with a non-Hermitian super-Hamiltonian ) efficiently, we utilize the matrix product state (MPS) decomposition of the extended wavefunction |Ψ(p t c ,x t c ,t)⟩, and the super-Hamiltonian H(p t c ,x t c ) is decomposed as the matrix product operator at each time point, along with a time-propagation scheme based on the time-dependent variational principle, as described in Refs. 64-66.