Fig. 2: This figure visualizes each step of the various forward- and backward-evolving equations of 1TDVP and 2TDVP indicated by the black dashed line.
From: Large-scale stochastic simulation of open quantum systems
This shows the reduced practical form of the network caused by the MPS's mixed canonical form. The tensors surrounded by the dashed lines (corresponding to Heff) are contracted, exponentiated with the Lanczos method, then applied to the remaining tensors to update them. Top 1TDVP forward-evolving and 2TDVP backward-evolving network where \({H}_{3}^{\,{{\mbox{eff}}}\,}\) (\({\tilde{H}}_{3,4}^{\,{{\mbox{eff}}}\,}\)) is a degree-6 tensor. Middle 1TDVP backward-evolving network where \({\tilde{H}}_{3}^{\,{{\mbox{eff}}}\,}\) is a degree-4 tensor. Bottom 2TDVP forward-evolving network where \({H}_{3,4}^{\,{{\mbox{eff}}}\,}\) is a degree-8 tensor.
