참고

이 페이지는 tutorials/noise/2_relaxation_and_decoherence.ipynb 에서 생성되었다.

Run interactively in the IBM Quantum lab.

풀림(relaxation)과 결깨짐(Decoherence)

이 노트북은 \(T_1\) 과 \(T_2\) 모듈을 사용하는지 보여준다.

import numpy as np
import matplotlib.pyplot as plt

import qiskit
from qiskit.providers.aer.noise.errors.standard_errors import thermal_relaxation_error
from qiskit.providers.aer.noise import NoiseModel

from qiskit.ignis.characterization.coherence import T1Fitter, T2StarFitter, T2Fitter
from qiskit.ignis.characterization.coherence import t1_circuits, t2_circuits, t2star_circuits

결맞음(Coherence) 회로 생성하기

이 튜토리얼은 회로를 생성하는 방법을 보여준다. 큐비트 목록은 특성화 회로를 생성하기 위한 큐비트를 지정하며, 이러한 회로는 병렬로 실행될 것이다. 이산 시간 단위(discrete unit of time) 는 Identity Gate(iden) 이므로 사용자는 시간 단위로 특성화 매개변수를 반환하기위해 각 Identity 게이트의 시간을 지정해야 한다. 이것은 백엔드에서 이용할 수 있어야 한다.

num_of_gates = (np.linspace(10, 300, 50)).astype(int)
gate_time = 0.1

# Note that it is possible to measure several qubits in parallel
qubits = [0, 2]

t1_circs, t1_xdata = t1_circuits(num_of_gates, gate_time, qubits)
t2star_circs, t2star_xdata, osc_freq = t2star_circuits(num_of_gates, gate_time, qubits, nosc=5)
t2echo_circs, t2echo_xdata = t2_circuits(np.floor(num_of_gates/2).astype(int),
                                         gate_time, qubits)
t2cpmg_circs, t2cpmg_xdata = t2_circuits(np.floor(num_of_gates/6).astype(int),
                                         gate_time, qubits,
                                         n_echos=5, phase_alt_echo=True)

백엔드 실행

backend = qiskit.Aer.get_backend('qasm_simulator')
shots = 400

# Let the simulator simulate the following times for qubits 0 and 2:
t_q0 = 25.0
t_q2 = 15.0

# Define T1 and T2 noise:
t1_noise_model = NoiseModel()
t1_noise_model.add_quantum_error(
    thermal_relaxation_error(t_q0, 2*t_q0, gate_time),
    'id', [0])
t1_noise_model.add_quantum_error(
    thermal_relaxation_error(t_q2, 2*t_q2, gate_time),
    'id', [2])

t2_noise_model = NoiseModel()
t2_noise_model.add_quantum_error(
    thermal_relaxation_error(np.inf, t_q0, gate_time, 0.5),
    'id', [0])
t2_noise_model.add_quantum_error(
    thermal_relaxation_error(np.inf, t_q2, gate_time, 0.5),
    'id', [2])

# Run the simulator
t1_backend_result = qiskit.execute(t1_circs, backend, shots=shots,
                                   noise_model=t1_noise_model, optimization_level=0).result()
t2star_backend_result = qiskit.execute(t2star_circs, backend, shots=shots,
                                       noise_model=t2_noise_model, optimization_level=0).result()
t2echo_backend_result = qiskit.execute(t2echo_circs, backend, shots=shots,
                                       noise_model=t2_noise_model, optimization_level=0).result()

# It is possible to split the circuits into multiple jobs and then give the results to the fitter as a list:
t2cpmg_backend_result1 = qiskit.execute(t2cpmg_circs[0:5], backend,
                                        shots=shots, noise_model=t2_noise_model,
                                        optimization_level=0).result()
t2cpmg_backend_result2 = qiskit.execute(t2cpmg_circs[5:], backend,
                                        shots=shots, noise_model=t2_noise_model,
                                        optimization_level=0).result()

결과 분석

# Fitting T1

%matplotlib inline

plt.figure(figsize=(15, 6))

t1_fit = T1Fitter(t1_backend_result, t1_xdata, qubits,
                  fit_p0=[1, t_q0, 0],
                  fit_bounds=([0, 0, -1], [2, 40, 1]))
print(t1_fit.time())
print(t1_fit.time_err())
print(t1_fit.params)
print(t1_fit.params_err)

for i in range(2):
    ax = plt.subplot(1, 2, i+1)
    t1_fit.plot(i, ax=ax)
plt.show()

[24.10436641574169, 15.1725404065493]
[2.2001166293232, 0.6420239307715634]
{'0': [array([ 0.97307515, 24.10436642,  0.02663813]), array([ 1.00092258e+00,  1.51725404e+01, -5.42259153e-03])]}
{'0': [array([0.04753859, 2.20011663, 0.05166528]), array([0.01408857, 0.64202393, 0.01729388])]}

백엔드를 다시 실행하여 더 많은 통계를 얻고 이전 결과에 이를 추가한다.

t1_backend_result_new = qiskit.execute(t1_circs, backend,
                                       shots=shots, noise_model=t1_noise_model,
                                       optimization_level=0).result()
t1_fit.add_data(t1_backend_result_new)

plt.figure(figsize=(15, 6))
for i in range(2):
    ax = plt.subplot(1, 2, i+1)
    t1_fit.plot(i, ax=ax)
plt.show()

# Fitting T2*

%matplotlib inline

t2star_fit = T2StarFitter(t2star_backend_result, t2star_xdata, qubits,
                          fit_p0=[0.5, t_q0, osc_freq, 0, 0.5],
                          fit_bounds=([-0.5, 0, 0, -np.pi, -0.5],
                                      [1.5, 40, 2*osc_freq, np.pi, 1.5]))

plt.figure(figsize=(15, 6))
for i in range(2):
    ax = plt.subplot(1, 2, i+1)
    t2star_fit.plot(i, ax=ax)
plt.show()

# Fitting T2 single echo

%matplotlib inline

t2echo_fit = T2Fitter(t2echo_backend_result, t2echo_xdata, qubits,
                      fit_p0=[0.5, t_q0, 0.5],
                      fit_bounds=([-0.5, 0, -0.5],
                                  [1.5, 40, 1.5]))

print(t2echo_fit.params)

plt.figure(figsize=(15, 6))
for i in range(2):
    ax = plt.subplot(1, 2, i+1)
    t2echo_fit.plot(i, ax=ax)
plt.show()

{'0': [array([ 0.46514794, 21.68047828,  0.53799714]), array([ 0.53077749, 16.98595852,  0.47459488])]}

# Fitting T2 CPMG

%matplotlib inline

t2cpmg_fit = T2Fitter([t2cpmg_backend_result1, t2cpmg_backend_result2],
                      t2cpmg_xdata, qubits,
                      fit_p0=[0.5, t_q0, 0.5],
                      fit_bounds=([-0.5, 0, -0.5],
                                  [1.5, 40, 1.5]))

plt.figure(figsize=(15, 6))
for i in range(2):
    ax = plt.subplot(1, 2, i+1)
    t2cpmg_fit.plot(i, ax=ax)
plt.show()

import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright

Version Information

Qiskit Software	Version
Qiskit	None
Terra	0.9.0
Aer	0.3.0
Ignis	0.2.0
Aqua	0.5.3
IBM Q Provider	0.3.2rc1
System information
Python	3.7.4 (default, Aug 13 2019, 15:17:50) [Clang 4.0.1 (tags/RELEASE_401/final)]
OS	Darwin
CPUs	4
Memory (Gb)	16.0
Wed Aug 21 21:30:54 2019 EDT

This code is a part of Qiskit

© Copyright IBM 2017, 2019.

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obtain a copy of this license in the LICENSE.txt file in the root directory
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Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.