量子ボリューム(Quantum Volume)¶
はじめに¶
Quantum Volume (QV) is a method to verify device performance and a metric to quantify the computational power of a quantum device. The method is based on the paper “Validating quantum computers using randomized model circuits” (https://arxiv.org/abs/1811.12926).
このノートブックは、 ignis.verification.quantum_volume モジュールの使用方法を示します。 この特定の例では、深さ6量子ボリューム回路まで実行し、ノイズがあるAerシミュレータを使用して実行する方法を示します。
[1]:
#Import general libraries (needed for functions)
import numpy as np
import matplotlib.pyplot as plt
from IPython import display
#Import Qiskit classes 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 qv function.
import qiskit.ignis.verification.quantum_volume as qv
QV 実行のパラメーターを選択します¶
この例では6量子ビットQ0,Q1,Q3,Q5,Q7,Q10があります。サブセットからフルセットまでみてみます。
[2]:
#Qubit list
qubit_lists = [[0,1,3],[0,1,3,5],[0,1,3,5,7],[0,1,3,5,7,10]]
ntrials = 50
QV シーケンスの生成¶
We generate the quantum volume sequences. We start with a small example (so it doesn’t take too long to run).
[3]:
qv_circs, qv_circs_nomeas = qv.qv_circuits(qubit_lists, ntrials)
[4]:
#pass the first trial of the nomeas through the transpiler to illustrate the circuit
qv_circs_nomeas[0] = qiskit.compiler.transpile(qv_circs_nomeas[0], basis_gates=['u1','u2','u3','cx'])
例として、最初のQVシーケンスに対応する回路を出力します。 理想的な回路は最初の n 個の量子ビット実行されることに注意してください(n はサブセットの量子ビット数です)。
[5]:
print(qv_circs_nomeas[0][0])
┌────────────────────────────┐ »
qr_0: |0>─┤ U3(0.88109,-3.974,0.67573) ├────────────────────────────────────»
┌┴────────────────────────────┤┌───┐ ┌───────────────────┐ ┌───┐»
qr_1: |0>┤ U3(2.6224,-0.97915,-4.0992) ├┤ X ├──┤ U3(pi/2,0,3.6893) ├───┤ X ├»
└─┬──────────────────────────┬┘└─┬─┘┌─┴───────────────────┴──┐└─┬─┘»
qr_2: |0>──┤ U3(1.3211,3.3206,1.9445) ├───■──┤ U3(0.76663,pi/2,-pi/2) ├──■──»
└──────────────────────────┘ └────────────────────────┘ »
cr_0: 0 ═══════════════════════════════════════════════════════════════════»
»
cr_1: 0 ═══════════════════════════════════════════════════════════════════»
»
cr_2: 0 ═══════════════════════════════════════════════════════════════════»
»
« ┌───┐»
«qr_0: ─────────────────────────────────────────────────────────────┤ X ├»
« ┌───────────────────┐ ┌───┐ ┌───────────────────────────┐ └─┬─┘»
«qr_1: ──┤ U3(pi/2,-pi,pi/2) ├──┤ X ├─┤ U3(2.3258,0.16961,1.9883) ├───■──»
« ┌─┴───────────────────┴─┐└─┬─┘┌┴───────────────────────────┴┐ »
«qr_2: ┤ U3(0.069147,pi,-pi/2) ├──■──┤ U3(2.6257,-0.40966,-4.1229) ├─────»
« └───────────────────────┘ └─────────────────────────────┘ »
«cr_0: ══════════════════════════════════════════════════════════════════»
« »
«cr_1: ══════════════════════════════════════════════════════════════════»
« »
«cr_2: ══════════════════════════════════════════════════════════════════»
« »
« ┌──────────────────┐ ┌───┐┌───────────────────┐ ┌───┐»
«qr_0: ───┤ U3(pi/2,0,3.648) ├───┤ X ├┤ U3(pi/2,-pi,pi/2) ├─┤ X ├»
« ┌──┴──────────────────┴──┐└─┬─┘├───────────────────┴┐└─┬─┘»
«qr_1: ┤ U3(0.67876,pi/2,-pi/2) ├──■──┤ U3(0.39769,0,pi/2) ├──■──»
« └────────────────────────┘ └────────────────────┘ »
«qr_2: ──────────────────────────────────────────────────────────»
« »
«cr_0: ══════════════════════════════════════════════════════════»
« »
«cr_1: ══════════════════════════════════════════════════════════»
« »
«cr_2: ══════════════════════════════════════════════════════════»
« »
« ┌───────────────────────────┐ ┌───┐ ┌───────────────────┐ ┌───┐»
«qr_0: ┤ U3(1.6714,0.26184,5.8406) ├─┤ X ├──┤ U3(pi/2,0,3.3447) ├──┤ X ├»
« ├───────────────────────────┴┐└─┬─┘ └───────────────────┘ └─┬─┘»
«qr_1: ┤ U3(2.0587,-0.39667,5.1684) ├──┼─────────────────────────────┼──»
« └────────────────────────────┘ │ ┌───────────────────────┐ │ »
«qr_2: ────────────────────────────────■──┤ U3(0.8297,pi/2,-pi/2) ├──■──»
« └───────────────────────┘ »
«cr_0: ═════════════════════════════════════════════════════════════════»
« »
«cr_1: ═════════════════════════════════════════════════════════════════»
« »
«cr_2: ═════════════════════════════════════════════════════════════════»
« »
« ┌───────────────────┐ ┌───┐┌──────────────────────────┐
«qr_0: ─┤ U3(pi/2,-pi,pi/2) ├─┤ X ├┤ U3(2.673,3.0342,0.69813) ├
« └───────────────────┘ └─┬─┘└──────────────────────────┘
«qr_1: ─────────────────────────┼──────────────────────────────
« ┌─────────────────────┐ │ ┌──────────────────────────┐
«qr_2: ┤ U3(0.032719,0,pi/2) ├──■──┤ U3(1.14,-1.5329,-1.9038) ├
« └─────────────────────┘ └──────────────────────────┘
«cr_0: ════════════════════════════════════════════════════════
«
«cr_1: ════════════════════════════════════════════════════════
«
«cr_2: ════════════════════════════════════════════════════════
«
理想回路をシミュレートする¶
量子ボリュームメッソッドでは、各回路の理想的な出力を知る必要があります。 Aerのステートベクトルシミュレータを使って理想的な結果を得ることができます
[6]:
#The Unitary is an identity (with a global phase)
backend = qiskit.Aer.get_backend('statevector_simulator')
ideal_results = []
for trial in range(ntrials):
print('Simulating trial %d'%trial)
ideal_results.append(qiskit.execute(qv_circs_nomeas[trial], backend=backend, optimization_level=0).result())
Simulating trial 0
Simulating trial 1
Simulating trial 2
Simulating trial 3
Simulating trial 4
Simulating trial 5
Simulating trial 6
Simulating trial 7
Simulating trial 8
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Simulating trial 40
Simulating trial 41
Simulating trial 42
Simulating trial 43
Simulating trial 44
Simulating trial 45
Simulating trial 46
Simulating trial 47
Simulating trial 48
Simulating trial 49
次に、理想的な結果を量子ボリュームフィッターにロードします。
[7]:
qv_fitter = qv.QVFitter(qubit_lists=qubit_lists)
qv_fitter.add_statevectors(ideal_results)
ノイズモデルを定義¶
シミュレータのノイズモデルを定義します。減衰をシミュレートするために、CNOTとUゲートに脱分極エラー確率を追加します。
[8]:
noise_model = NoiseModel()
p1Q = 0.002
p2Q = 0.02
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')
#noise_model = None
Aerシミュレータで実行¶
QV シーケンスは、Qiskit Aer Simulator (一部のノイズモデル) を使用するか、IBMQ プロバイダーを使用して実行できます。 そして、result_list の結果のリストを取得します。
[9]:
backend = qiskit.Aer.get_backend('qasm_simulator')
basis_gates = ['u1','u2','u3','cx'] # use U,CX for now
shots = 1024
exp_results = []
for trial in range(ntrials):
print('Running trial %d'%trial)
exp_results.append(qiskit.execute(qv_circs[trial], basis_gates=basis_gates, backend=backend, noise_model=noise_model, backend_options={'max_parallel_experiments': 0}).result())
Running trial 0
Running trial 1
Running trial 2
Running trial 3
Running trial 4
Running trial 5
Running trial 6
Running trial 7
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実験データをフィッターにロードします。データは再実行すると蓄積され続けます（フィッターが再インスタンス化されない限り）。
[10]:
qv_fitter.add_data(exp_results)
[11]:
plt.figure(figsize=(10, 6))
ax = plt.gca()
# Plot the essence by calling plot_rb_data
qv_fitter.plot_qv_data(ax=ax, show_plt=False)
# Add title and label
ax.set_title('Quantum Volume for up to %d Qubits \n and %d Trials'%(len(qubit_lists[-1]), ntrials), fontsize=18)
plt.show()
量子ボリューム(Quantum Volume)¶
各深さのリスト統計情報。各深さのリストは、その 深さで成功したかどうか、および信頼区間です。ある深さが成功とするためには、信頼区間が97.5%以上でなければなりません。
[12]:
qv_success_list = qv_fitter.qv_success()
qv_list = qv_fitter.ydata
for qidx, qubit_list in enumerate(qubit_lists):
if qv_list[0][qidx]>2/3:
if qv_success_list[qidx][0]:
print("Width/depth %d greater than 2/3 (%f) with confidence %f (successful). Quantum volume %d"%
(len(qubit_list),qv_list[0][qidx],qv_success_list[qidx][1],qv_fitter.quantum_volume()[qidx]))
else:
print("Width/depth %d greater than 2/3 (%f) with confidence %f (unsuccessful)."%
(len(qubit_list),qv_list[0][qidx],qv_success_list[qidx][1]))
else:
print("Width/depth %d less than 2/3 (unsuccessful)."%len(qubit_list))
Width/depth 3 greater than 2/3 (0.791562) with confidence 0.985155 (successful). Quantum volume 8
Width/depth 4 greater than 2/3 (0.707090) with confidence 0.735022 (unsuccessful).
Width/depth 5 greater than 2/3 (0.710508) with confidence 0.752867 (unsuccessful).
Width/depth 6 less than 2/3 (unsuccessful).
[13]:
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
Version Information
| Qiskit Software | Version |
|---|---|
| Qiskit | 0.14.0 |
| Terra | 0.11.0 |
| Aer | 0.3.4 |
| Ignis | 0.2.0 |
| Aqua | 0.6.1 |
| IBM Q Provider | 0.4.4 |
| System information | |
| Python | 3.7.5 (default, Oct 25 2019, 10:52:18) [Clang 4.0.1 (tags/RELEASE_401/final)] |
| OS | Darwin |
| CPUs | 4 |
| Memory (Gb) | 16.0 |
| Tue Dec 10 17:04:56 2019 EST | |
This code is a part of Qiskit
© Copyright IBM 2017, 2019.
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.
[ ]: