The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs). Despite the empirical achievements, the foundations and the potential advantages of QGLMs remain largely obscure. To narrow this knowledge gap, here we explore the generalization property of QGLMs, the capability to extend the model from learned to unknown data. We consider two prototypical QGLMs, quantum circuit Born machines and quantum generative adversarial networks, and explicitly give their generalization bounds. The result identifies superiorities of QGLMs over classical methods when quantum devices can directly access the target distribution and quantum kernels are employed. We further employ these generalization bounds to exhibit potential advantages in quantum state preparation and Hamiltonian learning. Numerical results of QGLMs in loading Gaussian distribution and estimating ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.
Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble
Macau University of Science and Technology（澳门科技大学）；New Jersey Institute of Technology（新泽西理工学院）；Foshan University（佛山大学）；University of Surrey（萨里大学）；South China Agricultural University（华南农业大学）
Noise robustness and experimental demonstration of a quantum generative adversarial network for continuous distributions
University of Toronto（多伦多大学）；Zapata Computing Inc.（Zapata Computing 公司）；Vector Institute（向量研究所）；Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院）
A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Stinger Ghaffarian Technologies Inc.（斯汀格·加法里安技术公司）；D-Wave Systems Inc.（D-Wave系统公司）；University of Florence（佛罗伦萨大学）；Simon Fraser University（西蒙弗雷泽大学）
Generative Modeling of Quantum Distribution with Functional Flow Matching
Graduate School of Data Science, Seoul National University, Seoul, Korea（首尔国立大学数据科学研究生院）；Department of Statistics and Data Science, Yonsei University, Seoul, Korea（延世大学统计与数据科学系）；Department of Applied Statistics, Yonsei University, Seoul, Korea（延世大学应用统计系）；Google Research, Mountain View, California, United States（谷歌研究）
On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators
Department of Computer Science and Research Initiative QC-AI（计算机科学系和QC-AI研究计划）；RPTU Kaiserslautern-Landau（凯撒斯劳滕-兰道大学）；Embedded Intelligence（嵌入式智能）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Department of Artificial Intelligence（人工智能系）；Korea University（韩国大学）；Department of Physics（物理系）
Quantum MeanFlow: single-shot generative sampling on NISQ hardware
Keio University（庆应义塾大学）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q)（人类生物学-微生物组-量子研究中心（WPI-Bio2Q））；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC)（庆应义塾大学可持续量子人工智能中心（KSQAIC））；University of California, Berkeley（加州大学伯克利分校）
Recent Advances for Quantum Neural Networks in Generative Learning
Defense Innovation Institute（国防创新研究院）；Tianjin Artificial Intelligence Innovation Center（天津人工智能创新中心）；Imperial College London（帝国理工学院）；JD Explore Academy（京东探索研究院）；National University of Defense Technology（国防科技大学）；The University of Sydney（悉尼大学）；Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）
A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models
Zapata Computing Canada Inc.（扎帕塔计算加拿大公司）；Vector Institute（向量研究所）；Department of Physics and Astronomy（物理与天文学系）；University of Waterloo（滑铁卢大学）；Department of Physics（物理系）；University of Toronto（多伦多大学）
Differentiable Learning of Quantum Circuit Born Machine
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）
Unsupervised Generative Modeling Using Matrix Product States
Peking University（北京大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Generative modelling powered by room-temperature polariton condensates
School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S10 2TN, United Kingdom（谢菲尔德大学数学与物理科学学院）；Department of Physics, City College of New York, New York, NY 10031, USA（纽约城市学院物理系）；Physics Doctoral Program, Graduate Center of the City University of New York, New York, NY 10016, USA（纽约城市大学研究生中心物理博士项目）；Chemistry Doctoral Program, Graduate Center of the City University of New York, New York, NY 10016, USA（纽约城市大学研究生中心化学博士项目）
Generative quantum advantage for classical and quantum problems
Google Quantum AI（谷歌量子AI）；Department of Physics, California Institute of Technology（加州理工学院物理系）；Department of Physics（物理系）；Astronomy, Purdue University（天文学，普渡大学）
Generative quantum combinatorial optimization by means of a novel conditional generative quantum eigensolver
National Institute of Advanced Industrial Science and Technology（日本先进工业科学技术研究所）；NVIDIA Corporation（英伟达公司）；University of Toronto（多伦多大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；DENSO CORPORATION（电装公司）
Learning and Inference on Generative Adversarial Quantum Circuits
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；College of Physics, Jilin University（吉林大学物理学院）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学卡弗里理论科学研究所）
School of Electronic and Information Engineering, Anhui University（安徽大学电子与信息工程学院）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥国家科学中心人工智能研究所）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）；School of Cyber Science and Technology, University of Science and Technology of China（中国科学技术大学网络科学与技术学院）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Origin Quantum Computing Technology Company（起源量子计算技术有限公司）
