In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum Circuit Born Machines (QCBMs) have been almost entirely evaluated on their capability to learn a given target distribution with high accuracy. While this aspect may be ideal for some tasks, it limits the scope of a generative model's assessment to its ability to memorize data rather than generalize. As a result, there has been little understanding of a model's generalization performance and the relation between such capability and the resource requirements, e.g., the circuit depth and the amount of training data. In this work, we leverage upon a recently proposed generalization evaluation framework to begin addressing this knowledge gap. We first investigate the QCBM's learning process of a cardinality-constrained distribution and see an increase in generalization performance while increasing the circuit depth. In the 12-qubit example presented here, we observe that with as few as 30% of the valid data in the training set, the QCBM exhibits the best generalization performance toward generating unseen and valid data. Lastly, we assess the QCBM's ability to generalize not only to valid samples, but to high-quality bitstrings distributed according to an adequately re-weighted distribution. We see that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set. To the best of our knowledge, this is the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models, and demonstrates the QCBM's ability to generalize to high-quality, desired novel samples.
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）
Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation
Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子器件中心）；NNF Quantum Computing Programme, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所NNF量子计算计划）
QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks
Department of Computer Science and Research Initiative QC-AI, RPTU Kaiserslautern-Landau（计算机科学系和QC-AI研究计划，鲁尔-帕绍大学（RPTU）凯斯贝赫-劳恩道分校）；Embedded Intelligence, German Research Center for Artificial Intelligence (DFKI)（嵌入式智能，德国人工智能研究中心（DFKI））；Department of Physics, RPTU Kaiserslautern-Landau（物理系，鲁尔-帕绍大学（RPTU）凯斯贝赫-劳恩道分校）
本研究利用量子电路 Born 机（QCBM）在混合与全量子形式下实现了 KAN 架构，通过预训练残差函数发挥参数化量子电路的表示能力，验证了 QuKAN 架构的可行性、可解释性与性能。
The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Laboratoire d’Informatique de Paris 6, CNRS, Sorbonne Université（巴黎第六大学计算机实验室，法国国家科学研究中心，索邦大学）；Fujitsu Research of Europe Ltd.（富士通欧洲研究有限公司）；National Quantum Computing Centre（国家量子计算中心）；School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh（爱丁堡大学数学学院和麦克斯韦数学科学研究所）
Generative modeling with Gaussian Boson Sampling: classically trainable Bosonic Born Machines
HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳研究物理中心）；Eötvös Loránd University（罗兰大学）；Center for Quantum Enabled-Computing, Center for Theoretical Physics of the Polish Academy of Sciences（波兰科学院理论物理中心量子计算中心）；Department of Physics, Korea Advanced Institute of Science and Technology（韩国科学技术院物理系）；University of Helsinki（赫尔辛基大学）；Algorithmiq Ltd（算法有限公司）
Learnability of the output distributions of local quantum circuits
Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（亥姆霍兹柏林材料与能源研究中心）；Stanford University（斯坦福大学）；Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland（马里兰大学量子信息与计算机科学联合中心）；NIST（美国国家标准与技术研究院）；TU Berlin（柏林工业大学）；FhG SIT（弗劳恩霍夫安全信息技术研究所）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）
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）
Calibrated Pressure-Observable Born and Hessian Actions for Quantum-Assisted Waveform Inversion
Jilin University（吉林大学）；Shenzhen Loop Area Institute (SLAI)（深圳环区研究所）；Key Laboratory of Digital Technology in Medical Diagnostics of Zhejiang Province（浙江省医学诊断数字技术重点实验室）；Beijing Normal University（北京师范大学）
Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models
Nanyang Technological University（南洋理工大学）；Centre for Quantum Technologies, Nanyang Technological University（南洋理工大学量子技术中心）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit（MajuLab，CNRS-UNS-NUS-NTU国际联合研究单元）
