Source code for pennylane.measurements.mutual_info

# 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.
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# pylint: disable=protected-access
This module contains the qml.mutual_info measurement.
from typing import Sequence, Optional

import pennylane as qml
from pennylane.wires import Wires

from .measurements import MutualInfo, StateMeasurement

[docs]def mutual_info(wires0, wires1, log_base=None): r"""Mutual information between the subsystems prior to measurement: .. math:: I(A, B) = S(\rho^A) + S(\rho^B) - S(\rho^{AB}) where :math:`S` is the von Neumann entropy. The mutual information is a measure of correlation between two subsystems. More specifically, it quantifies the amount of information obtained about one system by measuring the other system. Args: wires0 (Sequence[int] or int): the wires of the first subsystem wires1 (Sequence[int] or int): the wires of the second subsystem log_base (float): Base for the logarithm. Returns: MutualInfoMP: measurement process instance **Example:** .. code-block:: python3 dev = qml.device("default.qubit", wires=2) @qml.qnode(dev) def circuit_mutual(x): qml.IsingXX(x, wires=[0, 1]) return qml.mutual_info(wires0=[0], wires1=[1]) Executing this QNode: >>> circuit_mutual(np.pi/2) 1.3862943611198906 It is also possible to get the gradient of the previous QNode: >>> param = np.array(np.pi/4, requires_grad=True) >>> qml.grad(circuit_mutual)(param) 1.2464504802804612 .. note:: Calculating the derivative of :func:`~.mutual_info` is currently supported when using the classical backpropagation differentiation method (``diff_method="backprop"``) with a compatible device and finite differences (``diff_method="finite-diff"``). .. seealso:: :func:`~.vn_entropy`, :func:`pennylane.qinfo.transforms.mutual_info` and :func:`pennylane.math.mutual_info` """ wires0 = qml.wires.Wires(wires0) wires1 = qml.wires.Wires(wires1) # the subsystems cannot overlap if [wire for wire in wires0 if wire in wires1]: raise qml.QuantumFunctionError( "Subsystems for computing mutual information must not overlap." ) return MutualInfoMP(wires=[wires0, wires1], log_base=log_base)
[docs]class MutualInfoMP(StateMeasurement): """Measurement process that computes the mutual information between the provided wires. Please refer to :func:`mutual_info` for detailed documentation. Args: wires (Sequence[.Wires]): The wires the measurement process applies to. id (str): custom label given to a measurement instance, can be useful for some applications where the instance has to be identified log_base (float): base for the logarithm """ # pylint: disable=too-many-arguments def __init__( self, wires: Optional[Sequence[Wires]] = None, id: Optional[str] = None, log_base: Optional[float] = None, ): self.log_base = log_base super().__init__(wires=wires, id=id) def __repr__(self): return f"MutualInfo(wires0={self.raw_wires[0].tolist()}, wires1={self.raw_wires[1].tolist()}, log_base={self.log_base})" @property def hash(self): """int: returns an integer hash uniquely representing the measurement process""" fingerprint = ( self.__class__.__name__, tuple(self.raw_wires[0].tolist()), tuple(self.raw_wires[1].tolist()), self.log_base, ) return hash(fingerprint) @property def return_type(self): return MutualInfo @property def numeric_type(self): return float
[docs] def shape(self, device=None): if qml.active_return(): return self._shape_new(device) if device is None or device.shot_vector is None: return (1,) num_shot_elements = sum(s.copies for s in device.shot_vector) return (num_shot_elements,)
def _shape_new(self, device=None): if device is None or device.shot_vector is None: return () num_shot_elements = sum(s.copies for s in device.shot_vector) return tuple(() for _ in range(num_shot_elements))
[docs] def process_state(self, state: Sequence[complex], wire_order: Wires): return qml.math.mutual_info( state, indices0=list(self._wires[0]), indices1=list(self._wires[1]), c_dtype=state.dtype, base=self.log_base, )