We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the reproducing kernel Hilbert spaces induced by symmetric and antisymmetric Gaussian kernels are dense in the space of symmetric and antisymmetric functions, and propose a Slater determinant representation of the antisymmetric Gaussian kernel, which allows for an efficient evaluation even if the state space is high-dimensional. Furthermore, we show that by exploiting symmetries or antisymmetries the size of the training data set can be significantly reduced. The results are illustrated with guiding examples and simple quantum physics and chemistry applications.
Learning the gravitational force law and other analytic functions
Google Research（谷歌研究院）
Large neural network models have been successful in learning functions of importance in many branches of science, including physics, chemistry and biology. Recent theoretical work has shown explicit learning bounds for wide networks and kernel methods on some simple classes of functions, but not on more complex functions which arise in practice. We extend these techniques to provide learning bounds for analytic functions on the sphere for any kernel method or equivalent infinitely-wide network with the corresponding activation function trained with SGD. We show that a wide, one-hidden layer Re…
A Global Spacetime Optimization Approach to the Real-Space Time-Dependent Schrödinger Equation
Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生部）；AI for Science Institute（人工智能科学研究院）；Shanghai Jiao Tong University（上海交通大学）；National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所计算物理国家重点实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；HEDPS, CAPT, College of Engineering and School of Physics, Peking University（北京大学工学院和物理学院高能密度物理研究中心、量子材料科学中心）
Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Center for Theoretical Physics of the Polish Academy of Sciences（波兰科学院理论物理中心）；University of Helsinki（赫尔辛基大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络温格物理学研究中心）；Algorithmiq Ltd（Algorithmiq有限公司）
Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes
Cleveland Clinic Foundation（克利夫兰诊所基金会）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；IBM Quantum, IBM Research – Tokyo（IBM量子，IBM研究-东京）；IBM Quantum, T.J. Watson Research Center（IBM量子，T.J.沃森研究中心）
Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology（量子技术研究中心和先进光电量子架构与测量（MOE）重点实验室，物理系，北京理工大学）；Department of Mathematics and Physics, Shijiazhuang Tiedao University（数学物理系，石家庄铁道大学）；Yau Mathematical Sciences Center, Tsinghua University（叶中数学科学中心，清华大学）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing（燕奇湖北京应用数学科学研究所，北京）
Classification with Quantum Machine Learning: A Survey
Faculty of Computer Science, Nahda University（纳达大学计算机科学学院）；Faculty of Computers and Information, Mansoura University（曼苏拉大学计算机与信息学院）；Faculty of Computers and Information, Minia University（米尼亚大学计算机与信息学院）
由于量子计算（QC）在密码学、化学、大数据、机器学习、优化、物联网（IoT）、区块链、通信等许多应用中的优越性和显著进展。量子机器学习（Quantum Machine Learning，QML）是将经典机器学习与量子信息处理（Quantum Information Processing，QIP）相结合，解决和改进经典机器学习中存在的问题（如时间和能量消耗、核估计等）的一个新的量子领域。本文的目的是提出并总结量子机器学习（QML）的最新进展。特别是最近的QML分类工作。此外，我们还涵盖了最近在量子机器学习（QML）中发表的大约30篇出版物。我们提出了量子世界中的分类方案，并讨论了将经典数据映射到量子数据的编码方法。然后，我们给出了量子子程序和量子计算（QC）在提高经典机器学习（ML）性能和速度方面的一些方法。同时也介绍了QML在各个领域的应用、面临的挑战和未来的展望。
