Suzuki-Trotter分解及其他量子时间演化方法
Suzuki-Trotter Decompositions and other Methods for Quantum Time Evolution
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中文总结 AI 辅助
本文综述量子时间演化的Suzuki-Trotter分解等方法，聚焦近年高效算法与误差界改进，并讨论噪声硬件下的量子计算应用及多种替代方案。
中文摘要 AI 辅助
(Suzuki-)Trotter分解、分裂方法、(Lie)乘积公式……量子系统时间演化的最常用数值方法有许多名称。它们几乎被应用于所有领域，从经典运动方程的求解和各种蒙特卡洛模拟，到经典及量子计算机上的实时间和虚时间演化。在此，我们回顾了上述方法的最新进展，特别关注过去几年取得的进步。我们重点介绍了最近发现的高效时间演化算法，并解释了如何在实践中最好地使用它们。本工作的核心部分是对误差界的估计，这在过去十年中得到了极大改进。讨论了时间演化方法对量子计算的相关性，重点关注噪声硬件。最后，全面概述了Trotter化的推广、相关方法和替代方案，包括含时哈密顿动力学、处理方法、多乘积公式、辛积分器、张量网络的TDVP、量子信号处理、Crouch-Grossman方法等。本工作的整体视角是理论物理学家的视角。为了便于阅读，省略了所有数学证明及一些技术细节。相反，本综述作为一份实践指南，当然也作为提供进一步细节的参考文献的起点。
英文摘要
(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.
发表机构
- Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn（波恩大学赫尔姆霍兹射线与核物理研究所）
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