一种量子条件生成对抗网络算法

doi:10.12263/DZXB.20210512

电子学报 ›› 2022, Vol. 50 ›› Issue (7): 1586-1593.DOI: 10.12263/DZXB.20210512

一种量子条件生成对抗网络算法

刘文杰¹^,²(), 赵胶胶¹, 张颖³, 葛业波¹

^1.南京信息工程大学计算机与软件学院, 江苏南京 210044
^2.数字取证教育部工程研究中心, 江苏南京 210044
^3.南京信息工程大学自动化学院, 江苏南京 210044

收稿日期:2021-04-20 修回日期:2021-12-22 出版日期:2022-07-25
- 通讯作者:
- 刘文杰
- 作者简介:
- 刘文杰男，1979年11月生，湖北大治人，博士.南京信息工程大学计算机与软件学院副教授、硕士生导师，研究方向为量子算法、量子机器学习、量子安全多方计算和量子密码通信.E-mail: wenjieliu@nuist.edu.cn
  赵胶胶女，1996年8月生，江苏徐州人.南京信息工程大学计算机与软件学院硕士研究生，主要研究方向为量子机器学习和量子算法.E-mail: 2759312576@qq.com
- 基金资助:
- 国家自然科学基金 (62071240); 江苏省自然科学基金 (BK20171458)

A Quantum Conditional Generative Adversarial Network Algorithm

LIU Wen-jie¹^,²(), ZHAO Jiao-jiao¹, ZHANG Ying³, GE Ye-bo¹

^1.School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China
^2.Engineering Research Center of Digital Forensics（Ministry of Education）, Nanjing, Jiangsu 210044, China
^3.School of Automation, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China

Received:2021-04-20 Revised:2021-12-22 Online:2022-07-25 Published:2022-07-30
- Corresponding author:
- LIU Wen-jie
- Supported by:
- National Natural Science Foundation of China (62071240); Natural Science Foundation of Jiangsu Province, China (BK20171458)

摘要/Abstract

摘要：

量子生成对抗网络是量子机器学习算法领域研究热点之一，但其生成过程具有较大的随机性，不太适用于现实场景.为了解决该问题，提出了一种生成过程可控的量子条件生成对抗网络（Quantum Conditional Generative Adversarial Network，QCGAN）算法，其中条件信息采用one-hot形式进行多粒子W态编码，并通过向生成器和判别器输入条件信息达到稳定模型生成过程的目的.性能评估表明，与经典GAN、CGAN相比，本算法可生成离散数据，且将时间复杂度从 $O (N 2)$ 降为 $O (N)$ ；与带条件约束的量子生成对抗网络QuGAN相比，QCGAN消耗更少的量子资源.最后，以BAS（3，3）数据集和量子混合态生成为例，选用PennyLane平台进行仿真实验，结果表明QCGAN算法经过训练可有效收敛到Nash均衡点，进而验证了算法的实验可行性.

关键词: 量子生成对抗网络, 条件信息, W态编码, 参数化量子电路

Abstract:

Quantum generative adversarial network is one of the research hotspots in the quantum machine learning, but its generation process has a large randomness. To solve this problem, a quantum conditional generative adversarial network(QCGAN) algorithm is proposed. The one-hot method is used to encode conditional information into the multi-particle W state, and the purpose of stabilizing the model is achieved by inputting conditional information to the generator and discriminator. Compared with the classical GAN and CGAN, QCGAN can generate discrete data and reduce the time complexity from $O (N 2)$ to $O (N)$ . In addition, our algorithm consumes less quantum resources than the conditionally constrained quantum generative adversarial network QuGAN. Finally, taking the BAS(3, 3) dataset and the generation of quantum mixed states as examples, the PennyLane platform is selected for simulation experiments. The results show that QCGAN algorithm can effectively converge to the Nash equilibrium point after training, which verifies the experimental feasibility of the algorithm.

Key words: quantum generative adversarial network, conditional information, W-state coding, parameterized quantum circuits

中图分类号:

TP391.41

刘文杰, 赵胶胶, 张颖, 葛业波. 一种量子条件生成对抗网络算法[J]. 电子学报, 2022, 50(7): 1586-1593.

LIU Wen-jie, ZHAO Jiao-jiao, ZHANG Ying, GE Ye-bo. A Quantum Conditional Generative Adversarial Network Algorithm[J]. Acta Electronica Sinica, 2022, 50(7): 1586-1593.

图/表 20

图1 量子生成对抗网络算法示意图

图2 量子条件生成对抗网络算法框架

图3 制备m分类y的量子电路

图4 生成器G的量子电路

图5 判别器D的量子电路

表1 五种生成对抗网络算法性能对比(生成数据类型中,C表示连续数据,D表示离散数据)

算法名称	生成数据类型	时间复杂度	条件约束	量子资源消耗(qubits)
GAN^[1]	C	$O (N 2)$	无	—
CGAN^[6]	C	$O (N 2)$	有	—
GAQC^[11]	C& D	$O (N)$	无	$2 d$
QuGAN^[15]	C& D	$O (N)$	有	$2 d + 3 m + 2 n + s + 2$
QCGAN	C& D	$O (N)$	有	$2 d + 2 m$

表1 五种生成对抗网络算法性能对比(生成数据类型中,C表示连续数据,D表示离散数据)

算法名称	生成数据类型	时间复杂度	条件约束	量子资源消耗(qubits)
GAN^[1]	C	$O (N 2)$	无	—
CGAN^[6]	C	$O (N 2)$	有	—
GAQC^[11]	C& D	$O (N)$	无	$2 d$
QuGAN^[15]	C& D	$O (N)$	有	$2 d + 3 m + 2 n + s + 2$
QCGAN	C& D	$O (N)$	有	$2 d + 2 m$

图6 BAS(3,3)数据集分类示意图

图7 制备三粒子W态的量子电路

图8 生成BAS数据的生成器G的量子电路

图9 生成BAS数据的判别器D的量子电路

图10 GAQC算法的损失变化曲线

图11 QCGAN算法的损失变化曲线

图12 生成BAS(3,3)数据结果

(a)

(b)

(c)

(d)

表2 算法生成BAS数据集的准确率

算法	准确率
GAQC^[11]	95.32%
QCGAN	96.83%

图13 制备GHZ3的量子电路

图14 生成量子数据的生成器G的量子电路

图15 生成量子数据的判别器D的量子电路

图16 生成量子数据的损失变化曲线

图17 生成量子数据的保真度变化曲线

图18 分类生成量子态采样结果

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一种量子条件生成对抗网络算法

A Quantum Conditional Generative Adversarial Network Algorithm

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