The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the $L^1$ norm $\int_{0}^{t}\mathrm{d}τ\left\lVert H(τ)\right\lVert_{\max}$, whereas the best previous results scale with $t\max_{τ\in[0,t]}\left\lVert H(τ)\right\lVert_{\max}$. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry.
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）
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）
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）
Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
University of Tokyo（东京大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先锋研究本部）；University of Warwick（华威大学）；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）；RIKEN（理化学研究所）；Ritsumeikan University（立命馆大学）
Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
Department of Physics, Harvard University, Cambridge, MA 02138, USA（哈佛大学物理系）；Institute for Quantum Information and Matter, California Institute of Technology, CA 91125, USA（加州理工学院量子信息与物质研究所）；School of Engineering and Applied Sciences, Harvard University, Allston, Massachusetts 02134, USA（哈佛大学工程与应用科学学院）；Center for Quantum Information, IIIS, Tsinghua University, Beijing, China（清华大学信息中心）；Department of Mathematics, Duke University, Durham, NC 27708, USA（杜克大学数学系）；Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA（杜克大学电气与计算机工程系）；Duke Quantum Center, Duke University, Durham, NC 27701, USA（杜克大学量子中心）；Department of Computer Science, Virginia Tech, Alexandria, VA 22314, USA（弗吉尼亚理工大学计算机科学系）；Phasecraft Inc., Washington DC, USA（Phasecraft公司）
Learning many-body Hamiltonians with Heisenberg-limited scaling
California Institute of Technology（加州理工学院）；University of California, Berkeley（加州大学伯克利分校）；Simons Institute for the Theory of Computing（西蒙斯计算理论研究所）；Microsoft Quantum（微软量子）
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）
