* bin_size (int): Divides the shot range into bins of size ``bin_size``, and
returns the measurement statistic separately over each bin. If not
provided, the entire shot range is treated as a single bin.
**Example:**
Let's create a measurement that returns the sum of all samples of the given wires.
>>> class MyMeasurement(SampleMeasurement):
... def process_samples(self, samples, wire_order, shot_range=None, bin_size=None):
... return qml.math.sum(samples[..., self.wires])
We can now execute it in a QNode:
>>> dev = qml.device("default.qubit", wires=2, shots=1000)
>>> @qml.qnode(dev)
... def circuit():
... qml.PauliX(0)
... return MyMeasurement(wires=[0]), MyMeasurement(wires=[1])
>>> circuit()
tensor([1000, 0], requires_grad=True)
"""
[docs] @abstractmethod
def process_samples(
self,
samples: Sequence[complex],
wire_order: Wires,
shot_range: Tuple[int] = None,
bin_size: int = None,
):
"""Process the given samples.
Args:
samples (Sequence[complex]): computational basis samples generated for all wires
wire_order (Wires): wires determining the subspace that ``samples`` acts on
shot_range (tuple[int]): 2-tuple of integers specifying the range of samples
to use. If not specified, all samples are used.
bin_size (int): Divides the shot range into bins of size ``bin_size``, and
returns the measurement statistic separately over each bin. If not
provided, the entire shot range is treated as a single bin.
"""
[docs]class StateMeasurement(MeasurementProcess):
"""State-based measurement process.
Any class inheriting from ``StateMeasurement`` should define its own ``process_state`` method,
which should have the following arguments:
* state (Sequence[complex]): quantum state
* wire_order (Wires): wires determining the subspace that ``state`` acts on; a matrix of
dimension :math:`2^n` acts on a subspace of :math:`n` wires
**Example:**
Let's create a measurement that returns the diagonal of the reduced density matrix.
>>> class MyMeasurement(StateMeasurement):
... def process_state(self, state, wire_order):
... # use the already defined `qml.density_matrix` measurement to compute the
... # reduced density matrix from the given state
... density_matrix = qml.density_matrix(wires=self.wires).process_state(state, wire_order)
... return qml.math.diagonal(qml.math.real(density_matrix))
We can now execute it in a QNode:
>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit():
... qml.Hadamard(0)
... qml.CNOT([0, 1])
... return MyMeasurement(wires=[0])
>>> circuit()
tensor([0.5, 0.5], requires_grad=True)
"""
[docs] @abstractmethod
def process_state(self, state: Sequence[complex], wire_order: Wires):
"""Process the given quantum state.
Args:
state (Sequence[complex]): quantum state
wire_order (Wires): wires determining the subspace that ``state`` acts on; a matrix of
dimension :math:`2^n` acts on a subspace of :math:`n` wires
"""
[docs]class MeasurementTransform(MeasurementProcess):
"""Measurement process that applies a transform into the given quantum tape. This transform
is carried out inside the gradient black box, thus is not tracked by the gradient transform.
Any class inheriting from ``MeasurementTransform`` should define its own ``process`` method,
which should have the following arguments:
* tape (QuantumTape): quantum tape to transform
* device (pennylane.Device): device used to transform the quantum tape
"""
[docs] @abstractmethod
def process(self, tape, device):
"""Process the given quantum tape.
Args:
tape (QuantumTape): quantum tape to transform
device (pennylane.Device): device used to transform the quantum tape
"""
```

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