Advanced Photonic and Electronic Sciences Division, US DEVCOM Army Research Laboratory（美国国防部陆军研究实验室先进光子与电子科学部）；Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories（桑迪亚国家实验室量子算法与应用协作体）；Department of Physics, Loughborough University（拉夫堡大学物理系）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
Jacob M. Leamer, Alicia B. Magann, Gerard McCaul, Denys I. Bondar
The spectral gap occupies a role of central importance in many open problems in physics. We present an approach for evaluating the spectral gap of a Hamiltonian from a simple ratio of two expectation values, both of which are evaluated using a quantum state that is evolved in imaginary time. In principle, the only requirement is that the initial state is supported on both the ground and first excited states. We demonstrate this approach for the Fermi-Hubbard and transverse-field Ising models through numerical simulation. We then go on to explore avenues for its implementation on quantum computers using imaginary-time quantum dynamical emulation.
Imaginary Time Spectral Transforms for Excited State Preparation
IBM Quantum, IBM Research Europe（IBM量子，IBM欧洲研究院）；University of Southampton（南安普顿大学）；The Hartree Centre, STFC（哈特里中心，STFC）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；SUPA, School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院，SUPA）
Exact spectral gaps of random one-dimensional quantum circuits
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Department of Applied Physics, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU)（巴斯克国立大学吉普斯夸工程学院应用物理系）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家理论部）；Quantum Science Center, Oak Ridge, TN 37931, USA（橡树岭量子科学中心）
PT-symmetric potentials with imaginary asymptotic saturation
指出具有虚渐近饱和的PT对称势$V_{PT}(x)$：$V_{PT}(x=\pm \infty) =\pm i V_1, V_1 \in \Re$不含散射态和谱奇异性。我们证明了存在的实（正和负）离散谱的复共轭对（S）的特征值（CCPE）和不。如果状态按离散本征值的升序或实部排列，则初始状态的节点很少，但后面的状态振荡很快。$ψ(x)$的实部和虚部都渐近地消失，CCPE的$|ψ(x)|$是不对称的，并且对于实能量，它们关于原点是对称的。对于CCPE $E_{\pm}$，本征态$ψ_{\pm}$遵循一个有趣的性质，即$|ψ_+(x)|= N |ψ_-(-x)|, N \in \Re^+$。我们注意到，所讨论的快速振荡实离散能态很可能与无反射态、一维厄米的von Neumann态和复PT对称势的谱奇异态相混淆。
Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap
South China Agricultural University（华南农业大学）；Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（先进智能与计算研究所，科技研究局）；Division of Mathematical Sciences, Nanyang Technological University（南洋理工大学数学科学系）
