Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
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DOI：
10.1016/j.aop.2020.168165
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发表时间：
2020-07-01
影响因子：
3
通讯作者：
Zhang, Yikang
中科院分区：
文献类型：
--
作者：
Barthel, Thomas;Zhang, Yikang
Lie-Trotter-Suzuki分解是一种有效的近似算子指数exp（tH）的方法，当H是n（非交换）项的和时，这些项可以很容易地被取幂。它们被用于张量网络状态的时间演化算法、数字量子模拟协议、量子蒙特卡罗等路径积分方法以及经典哈密顿系统中辛积分器的分裂方法。我们提供了最优分解到t(6)阶。在嵌套换向器（霍尔基）中展开前导误差项，并最小化系数的1范数。对于n = 2项，我们发现的几个最优值与McLachlan（1995）的最优值接近。一般来说，我们的结果比Forest、Ruth、Yoshida和Suzuki的未优化分解有很大的改善。我们解释了为什么这些分解足以有效地模拟具有有限范围相互作用的任何一维或二维晶格模型。接下来是解决交互图的划分问题。(C) 2020爱思唯尔公司版权所有。
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials exp(tH) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. We provide optimized decompositions up to order t(6). The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph. (C) 2020 Elsevier Inc. All rights reserved.