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

TL;DR

This paper introduces a randomized SVD method to improve the efficiency of the TEBD algorithm in simulating quantum systems with limited entanglement, achieving significant speed-ups without sacrificing accuracy.

Contribution

The paper presents a novel application of Reduced-Rank Randomized SVD to accelerate TEBD, reducing computational complexity while maintaining accuracy.

Findings

RRSVD reduces TEBD complexity by one power law degree.

RRSVD achieves comparable accuracy to deterministic SVD routines.

Significant speed-up demonstrated on real-world quantum systems.

Abstract

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.