Fast time evolution of matrix product states using the QR decomposition

Abstract

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 ${d}^{3}$ 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.

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