Laziness, Barren Plateau, and Noise in Machine Learning
Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普利兹克分子工程学院）；Chicago Quantum Exchange（芝加哥量子交易所）；Kadanoff Center for Theoretical Physics, The University of Chicago（芝加哥大学卡达诺夫理论物理中心）；qBraid Co.（qBraid公司）
We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Center for Non-Linear Studies（非线性研究中心）；Institute of Physics（物理研究所）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Chulalongkorn University（朱拉隆梭大学）；Institute for Quantum Information and Matter（量子信息与物质研究所）；IBM Quantum（IBM 量子）；IBM T.J. Watson Research Center（IBM 汤普森研究中心）；Quantum Artificial Intelligence Laboratory（量子人工智能实验室）；NASA Ames Research Center（NASA 莱恩研究中心）；Simons Institute for the Theory of Computing（Simons 计算理论研究所）；University of California, Berkeley（加州大学伯克利分校）；Normal Computing Corporation（正常计算公司）；Theoretical Division（理论部）；Quantum Science Center（量子科学中心）；Google Quantum AI（谷歌量子人工智能）；Information Sciences（信息科学）
Structured quantum learning via em algorithm for Boltzmann machines
Department of Mathematical Informatics, Graduate School of Informatics, Nagoya University（数学信息学系，信息科学研究生院，名古屋大学）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（数据科学学院，香港中文大学（深圳））；International Quantum Academy（国际量子学院）；Graduate School of Mathematics, Nagoya University（数学研究生院，名古屋大学）
Does provable absence of barren plateaus imply classical simulability?
Information Sciences, Los Alamos National Laboratory（信息科学，洛斯阿拉莫斯国家实验室）；Quantum Science Center, Oak Ridge（量子科学中心，奥克兰岭）；Theoretical Division, Los Alamos National Laboratory（理论部，洛斯阿拉莫斯国家实验室）；Center for Nonlinear Studies, Los Alamos National Laboratory（非线性研究中心，洛斯阿拉莫斯国家实验室）；University of Strathclyde（斯特拉斯克莱德大学）；Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（物理研究所，洛桑联邦理工学院（EPFL））；Donostia International Physics Center（多斯通国际物理中心）；Department of Physics and Astronomy, University of Waterloo（物理与天文学系，滑铁卢大学）；Vector Institute, MaRS Centre（向量研究所，马尔伯里中心）；Complex Systems, Department of Physics, Faculty of Science, Chulalongkorn University（复杂系统，物理系，科学学院，朱拉隆梭大学）；Walter Burke Institute for Theoretical Physics, Caltech（沃尔特·伯克理论物理研究所，加州理工学院）
Noise-Induced Barren Plateaus in Variational Quantum Algorithms
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Imperial College London（伦敦帝国学院）；University of Strathclyde（思克莱德大学）；National Physical Laboratory（国家物理实验室）；Center for Nonlinear Studies, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室非线性研究中心）
Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility
Department of Computer Science and Technology, Tsinghua University, Beijing, China（计算机科学与技术系，清华大学，北京，中国）；Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China（叶阳数学科学中心，清华大学，北京，中国）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 100407, China（燕琦湖北京数学科学与应用研究所，北京，中国）；Department of Mathematics, Tsinghua University, Beijing 100084, China（数学系，清华大学，北京，中国）
Mitigating Barren Plateaus in Quantum Denoising Diffusion Probabilistic Model
School of Computer Science and Technology, University of Science and Technology of China（中国科学技术大学计算机科学与技术学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算机科学与数据科学学院）；Research Institute of Quantum Technology, The Hong Kong Polytechnic University（香港理工大学量子技术研究所）
Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）；Center for Nonlinear Studies, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室非线性研究中心）
Q-Capsule: A Localized Capsule-Based Quantum Neural Architecture for Barren Plateau Mitigation
Florida Atlantic University（佛罗里达大西洋大学）；Khulna University of Engineering & Technology（库尔纳工程与技术大学）；Southern Illinois University Carbondale（南伊利诺伊大学卡本代尔分校）
Evolutionary-enhanced quantum supervised learning model
Kipu Quantum GmbH（Kipu Quantum公司）；SENAI CIMATEC（SENAI CIMATEC研究院）；Federal University of Latin-American Integration（拉丁美洲一体化联邦大学）；University of Surrey（萨里大学）
Variational quantum simulation: a case study for understanding warm starts
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；IBM Quantum, IBM Research – Zurich（IBM量子（IBM苏黎世研究院））；Chulalongkorn University（朱拉隆功大学）
Special-Unitary Parameterization for Trainable Variational Quantum Circuits
Department of Electrical and Electronic Engineering, Imperial College London, London, UK（电气与电子工程系，帝国理工学院伦敦校区，伦敦，英国）；Centre for Quantum Engineering, Science and Technology (QuEST), Imperial College London, London, UK（量子工程、科学与技术中心（QuEST），帝国理工学院伦敦校区，伦敦，英国）；Brookhaven National Laboratory, New York, USA（布鲁克海文国家实验室，纽约，美国）；National Taiwan University, Taipei, Taiwan（台湾大学，台北，台湾）
Subtleties in the trainability of quantum machine learning models
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；National University of Singapore（新加坡国立大学）；Imperial College London（帝国理工学院）；State University of New York at Stony Brook（纽约州立大学石溪分校）
Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms
Chula Intelligent and Complex Systems Lab, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand, 10330（朱拉隆功大学科学学院物理系复杂系统实验室）；Siam Quantum Square, Faculty of Science, Chulalongkorn University, Bangkok, Thailand, 10330（朱拉隆功大学科学学院暹罗量子广场）；Centre for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland（瑞士洛桑联邦理工学院量子科学与工程中心）
Sculpting Quantum Landscapes: Fubini-Study Metric Conditioning for Geometry Aware Learning in Parameterized Quantum Circuits
Quantum Physics and Spintronic Team, LPMC, Faculty of Sciences Ben M’sick, Hassan II University of Casablanca, Morocco（量子物理与自旋电子团队，LPMC，科学学院本·梅西克，卡萨布兰卡哈桑二世大学，摩洛哥）
Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA（电子与计算机工程系，佐治亚理工学院）；NVIDIA Research, Santa Clara, CA 95051, USA（NVIDIA研究）；IBM Thomas J. Watson Research Center, NY, 10598, USA（IBM托马斯·J·沃森研究中心）；Hon Hai (Foxconn) Quantum Computing Research Center, Taipei, 114, Taiwan（鸿海（富士康）量子计算研究中心）
