참고

이 페이지는 tutorials/noise/4_randomized_벤치마킹 .ipynb ” __ 에서 생성되었다.

IBM 퀀텀 랩 에서 대화식으로 실행하십시오.

랜덤화된 벤치마킹

소개

** 랜덤화된 벤치마크 (RB) * * 는 초기 상태로 큐비트를 리턴해야 하는 랜덤 클리포드 게이트의 시퀀스를 실행함으로써 평균 게이트 성능을 측정하기 위한 잘 알려진 기술이다. Qiskit Ignis는 1개 및 2개의 큐비트 Clifford 게이트 서열을 동시에 생성하는 툴을 갖는다.

이 노트북은``ignis.verification.randomized_benchmarking``모듈을 사용하는 방법에 대한 예제를 제공한. 이 특정한 예는 1-qubit RB와 동시에 2-qubit 무작위화된 벤치마킹 을 실행하는 방법을 나타낸다. RB 신뢰도를 예측하기 위해 일부 도우미 기능을 사용하는 방법에 대한 예도 있다.

#Import general libraries (needed for functions)
import numpy as np
import matplotlib.pyplot as plt
from IPython import display

#Import Qiskit classes
import qiskit
from qiskit.providers.aer.noise import NoiseModel
from qiskit.providers.aer.noise.errors.standard_errors import depolarizing_error, thermal_relaxation_error

#Import the RB Functions
import qiskit.ignis.verification.randomized_benchmarking as rb

1) RB Run의 파라미터를 선택한다.

First, we need to choose the following parameters:

• nseeds: The number of seeds. For each seed you will get a separate list of output circuits in rb_circs.

• length_vector: The length vector of Clifford lengths. Must be in ascending order. RB sequences of increasing length grow on top of the previous sequences.

• rb_pattern: A list of the form [[i,j],[k],…] which will make simultaneous RB sequences where Qi,Qj are a 2-qubit RB sequence and Qk is a 1-qubit sequence, etc. The number of qubits is the sum of the entries. For ‘regular’ RB the qubit_pattern is just [[0]],[[0,1]].

• length_multiplier: 이 배열이면 각 rb_sequence를 곱셈기로 스케일링한다.

• seed_offset: What to start the seeds at (e.g. if we want to add more seeds later).

• align_cliffs: If true adds a barrier across all qubits in rb_pattern after each set of cliffords.

이 예제에서는 3개의 큐비트가 (Q0, Q1, Q2) 있다. 2Q RB (큐비트 Q0, Q2) 와 1Q RB (큐비트 Q1) 가 동시에 실행하고 있는데, 여기서, 1 Q 클리퍼드 게이트가 2배 더 많다.

#Number of qubits
nQ = 3
#There are 3 qubits: Q0,Q1,Q2.
#Number of seeds (random sequences)
nseeds = 5
#Number of Cliffords in the sequence (start, stop, steps)
nCliffs = np.arange(1,200,20)
#2Q RB on Q0,Q2 and 1Q RB on Q1
rb_pattern = [[0,2],[1]]
#Do three times as many 1Q Cliffords
length_multiplier = [1,3]

2) RB 서열을 생성한다.

We generate RB sequences. We start with a small example (so it doesn’t take too long to run).

In order to generate the RB sequences rb_circs, which is a list of lists of quantum circuits, we run the function rb.randomized_benchmarking_seq.

이 함수는 다음을 리턴한다.

• rb_circs: A list of lists of circuits for the rb sequences (separate list for each seed).

• ** xdata:** Clifford 길이 (mulitplier 가있다면 포함되어 있음).

rb_opts = {}
rb_opts['length_vector'] = nCliffs
rb_opts['nseeds'] = nseeds
rb_opts['rb_pattern'] = rb_pattern
rb_opts['length_multiplier'] = length_multiplier
rb_circs, xdata = rb.randomized_benchmarking_seq(**rb_opts)

예를 들어 첫 번째 RB 시퀀스에 해당하는 회로를 출력한다.

print(rb_circs[0][0])

                        ┌───┐┌───┐┌───┐      ░  ┌───┐ ┌─────┐┌───┐            »
qr_0: |0>────────────■──┤ H ├┤ S ├┤ X ├──────░──┤ X ├─┤ Sdg ├┤ H ├────────────»
         ┌───┐┌───┐  │  ├───┤└─░─┘├───┤┌───┐ ░  ├───┤ └──░──┘├───┤┌─────┐┌───┐»
qr_1: |0>┤ H ├┤ H ├──┼──┤ S ├──░──┤ H ├┤ S ├────┤ X ├────░───┤ H ├┤ Sdg ├┤ H ├»
         ├───┤├───┤┌─┴─┐├───┤┌───┐└───┘└───┘ ░ ┌┴───┴┐ ┌───┐ └───┘└─────┘└───┘»
qr_2: |0>┤ H ├┤ S ├┤ X ├┤ H ├┤ S ├───────────░─┤ Sdg ├─┤ H ├──────────────────»
         └───┘└───┘└───┘└───┘└───┘           ░ └─────┘ └───┘                  »
 cr_0: 0 ═════════════════════════════════════════════════════════════════════»
                                                                              »
 cr_1: 0 ═════════════════════════════════════════════════════════════════════»
                                                                              »
 cr_2: 0 ═════════════════════════════════════════════════════════════════════»
                                                                              »
«                  ┌─┐
«qr_0: ──■─────────┤M├───────────
«        │     ░   └╥┘     ┌─┐
«qr_1: ──┼─────░────╫──────┤M├───
«      ┌─┴─┐┌─────┐ ║ ┌───┐└╥┘┌─┐
«qr_2: ┤ X ├┤ Sdg ├─╫─┤ H ├─╫─┤M├
«      └───┘└─────┘ ║ └───┘ ║ └╥┘
«cr_0: ═════════════╩═══════╬══╬═
«                           ║  ║
«cr_1: ═════════════════════╬══╩═
«                           ║
«cr_2: ═════════════════════╩════
«

1회로의 유니터리(unitary) 를 보면

각각의 RB 회로를 나타내는 유니체는 (글로벌 페이즈와 함께) 아이덴티티가 되어야 하며, 그 이유는, 우리가 계산된 반전 게이트를 포함하는 랜덤 Clifford 요소들을 곱하기 때문이다. Aer 단일 시뮬레이터를 사용하여 이를 시뮬레이션합니다.

#Create a new circuit without the measurement
qc = qiskit.QuantumCircuit(*rb_circs[0][-1].qregs,*rb_circs[0][-1].cregs)
for i in rb_circs[0][-1][0:-nQ]:
    qc.data.append(i)

#The Unitary is an identity (with a global phase)
backend = qiskit.Aer.get_backend('unitary_simulator')
basis_gates = ['u1', 'u2', 'u3', 'cx'] # use U,CX for now
job = qiskit.execute(qc, backend=backend, basis_gates=basis_gates)
print(np.around(job.result().get_unitary(), 3))

[[ 0.+1.j -0.+0.j  0.-0.j  0.-0.j -0.-0.j  0.+0.j -0.+0.j  0.-0.j]
 [-0.-0.j  0.+1.j -0.+0.j  0.-0.j  0.-0.j  0.+0.j -0.-0.j -0.+0.j]
 [ 0.+0.j -0.+0.j  0.+1.j -0.+0.j -0.-0.j  0.+0.j -0.-0.j  0.+0.j]
 [-0.+0.j  0.+0.j -0.-0.j  0.+1.j  0.-0.j -0.-0.j  0.-0.j  0.+0.j]
 [ 0.+0.j  0.-0.j  0.+0.j -0.-0.j  0.+1.j -0.+0.j  0.-0.j -0.+0.j]
 [ 0.-0.j -0.+0.j -0.+0.j -0.+0.j  0.+0.j  0.+1.j  0.-0.j  0.-0.j]
 [ 0.+0.j  0.-0.j -0.+0.j  0.-0.j  0.+0.j  0.-0.j  0.+1.j  0.-0.j]
 [-0.-0.j  0.+0.j  0.-0.j -0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.+1.j]]

노이즈 모델 정의하기

우리는 시뮬레이터에 대한 잡음 모델을 정의한다. 감쇠를 시뮬레이션하기 위해, CNOT과 U 게이트에 편광 에러 확률을 추가한다.

noise_model = NoiseModel()
p1Q = 0.002
p2Q = 0.01
noise_model.add_all_qubit_quantum_error(depolarizing_error(p1Q, 1), 'u2')
noise_model.add_all_qubit_quantum_error(depolarizing_error(2*p1Q, 1), 'u3')
noise_model.add_all_qubit_quantum_error(depolarizing_error(p2Q, 2), 'cx')

3) Aer 시뮬레이터에서 RB 시퀀스 실행하기

Qiskit Aer Simulator를 사용하거나 IBMQ 공급자를 사용하여 RB 시퀀스를 실행하고, 결과 목록을 얻을 수 있다.

backend = qiskit.Aer.get_backend('qasm_simulator')
basis_gates = ['u1','u2','u3','cx'] # use U,CX for now
shots = 200
result_list = []
transpile_list = []
import time
for rb_seed,rb_circ_seed in enumerate(rb_circs):
    print('Compiling seed %d'%rb_seed)
    rb_circ_transpile = qiskit.transpile(rb_circ_seed, basis_gates=basis_gates)
    print('Simulating seed %d'%rb_seed)
    job = qiskit.execute(rb_circ_transpile, noise_model=noise_model, shots=shots, backend=backend, backend_options={'max_parallel_experiments': 0})
    result_list.append(job.result())
    transpile_list.append(rb_circ_transpile)
print("Finished Simulating")

Compiling seed 0
Simulating seed 0
Compiling seed 1
Simulating seed 1
Compiling seed 2
Simulating seed 2
Compiling seed 3
Simulating seed 3
Compiling seed 4
Simulating seed 4
Finished Simulating

4) RB 결과를 채우고 게이트 충실도 계산

생존 확률에 대한 통계 가져오기

The results in result_list should fit to an exponentially decaying function \(A \cdot \alpha ^ m + B\), where \(m\) is the Clifford length.

From \(\alpha\) we can calculate the Error per Clifford (EPC):

\[EPC = \frac{2^n-1}{2^n} (1-\alpha)\]

(여기서 :math:`n=nQ`는 큐비트의 수이다).

#Create an RBFitter object with 1 seed of data
rbfit = rb.fitters.RBFitter(result_list[0], xdata, rb_opts['rb_pattern'])

1시드 후 그래프

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

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

    # Plot the essence by calling plot_rb_data
    rbfit.plot_rb_data(pattern_ind, ax=ax, add_label=True, show_plt=False)

    # Add title and label
    ax.set_title('%d Qubit RB'%(len(rb_opts['rb_pattern'][i])), fontsize=18)

plt.show()

나머지 시드로 그래프하기

The plot is being updated after each seed.

rbfit = rb.fitters.RBFitter(result_list[0], xdata, rb_opts['rb_pattern'])

for seed_num, data in enumerate(result_list):#range(1,len(result_list)):
    plt.figure(figsize=(15, 6))
    axis = [plt.subplot(1, 2, 1), plt.subplot(1, 2, 2)]

    # Add another seed to the data
    rbfit.add_data([data])

    for i in range(2):
        pattern_ind = i

        # Plot the essence by calling plot_rb_data
        rbfit.plot_rb_data(pattern_ind, ax=axis[i], add_label=True, show_plt=False)

        # Add title and label
        axis[i].set_title('%d Qubit RB - after seed %d'%(len(rb_opts['rb_pattern'][i]), seed_num), fontsize=18)

    # Display
    display.display(plt.gcf())

    # Clear display after each seed and close
    display.clear_output(wait=True)
    time.sleep(1.0)
    plt.close()

데이터에 추가로 샷 추가하기

shots = 200
result_list = []
transpile_list = []
for rb_seed,rb_circ_seed in enumerate(rb_circs):
    print('Compiling seed %d'%rb_seed)
    rb_circ_transpile = qiskit.transpile(rb_circ_seed, basis_gates=basis_gates)
    print('Simulating seed %d'%rb_seed)
    job = qiskit.execute(rb_circ_transpile, noise_model=noise_model, shots=shots, backend=backend, backend_options={'max_parallel_experiments': 0})
    result_list.append(job.result())
    transpile_list.append(rb_circ_transpile)
print("Finished Simulating")

Compiling seed 0
Simulating seed 0
Compiling seed 1
Simulating seed 1
Compiling seed 2
Simulating seed 2
Compiling seed 3
Simulating seed 3
Compiling seed 4
Simulating seed 4
Finished Simulating

#Add this data to the previous fit
rbfit.add_data(result_list)

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

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

    # Plot the essence by calling plot_rb_data
    rbfit.plot_rb_data(pattern_ind, ax=ax, add_label=True, show_plt=False)

    # Add title and label
    ax.set_title('%d Qubit RB'%(len(rb_opts['rb_pattern'][i])), fontsize=18)

plt.show()

예측된 게이트 피델리티

From the known depolarizing errors on the simulation we can predict the fidelity. First we need to count the number of gates per Clifford.

The function gates_per_clifford takes a list of transpiled RB circuits and outputs the number of basis gates in each circuit.

#Count the number of single and 2Q gates in the 2Q Cliffords
gates_per_cliff = rb.rb_utils.gates_per_clifford(transpile_list,xdata[0],basis_gates,rb_opts['rb_pattern'][0])
for basis_gate in basis_gates:
    print("Number of %s gates per Clifford: %f "%(basis_gate ,
                                                  np.mean([gates_per_cliff[0][basis_gate],
                                                           gates_per_cliff[2][basis_gate]])))

Number of u1 gates per Clifford: 0.271522
Number of u2 gates per Clifford: 0.923587
Number of u3 gates per Clifford: 0.490109
Number of cx gates per Clifford: 1.526739

The function calculate_2q_epc gives measured errors in the basis gates that were used to construct the Clifford. It assumes that the error in the underlying gates is depolarizing. It outputs the error per a 2-qubit Clifford.

The input to this function is: - gate_per_cliff: dictionary of gate per Clifford. - epg_2q: EPG estimated by error model. - qubit_pair: index of two qubits to calculate EPC. - list_epgs_1q: list of single qubit EPGs of qubit listed in qubit_pair. - two_qubit_name: name of two qubit gate in basis gates (default is cx).

# Error per gate from noise model
epgs_1q = {'u1': 0, 'u2': p1Q/2, 'u3': 2*p1Q/2}
epg_2q = p2Q*3/4
pred_epc = rb.rb_utils.calculate_2q_epc(
    gate_per_cliff=gates_per_cliff,
    epg_2q=epg_2q,
    qubit_pair=[0, 2],
    list_epgs_1q=[epgs_1q, epgs_1q])

# Calculate the predicted epc
print("Predicted 2Q Error per Clifford: %e"%pred_epc)

Predicted 2Q Error per Clifford: 1.591172e-02

T1, T2 오류로 RB 시퀀스 실행하기

이제 2-쿼트 캐리시드만 포함하는 RB 시퀀스를 선택합니다.

이전과 같이 이러한 시퀀스를 실행하지만, T1/T2열적 완화 오류로 확장된 노이즈 모델을 사용하여 지수적으로 구성된 곡선을 적합하게 합니다.

rb_opts2 = rb_opts.copy()
rb_opts2['rb_pattern'] = [[0,1]]
rb_opts2['length_multiplier'] = 1
rb_circs2, xdata2 = rb.randomized_benchmarking_seq(**rb_opts2)

noise_model2 = NoiseModel()

#Add T1/T2 noise to the simulation
t1 = 100.
t2 = 80.
gate1Q = 0.1
gate2Q = 0.5
noise_model2.add_all_qubit_quantum_error(thermal_relaxation_error(t1,t2,gate1Q), 'u2')
noise_model2.add_all_qubit_quantum_error(thermal_relaxation_error(t1,t2,2*gate1Q), 'u3')
noise_model2.add_all_qubit_quantum_error(
    thermal_relaxation_error(t1,t2,gate2Q).tensor(thermal_relaxation_error(t1,t2,gate2Q)), 'cx')

backend = qiskit.Aer.get_backend('qasm_simulator')
basis_gates = ['u1','u2','u3','cx'] # use U,CX for now
shots = 500
result_list2 = []
transpile_list2 = []
for rb_seed,rb_circ_seed in enumerate(rb_circs2):
    print('Compiling seed %d'%rb_seed)
    rb_circ_transpile = qiskit.transpile(rb_circ_seed, basis_gates=basis_gates)
    print('Simulating seed %d'%rb_seed)
    job = qiskit.execute(rb_circ_transpile, noise_model=noise_model, shots=shots, backend=backend, backend_options={'max_parallel_experiments': 0})
    result_list2.append(job.result())
    transpile_list2.append(rb_circ_transpile)
print("Finished Simulating")

Compiling seed 0
Simulating seed 0
Compiling seed 1
Simulating seed 1
Compiling seed 2
Simulating seed 2
Compiling seed 3
Simulating seed 3
Compiling seed 4
Simulating seed 4
Finished Simulating

#Create an RBFitter object
rbfit = rb.RBFitter(result_list2, xdata2, rb_opts2['rb_pattern'])

plt.figure(figsize=(10, 6))
ax = plt.gca()

# Plot the essence by calling plot_rb_data
rbfit.plot_rb_data(0, ax=ax, add_label=True, show_plt=False)

# Add title and label
ax.set_title('2 Qubit RB with T1/T2 noise', fontsize=18)

plt.show()

We count again the number of gates per Clifford as before, and calculate the two-qubit Clifford gate error, using the predicted primitive gate errors from the coherence limit.

#Count the number of single and 2Q gates in the 2Q Cliffords
gates_per_cliff = rb.rb_utils.gates_per_clifford(transpile_list2,xdata[0],basis_gates,rb_opts2['rb_pattern'][0])
for basis_gate in basis_gates:
    print("Number of %s gates per Clifford: %f "%(basis_gate ,
                                                  np.mean([gates_per_cliff[0][basis_gate],
                                                           gates_per_cliff[1][basis_gate]])))

Number of u1 gates per Clifford: 0.250761
Number of u2 gates per Clifford: 0.969565
Number of u3 gates per Clifford: 0.489130
Number of cx gates per Clifford: 1.503696

# Predicted primitive gate errors from the coherence limit
u2_error = rb.rb_utils.coherence_limit(1,[t1],[t2],gate1Q)
u3_error = rb.rb_utils.coherence_limit(1,[t1],[t2],2*gate1Q)
epg_2q = rb.rb_utils.coherence_limit(2,[t1,t1],[t2,t2],gate2Q)
epgs_1q = {'u1': 0, 'u2': u2_error, 'u3': u3_error}
pred_epc = rb.rb_utils.calculate_2q_epc(
    gate_per_cliff=gates_per_cliff,
    epg_2q=epg_2q,
    qubit_pair=[0, 1],
    list_epgs_1q=[epgs_1q, epgs_1q])

# Calculate the predicted epc
print("Predicted 2Q Error per Clifford: %e"%pred_epc)

Predicted 2Q Error per Clifford: 1.313111e-02

import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright

Version Information

Qiskit Software	Version
Qiskit	0.16.1
Terra	0.13.0.dev0+98fd14e
Aer	0.4.1
Ignis	0.3.0.dev0+dd2c926
Aqua	0.6.4
IBM Q Provider	0.5.0
System information
Python	3.7.6 (default, Jan 8 2020, 19:59:22) [GCC 7.3.0]
OS	Linux
CPUs	8
Memory (Gb)	62.920127868652344
Fri Mar 27 15:44:43 2020 IST

This code is a part of Qiskit

© Copyright IBM 2017, 2020.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

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.