标题： 通过降低秩的随机奇异值分解改进时间演化块消减算法的缩放特性 显示英文标题

标题： Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition

摘要： 当量子系统的纠缠量受到限制时，系统的相关动力学被限制在状态空间的很小一部分。 当局限于这个子空间时，系统描述在系统规模上变得高效。 一类算法，以时间演化块消减（TEBD）算法为例，通过利用这一观察结果，借助基于奇异值分解（SVD）的消减技术来选择相关的子空间。 在这些算法中，每次时间演化步骤的复杂性主要由SVD决定。 在这里，我们展示了一种基于随机化SVD（RRSVD）方法的应用，该方法将TEBD计算复杂性的幂律降低了一阶，从而带来了显著的速度提升。 我们通过一些TEBD可以成功应用到的实际例子来举例说明效率上的潜在收益，并证明对于这些系统，RRSVD得到的结果与最先进的确定性SVD方法一样准确。 显示英文摘要

摘要： When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in the system size. A class of algorithms, exemplified by the Time-Evolving Block-Decimation (TEBD) algorithm, make use of this observation by selecting the relevant subspace through a decimation technique relying on the Singular Value Decomposition (SVD). In these algorithms, the complexity of each time-evolution step is dominated by the SVD. Here we show that, by applying a randomized version of the SVD routine (RRSVD), the power law governing the computational complexity of TEBD is lowered by one degree, resulting in a considerable speed-up. We exemplify the potential gains in efficiency at the hand of some real world examples to which TEBD can be successfully applied to and demonstrate that for those system RRSVD delivers results as accurate as state-of-the-art deterministic SVD routines.