Fig. 3: Two components of the tensor jump method (TJM).
From: Large-scale stochastic simulation of open quantum systems
Top Illustration of the application of the factorized dissipative MPO \({{{\mathcal{D}}}}\) (constructed from local matrices) to an MPS \(\left\vert \Psi \right\rangle\). Each local tensor corresponds to the exponentiation of local jump operators: \({{{{\mathcal{D}}}}}_{\ell }={e}^{-\frac{1}{2}\delta t{\sum }_{j\in S(\ell )}{L}_{j}^{[\ell ]{{\dagger}} }{L}_{j}^{[\ell ]}}\). This operation does not change the bond dimension and does not require canonicalization. Bottom Visualization of the tensor network required to compute δpm for a given jump operator Lm, which corresponds to the expectation value \(\langle {L}_{m}^{{{\dagger}} }{L}_{m}\rangle\). By putting the MPS in mixed canonical form centered at site ℓ, contractions over tensors to the left and right reduce to identities. This enables efficient computation of the probability distribution Π(t) via a sweep across the network, evaluating local jump probabilities Lj at each site j ∈ S(ℓ).
