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

by Prof. David Luitz

Wednesday 1 Feb 2023, 15:00 → 16:00 Europe/Berlin

This talk discusses the following paper by Jakob Unfried, Johannes Hauschild, and Frank Pollmann. The abstract of the same is attached below.

Link:https://arxiv.org/abs/2212.09782

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 d3 down to d2. 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.