# SimQN: a discrete-event simulator for the quantum networks
# Copyright (C) 2021-2022 Lutong Chen, Jian Li, Kaiping Xue
# University of Science and Technology of China, USTC.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from typing import Optional, List
from qns.models.epr.entanglement import BaseEntanglement
from qns.models.core.backend import QuantumModel
from qns.models.qubit.qubit import Qubit, QState
from qns.models.qubit.const import QUBIT_STATE_0, QUBIT_STATE_P
import numpy as np
from qns.utils.rnd import get_rand
[docs]class WernerStateEntanglement(BaseEntanglement, QuantumModel):
"""
`WernerStateEntanglement` is a pair of entangled qubits in Werner State with a hidden-variable.
"""
def __init__(self, fidelity: float = 1, name: Optional[str] = None):
"""
generate an entanglement with certain fidelity
Args:
fidelity (float): the fidelity
name (str): the entanglement name
"""
self.w = (fidelity * 4 - 1) / 3
self.name = name
self.is_decoherenced = False
@property
def fidelity(self) -> float:
return (self.w * 3 + 1) / 4
@fidelity.setter
def fidelity(self, fidelity: float = 1):
self.w = (fidelity * 4 - 1) / 3
[docs] def swapping(self, epr: "WernerStateEntanglement", name: Optional[str] = None):
"""
Use `self` and `epr` to perfrom swapping and distribute a new entanglement
Args:
epr (WernerEntanglement): another entanglement
name (str): the name of the new entanglement
Returns:
the new distributed entanglement
"""
ne = WernerStateEntanglement(name=name)
if self.is_decoherenced or epr.is_decoherenced:
ne.is_decoherenced = True
ne.fidelity = 0
epr.is_decoherenced = True
self.is_decoherenced = True
ne.w = self.w * epr.w
return ne
[docs] def distillation(self, epr: "WernerStateEntanglement", name: Optional[str] = None):
"""
Use `self` and `epr` to perfrom distillation and distribute a new entanglement.
Using Bennett 96 protocol and estimate lower bound.
Args:
epr (WernerEntanglement): another entanglement
name (str): the name of the new entanglement
Returns:
the new distributed entanglement
"""
ne = WernerStateEntanglement()
if self.is_decoherenced or epr.is_decoherenced:
ne.is_decoherenced = True
ne.fidelity = 0
return
epr.is_decoherenced = True
self.is_decoherenced = True
fmin = min(self.fidelity, epr.fidelity)
if get_rand() > (fmin ** 2 + 5 / 9 * (1 - fmin) ** 2 + 2 / 3 * fmin * (1 - fmin)):
ne.is_decoherenced = True
ne.fidelity = 0
return
ne.fidelity = (fmin ** 2 + (1 - fmin) ** 2 / 9) /\
(fmin ** 2 + 5 / 9 * (1 - fmin) ** 2 + 2 / 3 * fmin * (1 - fmin))
return ne
[docs] def store_error_model(self, t: float, decoherence_rate: Optional[float] = 0, **kwargs):
"""
The default error model for storing this entangled pair in a quantum memory.
The default behavior is: w = w*e^{-decoherence_rate*t}, default a = 0
Args:
t: the time stored in a quantum memory. The unit it second.
decoherence_rate: the decoherence rate, equals to 1/T_coh, where T_coh is the coherence time.
kwargs: other parameters
"""
self.w = self.w * np.exp(-decoherence_rate * t)
[docs] def transfer_error_model(self, length: float, decoherence_rate: Optional[float] = 0, **kwargs):
"""
The default error model for transmitting this entanglement.
The success possibility of transmitting is: w = w* e^{decoherence_rate * length}
Args:
length (float): the length of the channel
kwargs: other parameters
"""
self.w = self.w * np.exp(-decoherence_rate * length)
[docs] def to_qubits(self) -> List[Qubit]:
if self.is_decoherenced:
q0 = Qubit(state=QUBIT_STATE_P, name="q0")
q1 = Qubit(state=QUBIT_STATE_P, name="q1")
return [q0, q1]
q0 = Qubit(state=QUBIT_STATE_0, name="q0")
q1 = Qubit(state=QUBIT_STATE_0, name="q1")
phi_p = 1/np.sqrt(2) * np.array([[1], [0], [0], [1]])
rho = self.w * np.dot(phi_p, phi_p.T.conjugate()) + (1-self.w)/4 * np.identity(4)
print(rho)
qs = QState([q0, q1], rho=rho)
q0.state = qs
q1.state = qs
self.is_decoherenced = True
return [q0, q1]