Source code for pennylane.measurements.purity

# 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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#     http://www.apache.org/licenses/LICENSE-2.0

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"""
This module contains the qml.purity measurement.
"""

from typing import Optional, Sequence

import pennylane as qml
from pennylane.wires import Wires

from .measurements import Purity, StateMeasurement


[docs]def purity(wires) -> "PurityMP": r"""The purity of the system prior to measurement. .. math:: \gamma = \text{Tr}(\rho^2) where :math:`\rho` is the density matrix. The purity of a normalized quantum state satisfies :math:`\frac{1}{d} \leq \gamma \leq 1`, where :math:`d` is the dimension of the Hilbert space. A pure state has a purity of 1. Args: wires (Sequence[int] or int): The wires of the subsystem Returns: PurityMP: Measurement process instance **Example** .. code-block:: python3 dev = qml.device("default.mixed", wires=2) @qml.qnode(dev) def circuit_purity(p): qml.Hadamard(wires=0) qml.CNOT(wires=[0, 1]) qml.BitFlip(p, wires=0) qml.BitFlip(p, wires=1) return qml.purity(wires=[0,1]) >>> circuit_purity(0.1) array(0.7048) .. seealso:: :func:`pennylane.qinfo.transforms.purity` and :func:`pennylane.math.purity` """ wires = Wires(wires) return PurityMP(wires=wires)
[docs]class PurityMP(StateMeasurement): """Measurement process that computes the purity of the system prior to measurement. Please refer to :func:`pennylane.purity` for detailed documentation. Args: wires (.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 """ def __init__(self, wires: Wires, id: Optional[str] = None): super().__init__(wires=wires, id=id) @property def return_type(self): return Purity @property def numeric_type(self): return float
[docs] def shape(self, device, shots): if not shots.has_partitioned_shots: return () num_shot_elements = sum(s.copies for s in shots.shot_vector) return tuple(() for _ in range(num_shot_elements))
[docs] def process_state(self, state: Sequence[complex], wire_order: Wires): wire_map = dict(zip(wire_order, list(range(len(wire_order))))) indices = [wire_map[w] for w in self.wires] state = qml.math.dm_from_state_vector(state) return qml.math.purity(state, indices=indices, c_dtype=state.dtype)