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量子生成对抗网络

        生成对抗网络是由两部分神经网络组成，分别为生成器和判别器。量子生成对抗网络的基本原理与经典的GAN基本相同。

        生成对抗网络由GoodFellow等人提出，主要功能是生成伪造的样本。生成器G的输入为一个随机向量z，输出为一个生成样本G(z)。判别器D的输入为一个真实的或生成的样本x，输出为对该样本的判断。当输入真实样本x时，判别器的输出为D(x)，接近1。当输入生成样本G(z)时，判别器的输出为D(G(z))，接近0。

GAN的优化目标函数可以表示为：

 

参数化量子线路 

量子生成对抗网络所用的参数化量子线路主要由三部分组成：旋转层、叠加层和纠缠层

旋转层由旋转门Ry(θ) 组成

叠加层使用的是双量子比特门

 其中 旋转层由旋转门R_{y}(\Theta )组成。叠加层使用的是双量子比特门R_{yy}(\Theta )

 

        相比起神经网络，多了一个叠加层，主要是因为量子资源和设备的限制，退相干会导致系统内部的相互作用关系发生变化，影响了系统的纠缠程度，进而影响QGAN中生成器和判别器的功能，而叠加层可以减少这种影响。

        量子判别器和量子生成器都采用前述的参数化量子线路

        QGAN通过经典计算机和量子计算机之间的迭代切换，找到参数化量子线路的最优参数

   QGAN将保真度作为目标函数 ，因此用交换测试得到保真度
   量子判别器之后量子态为|\delta _{1}\rangle，量子生成器之后量子态为|\gamma \rangle，保真度|\langle \gamma|\delta _{1} \rangle|^{2}要尽量接近0
   量子判别器之后量子态为|\delta _{2}\rangle  ，真实样本为|\xi \rangle，保真度|\langle \gamma|\delta _{2} \rangle|^{2}要尽量接近1
   因此 训练量子判别器时要最小化  -log(1-|\langle \gamma|\delta _{1} \rangle|^{2}) 和 -log(|\langle \gamma|\delta _{2} \rangle|^{2})
    训练量子生成器时要最小化 -log(|\langle \gamma|\delta _{2} \rangle|^{2})

 

 生成一个带有数字3或9的图片，真实图片由手写数字3和9组成，特征为2维

 

代码

#qiskit版本>1.0.0
import random
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn import datasets
from qiskit import QuantumRegister, ClassicalRegister,transpile
from qiskit import QuantumCircuit
from qiskit_aer import Aer
from math import pi
from qiskit import *  
import tensorflow as tf
from sklearn.decomposition import PCA
import time
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.patheffects as PathEffects


#数据准备
test_images,test_labels = tf.keras.datasets.mnist.load_data()
train_images = test_images[0].reshape(60000,784)
train_labels = test_images[1]
labels = test_images[1]
train_images = train_images/255
k=2
pca = PCA(n_components=k)
pca.fit(train_images)
pca_data = pca.transform(train_images)[:10000]
train_labels = train_labels[:10000]
t_pca_data = pca_data.copy()
pca_descaler = [[] for _ in range(k)]
for i in range(k):
    if pca_data[:,i].min() < 0:
        pca_descaler[i].append(pca_data[:,i].min())
        pca_data[:,i] += np.abs(pca_data[:,i].min())
    else:
        pca_descaler[i].append(pca_data[:,i].min())
        pca_data[:,i] -= pca_data[:,i].min()
    pca_descaler[i].append(pca_data[:,i].max())
    pca_data[:,i] /= pca_data[:,i].max()
pca_data_rot= 2*np.arcsin(np.sqrt(pca_data))
valid_labels = None
valid_labels = train_labels==9
valid_labels = train_labels == 3 
pca_data_rot = pca_data_rot[valid_labels]
pca_data = pca_data[valid_labels]

#利用特征重构图像
def descale_points(d_point,scales=pca_descaler,tfrm=pca):
    for col in range(d_point.shape[1]):
        d_point[:,col] *= scales[col][1]
        d_point[:,col] += scales[col][0]
    reconstruction = tfrm.inverse_transform(d_point)
    return reconstruction
learning_rate=0.01

#初始化判别器和生成器参数
thetaD=[np.random.rand()*np.pi for i in range(4)]
thetaG=[np.random.rand()*np.pi for i in range(4)]
#定义数组分别保存更新后判别器和生成器的参数
thetaD_new=[0,0,0,0]
thetaG_new=[0,0,0,0]
#保存被加载的真数据
data=[0,0]

#定义训练判别器的量子线路
circuit=QuantumCircuit(5,5)
for i in range(1,3):
    circuit.ry(thetaD[i-1],i)
circuit.ryy(thetaD[2],1,2)
circuit.cry(thetaD[3],1,2)
for i in range(1,3):
    circuit.ry(thetaG[i-1],i+2)
circuit.ryy(thetaG[2],3,4)
circuit.cry(thetaG[3],3,4)
circuit.barrier(0,1,2,3,4)
circuit.h(0)
for i in range(1,3):
    circuit.cswap(0,i,i+2)
circuit.h(0)
circuit.measure(0,0)
circuit.draw(output='mpl', plot_barriers=False)

#定义训练生成器的量子线路
circuit1=QuantumCircuit(5,5)
for i in range(1,3):
    circuit1.ry(thetaD[i-1],i)
circuit1.ryy(thetaD[2],1,2)
circuit1.cry(thetaD[3],1,2)
circuit1.ry(data[0],3)
circuit1.ry(data[1],4)
circuit1.barrier(0,1,2,3,4)
circuit1.h(0)
for i in range(1,3):
    circuit1.cswap(0,i,i+2)
circuit1.h(0)
circuit1.measure(0,0)
circuit1.draw(output='mpl', plot_barriers=False)

#定义生成器线路，便于得到训练后生成的数据
circuit2=QuantumCircuit(2,2)
circuit2.ry(thetaG[0],0)
circuit2.ry(thetaG[1],1)
circuit2.ryy(thetaG[2],0,1)
circuit2.cry(thetaG[3],0,1)
circuit2.measure(0,0)
circuit2.measure(1,1)
circuit2.draw(output='mpl')
value1=0
value2=0
f_diff=0
b_diff=0
backend=Aer.get_backend('qasm_simulator')
for epoch in range(0,50):
    print(f'第--{epoch}--次训练')
    par_shift = 0.5*np.pi
    # 通过circuit线路，使用假数据训练判别器

    for i in range(1):
        for j in range(0,4):
            thetaD[j]+=par_shift
            # Set up the backend
            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc = transpile(circuit, backend)
             # Run the transpiled circuit
            job_sim1 = backend.run(transpiled_qc, shots=2000)
            sim_result1 = job_sim1.result()
            measurement_result1 = sim_result1.get_counts(circuit)
            value1=2*(measurement_result1['00000']/2000-0.5)
            if value1 <= 0.005:
                value1 = 0.005
            f_diff=-np.log(1-value1)
            thetaD[j]-=2*par_shift

            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc = transpile(circuit, backend)
             # Run the transpiled circuit
            job_sim1 = backend.run(transpiled_qc, shots=2000)
            sim_result1 = job_sim1.result()
            measurement_result1 = sim_result1.get_counts(circuit)
            value2=2*(measurement_result1['00000']/2000-0.5)
            if value2 <= 0.005:
                value2 = 0.005
            b_diff=-np.log(1-value2)
            thetaD[j]+=par_shift
            df=0.5*(f_diff-b_diff)
            if abs(df)>1:
                df = df/abs(df)
            thetaD_new[j]=thetaD[j]-learning_rate*df/10
        thetaD=thetaD_new
    # 使用circuit1线路训练判别器
    for index,point in enumerate(pca_data_rot):
        data[0] = point[0]
        data[1] = point[1]
        for j in range(0,4):
            thetaD[j]+=par_shift
            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc1 = transpile(circuit1, backend)
             # Run the transpiled circuit
            job_sim = backend.run(transpiled_qc1, shots=1000)
            sim_result = job_sim.result()
            measurement_result = sim_result.get_counts(circuit1)
            value1=2*(measurement_result['00000']/1000-0.5)
            if value1 <= 0.005:
                value1 = 0.005
            f_diff=-np.log(value1)
            thetaD[j]-=2*par_shift
            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc1 = transpile(circuit1, backend)
             # Run the transpiled circuit
            job_sim = backend.run(transpiled_qc1, shots=1000)
            sim_result = job_sim.result()
            measurement_result = sim_result.get_counts(circuit1)
            value2=2*(measurement_result['00000']/1000-0.5)
            if value2 <= 0.005:
                value2 = 0.005
            thetaD[j]+=par_shift
            b_diff=-np.log(value2)
            df=0.5*(f_diff-b_diff)
            thetaD_new[j]=thetaD[j]-learning_rate*df/10
        thetaD=thetaD_new
    # 通过circuit线路，利用判别器训练生成器
    for i in range(len(pca_data_rot)//10):
        for j in range(0,4):
            thetaG[j]+=par_shift
            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc = transpile(circuit, backend)
             # Run the transpiled circuit
            job_sim = backend.run(transpiled_qc, shots=1000)
            sim_result = job_sim.result()
            measurement_result = sim_result.get_counts(circuit)
            value1=2*(measurement_result['00000']/1000-0.5)
            if value1 <= 0.005:
                value1 = 0.005
            f_diff=-np.log(value1)
            thetaG[j]-=2*par_shift
            backend = Aer.get_backend('qasm_simulator')
            transpiled_qc = transpile(circuit, backend)
             # Run the transpiled circuit
            job_sim = backend.run(transpiled_qc, shots=1000)
            sim_result = job_sim.result()
            measurement_result = sim_result.get_counts(circuit)
            value2=2*(measurement_result['00000']/1000-0.5)
            if value2 <= 0.005:
                value2 = 0.005
            thetaG[j]+=par_shift
            b_diff=-np.log(value2)
            df=0.5*(f_diff-b_diff)
            thetaG_new[j]=thetaG[j]-learning_rate*df*5
        thetaG=thetaG_new
    data = []
    n_results = 2
    #使用训练好的生成器生成数据并使用逆PCA生成图像
    for _ in range(16):
        backend = Aer.get_backend('qasm_simulator')
        transpiled_qc2 = transpile(circuit2, backend)
        # Run the transpiled circuit
        job = backend.run(transpiled_qc2, shots=1000)
        results = job.result()
        measurement_result2 = results.get_counts(circuit2)
        
        bins = [[0,0] for _ in range(n_results)]
        for key,value in measurement_result2.items():
            for i in range(n_results):
                if key[-i-1]== '1':
                    bins[i][0] += value
                bins[i][1] += value
        for i,pair in enumerate(bins):
            bins[i]= pair[0]/pair[1]
        data.append(bins)
    data = np.array(data)
    new_info = descale_points(data[:16])
    new_info = new_info.reshape(new_info.shape[0],28,28)
    print(f"Epoch {epoch} Generated Images")
    for i in range(new_info.shape[0]):
        plt.subplot(4, 4, i+1)
        plt.imshow(new_info[i, :, :], cmap='gray')
        plt.axis('off')
    plt.show()

 

悦读

道可道，非常道；名可名，非常名。 无名，天地之始，有名，万物之母。 故常无欲，以观其妙，常有欲，以观其徼。 此两者，同出而异名，同谓之玄，玄之又玄，众妙之门。

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