Fast Time-Evolution of Matrix-Product States using the QR decomposition

TL;DR

This paper introduces a modified TEBD algorithm that replaces SVD with QR decomposition, significantly reducing computational complexity and enabling faster simulations of quantum systems on GPUs.

Contribution

The paper presents a novel TEBD algorithm using QR decomposition for truncation, improving efficiency and scalability over traditional SVD-based methods.

Findings

Achieves up to 1000x speedup on GPU hardware.

Reduces computational complexity from d^3 to d^2.

Demonstrates effective simulation of quantum quenches.

Abstract

We propose and benchmark a modified time evolution block decimation (TEBD) algorithm that uses a truncation scheme based on the QR decomposition instead of the singular value decomposition (SVD). The modification reduces the scaling with the dimension of the physical Hilbert space $d$ from $d^3$ down to $d^2$. Moreover, the QR decomposition has a lower computational complexity than the SVD and allows for highly efficient implementations on GPU hardware. In a benchmark simulation of a global quench in a quantum clock model, we observe a speedup of up to three orders of magnitude comparing QR and SVD based updates on an A100 GPU.