通过局域性加速量子稠密输出模拟
Accelerating Quantum Dense-Output Simulation through Locality
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中文总结 AI 辅助
针对量子模拟中稠密输出估计问题，提出基于局域性的截断框架，利用Lieb-Robinson界控制误差，将查询成本从全局范数依赖降至局部，适用于费米子、玻色子及开放系统，改进幅度随规模增长从常数到无界。
中文摘要 AI 辅助
估计时间累积可观测量（即稠密输出）是从量子模拟中提取经典信息的核心。虽然大多数量子模拟算法旨在重现最终状态或单时间期望值，但许多应用需要积分信号 $J_H(O)=\int_0^T \langle \psi(t)|O(t)|\psi(t)\rangle\\,dt$。先前基于哈密顿量模拟的稠密输出算法的查询成本依赖于整个哈密顿量的范数，该范数可能随系统规模增长。然而，当系统结构已知时，可以自然地优化模拟算法。因此，我们为晶格哈密顿量上的稠密输出问题开发了一个基于局域性的截断框架。通过截断哈密顿量并利用Lieb-Robinson界收紧由此产生的误差，我们证明局部模拟可以恢复稠密输出。我们限制了空间截断引起的量子模拟误差，并将其转化为局部模拟查询界。我们的分析包括费米子和玻色子的自由及相互作用系统，以及由Lindbladians控制的开放量子系统。我们的截断算法带来的改进随系统规模增长从常数到无界不等。我们还给出了示例应用并进行了相关数值实验以支持我们的发现。
英文摘要
Estimating time-accumulated observables, or dense outputs, is central to extracting classical information from quantum simulations. Whereas most quantum-simulation algorithms aim to reproduce a final state or a single-time expectation value, many applications require the integrated signal $J_H(O)=\int_0^T \langle ψ(t)|O(t)|ψ(t)\rangle\,dt$. Previous Hamiltonian-simulation-based dense-output algorithms have query costs that depend on the norm of the full Hamiltonian, which can grow with system size. However, one can naturally optimize the simulation algorithm when the system structure is known. Consequently, we develop a locality-based truncation framework for the dense-output problem on lattice Hamiltonians. By truncating the Hamiltonian and tightening the resulting error with Lieb-Robinson bounds, we show that a local simulation can recover the dense output. We bound the quantum simulation error from spatial truncation and translate it into local-simulation query bounds. Our analysis includes free and interacting systems for both fermions and bosons, as well as open quantum systems governed by Lindbladians. The improvement from our truncation algorithm varies from constant to unbounded as the system size grows. We also give example applications and conduct relevant numerical experiments to support our findings.
发表机构
- Cavendish Lab., Department of Physics, University of Cambridge（剑桥大学卡文迪许实验室物理系）
- Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
- Institute for Applied Mathematics, Tsinghua University（清华大学应用数学中心）
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京雁栖湖应用数学研究院）
机构由 AI 辅助整理，请以论文原文为准。
