Supplementary data: Scalable Distributed Memory Implementation of the Quasi-Adiabatic Propagator Path Integral

The accurate simulation of dissipative quantum dynamics subject to a non-Markovian environment poses persistent numerical challenges, in particular for structured environments where sharp mode resonances induce long-time system bath correlations. We present a scalable distributed memory implementation of the Mask Assisted Coarse Graining of Influence Coefficients (MACGIC) - Quasi-Adiabatic Propagator Path Integral (-QUAPI) method that exploits the memory resources of multiple compute nodes and mitigates the memory bottleneck of the method via a new pre-merging algorithm and a hash-based look-up (hMACGIC-QUAPI) while preserving numerical accuracy. The distributed memory implementation spreads the paths over the computing nodes by means of the MPI protocol and efficient high level path management is achieved via the hash map-based implementation with constant access time. The efficiency of the implementation is demonstrated in large-scale dissipative quantum dynamics simulations that account for the coupling to a structured non-Markovian environment containing a sharp resonance, a setup for which convergence properties are investigated in depth. Broad applicability and the non-perturbative nature of the simulation method is illustrated via the tuning of the mode resonance frequency of the structured environment with respect to the characteristic system frequency. The simulations reveal a splitting of resonances due to strong system-environment interaction and the emergence of sidebands due to multi-excitations of the bosonic mode that are not accounted for in perturbative approaches. The simulations demonstrate the versatility of the new hMACGIC-QUAPI method in the presence of strong non-Markovian system bath correlations. Data to: R. Ovcharenko and B. P. Fingerhut, Scalable Distributed Memory Implementation of the Quasi-Adiabatic Propagator Path Integral, submitted to JCTC (2025) Available under: https://doi.org/10.48550/arXiv.2506.03127