变分量子电路因在组合优化、量子模拟、概率分布建模等实际应用中的价值，近期受到广泛关注。尽管潜力巨大，但这类电路在数十量子比特规模以上的实际实用性仍受到很大质疑，其中一个核心问题就是所谓的贫瘠高原（barren plateaus）现象：具有随机结构的量子电路往往会呈现平坦的代价函数景观，因此无法被高效训练。\n本文提出了两种全新的参数条件，在这两种条件下，硬件高效拟设（hardware-efficient ansatz，HEA）在任意电路深度下都不会出现贫瘠高原。第一种条件下，HEA近似于由局域哈密顿量生成的时间演化算符，我们借助[Park and Killoran, Quantum 8, 1239 (2024)]的最新研究结果，证明了无论电路深度如何，局域可观测量和全局可观测量的梯度幅值都存在恒定下界。第二种参数条件下，HEA处于多体局域（many-body localized，MBL）相，我们利用MBL系统的唯象模型论证了该相中的HEA对局域可观测量具有较大的梯度分量。\n通过用上述条件初始化HEA的参数，我们证明了该发现在求解多体哈密顿量问题时整体性能更优。研究结果表明，只要巧妙选择初始参数，贫瘠高原就不再是问题，而局域极小值、电路表达能力等其他因素才是更关键的制约因素。
英文摘要：
Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.
Defeating Barren Plateaus with Task-Aligned Symmetry
Faculty of Information Science and Engineering, Ocean University of China（中国海洋大学信息科学与工程学部）；China Telecom Quantum Information Technology Group Co., LTD.（中国电信量子信息技术集团有限公司）
From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits
Institut für Theoretische Physik Leibniz Universität Hannover（汉诺威莱布尼茨大学理论物理研究所）；Institute for Quantum Information RWTH Aachen University（亚琛工业大学量子信息研究所）
Can Chemically Inspired Parameter Initialization Mitigate Barren Plateaus in Variational Quantum Eigensolvers?
Guangdong Basic Research Center of Excellence for Aggregate Science, School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（广东聚合科学卓越研究中心，科学与工程学部，香港中文大学（深圳））；School of Physical and Chemical Sciences, Queen Mary University of London（物理与化学科学学院，伦敦大学玛丽女王学院）
A Representation-Theoretic Framework for Characterizing Barren Plateaus
International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；Instituto de Física de São Carlos, Universidade de São Paulo（圣保罗大学圣卡洛斯物理研究所）
Experimental demonstration of the absence of noise-induced barren plateaus using information content landscape analysis
Honda Research Institute Europe GmbH（本田欧洲研究院）；Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（皮塔耶夫斯基玻色-爱因斯坦凝聚中心，意大利国家研究委员会光学研究所及特伦托大学物理系）；INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（INFN-TIFPA，特伦托基础物理与应用研究院）
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）
Exponentially many initializations to avoid barren plateaus
Fujitsu Research of America, Santa Clara, CA 95054, USA（美国富士通美洲研究部）；University of Delaware, Newark, DE 19716, USA（德雷克塞尔大学）；Department for Quantum Information and Computation at Kepler (QUICK), Johannes Kepler University, Linz, Austria（约翰·凯撒大学量子信息与计算部门）；Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA（洛斯阿拉莫斯国家实验室信息科学部）
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）
Measurement-Induced Landscape Transitions and Coding Barren Plateaus in Hybrid Variational Quantum Circuits
Hewlett Packard Enterprise Labs（惠普企业实验室）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固体物理实验室）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics, Applied Physics, and Astronomy, Binghamton University（宾汉姆顿大学物理、应用物理和天文学系）；School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院）
