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

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.