准备给定哈密顿量的基态并估计其基态能量是重要的但计算困难的任务。然而，如果有一些额外的信息，这些问题可以在量子计算机上有效地解决。我们假设可以有效地制备与基态具有非平凡重叠的初始态，并且基态能量和第一激发能之间的光谱间隙从下面被限制。有了这些假设，我们设计了一个算法，准备的基态时，地面能量的上限是已知的，其运行时间有一个对数依赖于逆误差。当这样的上限未知时，我们提出了一种混合量子经典算法来估计基态能量，其中与[Ge et al. 2019]中提出的当前最先进的算法相比，查询数量对初始状态对所需精度的依赖性呈指数级改善。这两种算法可以结合起来准备一个基态，而不需要知道基态能量的上限。我们还将其应用于非结构化搜索问题和量子近似计数问题，证明了我们的算法达到了复杂度下限。
英文摘要：
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.
Simple and efficient end-to-end quantum thermal and ground state preparation
University of Michigan（密歇根大学）；California Institute of Technology（加州理工学院）；AWS Center for Quantum Computing（亚马逊量子计算中心）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Adiabatic state preparation from general initial states
IBM Quantum, IBM T. J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；ExxonMobil Corporate Strategic Research（埃克森美孚企业战略研究部）；IBM Quantum, IBM Research Almaden（IBM量子，IBM阿尔马登研究中心）
Benchmark of quantum algorithms for ground state preparation in the presence of noise
Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）
Imaginary time evolution and ground state preparation using unitary multi-copy protocols
ITAMP, Center for Astrophysics | Harvard & Smithsonian（哈佛大学与史密森尼天体物理中心）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
Hardware-Efficient Ground-State Preparation using Variational Imaginary-Time Majorana Evolution
IQM Quantum Computers GmbH（IQM量子计算机有限公司）；RPTU Kaiserslautern-Landau（莱布尼茨技术大学凯泽斯劳滕-兰道分校）；Universidad Autónoma de Madrid（马德里自治大学）；Technical University of Munich（慕尼黑工业大学）
Rapid quantum ground state preparation via dissipative dynamics
Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Division of Physics, Mathematics, and Astronomy, California Institute of Technology（加州理工学院物理、数学与天文学部）；Department of Mathematics, University of California, Berkeley（加州大学伯克利分校数学系）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理系及阿诺德·索末菲理论物理中心）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）；Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室应用数学与计算研究部）
Double-bracket quantum algorithms for high-fidelity ground state preparation
European Organization for Nuclear Research (CERN)（欧洲核子研究组织）；TIF Lab, Dipartimento di Fisica, Università degli Studi di Milano（米兰大学物理系TIF实验室）；Quantum Research Center, Technology Innovation Institute（技术革新研究所量子研究中心）；INFN Sezione di Milano（意大利国家核物理研究所米兰分部）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；Department of Nuclear and Particle Physics, University of Geneva（日内瓦大学核与粒子物理系）；Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）
Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems
Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Graduate School of Informatics, Kyoto University（京都大学情报学府）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）；Center for Quantum Computing, RIKEN（理化学研究所量子计算中心）
