论文标题
使用QR分解的基质态的快速时间进化
Fast Time-Evolution of Matrix-Product States using the QR decomposition
论文作者
论文摘要
我们提出并基准了修改的时间演化块分解（TEBD）算法，该算法使用基于QR分解的截断方案而不是单数值分解（SVD）。修改用物理希尔伯特空间的尺寸从$ d^3 $降低到$ d^2 $。此外，QR分解的计算复杂性低于SVD，并允许在GPU硬件上实现高效的实现。在量子时钟模型中全局淬火的基准模拟中，我们观察到比较A100 GPU上基于QR和SVD的更新的最多三个数量级的速度。
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.
