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.

6 pages, 4 figures

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• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Thermal Drude weight in an integrable chiral clock model
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations