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

• URL: http://arxiv.org/abs/2212.09782v1
• Date: Mon, 19 Dec 2022 19:00:05 GMT
• Title: Fast Time-Evolution of Matrix-Product States using the QR decomposition
• Authors: Jakob Unfried, Johannes Hauschild and Frank Pollmann
• Abstract summary: We propose and benchmark a modified time evolution 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 $d2$. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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