Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This work stresses that for translationally invariant lattice Hamiltonians with periodic boundary conditions, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semi-definite relaxations both provide approximations with performance guarantees that scale like a constant in the energy density for cubic lattices. (iii) Also, the Anderson bound is systematically improved as a hierarchy of semi-definite relaxations inspired by the quantum marginal problem.
Theoretical Guarantees of Variational Quantum Algorithm with Guiding States
Centre for Quantum Software and Information, School of Computer Science, Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程与信息科技学院计算机科学学院量子软件与信息中心）；Centre for Quantum Computation and Communication Technology, University of Technology Sydney（悉尼科技大学量子计算与通信技术研究中心）
Noise Resilience and Robust Convergence Guarantees for the Variational Quantum Eigensolver
Institute for Systems Theory and Automatic Control, University of Stuttgart（斯图加特大学系统理论与自动控制研究所）；Center for Integrated Quantum Science and Technology (IQST), University of Stuttgart（斯图加特大学集成量子科学与技术中心）
Performance guarantees of light-cone variational quantum algorithms for the maximum cut problem
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心 (iTHEMS)）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心 (R-CCS)）；Center on Frontiers of Computing Studies, Peking University（北京大学前沿计算研究中心）；School of Computer Science, Peking University（北京大学计算机学院）
A rigorous hybridization of variational quantum eigensolver with classical neural network
Seoul National University（首尔大学）；NextQuantum, Seoul National University（NextQuantum，首尔大学）；Automation and Systems Research Institute, Seoul National University（自动化与系统研究所，首尔大学）；Institute for Convergence Research and Education in Advanced Technology, Yonsei University（先进技术研究融合教育与研究所，延世大学）；Department of Quantum Information, Yonsei University（量子信息系，延世大学）
Subspace Variational Quantum Simulation: Fidelity Lower Bounds as Measures of Training Success
Institute for Convergence Research and Education in Advanced Technology, Yonsei University（延世大学先进技术与教育融合研究院）；Department of Quantum Information, Graduate School, Yonsei University（延世大学研究生院量子信息系）；School of Computer Engineering, Kumoh National Institute of Technology（庆北国立科技大学生物计算机工程学院）
Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inference
Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology（埃因霍温理工大学电子工程系信号处理系统组）；KCLIP lab, Center for Intelligent Information Processing Systems, Department of Engineering, King’s College London（伦敦国王学院工程系智能信息处理系统中心）
On the convergence of the variational quantum eigensolver and quantum optimal control
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Technische Universität München（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Munich Quantum Valley (MQV)（慕尼黑量子谷）；Arizona State University（亚利桑那州立大学）
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）
