Multi-Product Hamiltonian Simulation with Explicit Commutator Scaling
University of Maryland, College Park（马里兰大学帕克分校）；Joint Center for Quantum Information and Computer Science, University of Maryland, College Park（马里兰大学帕克分校量子信息与计算机科学联合中心）；Institute for Physical Science and Technology, University of Maryland, College Park（马里兰大学帕克分校物理科学与技术研究所）
Junaid Aftab, Dong An, Konstantina Trivisa
备注：
v2: 46 pages. Includes: better exposition of proofs , discussion of various developments since v1 appeared, new applications in section 4. Comments are welcome
The well-conditioned multi-product formula (MPF), proposed by Low-Kliuchnikov-Wiebe (2019), is a high-order, time-independent Hamiltonian simulation algorithm that implements a linear combination of low-order product formulas. Prior work established its well-conditioned algorithmic construction and near-optimal time and precision dependence, but did not simultaneously provide an explicit error bound in terms of nested commutators, which has left its practical advantage uncertain. In this work, we provide a rigorous complexity analysis of the well-conditioned MPF, explicitly establishing both commutator scaling and near-optimal dependence on time and precision through a rigorous Baker-Campbell-Hausdorff (BCH) and variation-of-parameters-based error analysis. Using our improved complexity estimates, we present several physically relevant applications where the second-order-based MPF asymptotically outperforms the second-order product formula in all three aspects of system size, time, and precision. We further demonstrate that, while MPF yields worse scalings than the best post-Trotter methods in most applications, there exist certain parameter regimes in the nonlocal fast-transform Bogoliubov-de Gennes model where MPF can outperform both leading post-Trotter methods and product formulas with fixed or adaptively optimized order.
Explicit error bounds with commutator scaling for time-dependent product and multi-product formulas
The University of Tokyo（东京大学）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；ZEN University（禅大学）；Hokkaido University（北海道大学）；Osaka University（大阪大学）
Center on Frontiers of Computing Studies, Peking University（前沿计算研究中心，北京大学）；School of Computer Science, Peking University（计算机学院，北京大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科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））；Tencent Quantum Laboratory, Tencent（腾讯量子实验室，腾讯）
QCommute: a tool for symbolic computation of nested commutators in quantum many-body spin-1/2 systems
Skolkovo Institute of Science and Technology（斯科尔科沃科学与技术学院）；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）；HSE University（高等经济学院）；Moscow State University, Faculty of Physics（莫斯科大学物理系）
Commutator Estimates for Low-Temperature Fermi Gases
Beijing Institute of Technology（北京理工大学）；École Normale Supérieure de Lyon（里昂高等师范学院）；Kyung Hee University（庆熙大学）；Universität Freiburg（弗赖堡大学）；Universität Basel（巴塞尔大学）
Trotter error compensation with polylogarithmic precision and nested-commutator scaling without ancillas
Center on Frontiers of Computing Studies, Peking University（前沿计算研究中心，北京大学）；School of Computer Science, Peking University（计算机学院，北京大学）；Institute of Natural Sciences, Shanghai Jiao Tong University（自然科学研究院，上海交通大学）；School of Physics and Astronomy, Shanghai Jiao Tong University（物理与天文学院，上海交通大学）；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）
Quantum matrix arithmetics with Hamiltonian evolution
Azure Quantum, Microsoft（微软 Azure 量子）；Department of Computer Science, The University of Chicago（芝加哥大学计算机科学系）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）
Quantum annealing for hard 2-SAT problems : Distribution and scaling of minimum energy gap and success probability
近年来，量子退火已经获得了作为解决各种优化问题的一个有前途的候选人的地位。利用一组多达18个变量的2-SAT问题，分析了量子退火算法的标度复杂性，研究了最小能隙和成功概率的分布.我们扩展了标准量子退火哈密顿量的分析，通过引入一个额外的术语，触发哈密顿量，它可以是两种类型：铁磁和反铁磁。我们使用这些触发哈密顿研究他们的成功概率解决选定的2-SAT问题的影响。我们发现，尽管标准和修改的量子退火哈密顿量的运行时间的缩放是指数的，但在添加触发哈密顿量的情况下的缩放常数可以显著更小。此外，对触发哈密顿量和退火时间的某些选择可以导致比模拟退火更好的缩放。最后，我们还使用D-Wave Systems Inc.的量子退火机。研究它们在求解2-SAT问题时的性能，并与仿真结果进行比较。
A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory
Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn（波恩大学赫姆霍兹射线与核物理研究所）；Bethe Center for Theoretical Physics, University of Bonn（波恩大学贝特理论物理中心）；Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter), University of Bonn（波恩大学跨学科研究领域“物质基本组成与基本相互作用”（TRA Matter））；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器中心）
Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
Technical University of Munich（慕尼黑工业大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
