基于降秩随机奇异值分解的时变分块抽取算法的改进
Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
摘要：
当量子系统中的纠缠量有限时，系统的相关动力学被限制在状态空间的一小部分。当被限制到这个子空间时，系统的描述在系统规模上变得有效。以时间演进块抽取（TEBD）算法为例的一类算法通过依赖于奇异值分解（SVD）的抽取技术选择相关子空间来利用这种观察。在这些算法中，每个时间演化步骤的复杂度由SVD决定。在这里，我们表明，通过应用一个随机版本的SVD例程（RRSVD），幂律管理TEBD的计算复杂性降低了一度，导致相当大的速度。我们在一些现实世界的例子，TEBD可以成功地应用于和证明，对于这些系统RRSVD提供的结果一样准确的最先进的确定性SVD例程的手，在效率上的潜在收益。
英文摘要：
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.
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