Fast time evolution of matrix product states using the QR decomposition

We propose and benchmark a modified time-evolving block decimation 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.

Automated summary

We propose a modified time-evolving block decimation algorithm that uses QR decomposition for truncation instead of SVD. The modification reduces the scaling with the dimension of the physical Hilbert space and allows for efficient GPU implementations. Benchmark simulation shows a significant speedup using QR updates compared to SVD updates on an A100 GPU.