Sublinear scaling in non-Markovian open quantum systems simulations

Understand

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$.

• Here, we introduce a numerically exact algorithm to calculate process tensors -- compact representations of environmental influences -- which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent Gaussian environments.
• Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory.
• Where the memory can be truncated after $n_c$ time steps, a scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$.