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arXiv:2506.03127 · Journal of Chemical Theory and Computation

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

Roman Ovcharenko, Xiangyu Xu, Benjamin Philipp Fingerhut

Published Apr 8, 2026• 2 citations
arXivHTMLPDF

Abstract

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 premerging algorithm and a hash-based look-up (hMACGIC-QUAPI) while preserving numerical accuracy. The source code of the hMACGIC-QUAPI implementation is available in a publicly accessible Git repository under GPL license. The developed 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 nonperturbative 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 a strong system–environment interaction and the emergence of sidebands due to multiexcitations 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.

DOI
10.1021/acs.jctc.6c00002

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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 premerging algorithm and a hash-based look-up (hMACGIC-QUAPI) while preserving numerical accuracy. The source code of the hMACGIC-QUAPI implementation is available in a publicly accessible Git repository under GPL license. The developed 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 nonperturbative 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 a strong system–environment interaction and the emergence of sidebands due to multiexcitations 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.
Path integral methods, such as the quasi-adiabatic propagator path integral (QUAPI), are widely used in general-purpose and highly accurate numerical benchmark simulations of open quantum systems, particularly in regimes inaccessible to perturbative methods. Nevertheless, the applicability of the QUAPI method to realistic systems of interest is restricted by the exponentially growing computer memory requirements with respect to the size of the quantum system and the time range of non-Markovian correlation effects. This exponential "wall" becomes even more severe for multiple non-commuting fluctuating environments. In the present work, we address the numerical efficiency and accuracy of approximations that have been introduced for the QUAPI method with a single general environment, for the case of two independent non-commuting environments where one of them is considered as a pure dephasing environment. In particular, we consider a sharply defined cutoff of the memory time, path filtering, and mask assisted coarse graining of influence functional coefficients as approximations. We demonstrate that commonly applied numerical techniques, such as path filtering, cannot be straightforwardly transferred to the two-bath case even in the weak-coupling and quasi-Markovian limits. On the other hand, the sharply defined memory cutoff can be accurately handled with the mask assisted coarse graining approach. Our findings demonstrate that if system coupling operators to different baths do not commute, the additive nature of the statistically independent environments may be misleading. In particular, the quasi-Markovian nature of a pure dephasing bath is lost once there simultaneously exists another non-commuting source of fluctuations.
Accurately simulating non-Markovian quantum dynamics in system-bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.
The reduced density matrix of a system coupled to a harmonic dissipative bath can be obtained accurately using an iterative path integral methodology that involves a propagator tensor, whose rank is roughly equal to the number of time steps that span the bath-induced memory. The present work shows that even in situations where the bath is characterized by high-frequency modes (which necessitate a small time step) and slow oscillators (which give rise to very long memory), efficient propagation that takes into account the memory on all time scales is feasible by renormalizing the propagator matrix to include successively larger-length influence functional correlations. At its crudest level, the renormalized propagator is an ordinary matrix, thus the computational demands of the method are very modest, similar to those for propagating the bare system. Yet, test applications on dissipative two-level systems show that the method produces accurate results in demanding situations. By including memory on successively increasing time scales, the method is capable of capturing nonexponential kinetics induced by sluggish solvents.
The Tight-Binding Propagation Method (TBPM) is a robust computational framework for large-scale quantum simulations with linear scaling in memory and computational time. Building upon shared-memory implementations, this study presents an MPI-accelerated batched TBPM algorithm to exploit distributed-memory high-performance computing systems through domain decomposition and cross-node parallel execution. The approach distributes both the Hamiltonian matrix and wave function states across multiple nodes, enabling memory aggregation and simultaneous utilization of computational resources throughout clusters. The maximum tractable system size is determined primarily by the number of available supercomputing nodes. The batched processing strategy transforms the computational characteristics by reducing matrix access frequency and enhancing computational intensity by a factor of 64, shifting the algorithm from memory-bound to compute-bound regimes. Comprehensive benchmarks on graphene and twisted bilayer graphene demonstrate substantial speedup and memory scalability improvements. Super-linear speedup is consistently observed across both systems, attributed to superior cache efficiency when local Hamiltonian partitions fit within the Last Level Cache, confirming the efficiency and broad applicability of this MPIbased distributed architecture for ultra-large-scale tight-binding calculations.
Recent progress in numerical methods for evaluating the real-time path integral in dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed numerically allow convergence of the path integral with large time increments. Integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiabatic path, with an influence functional that describes nonadiabatic corrections. The resulting quasi-adiabatic propagator path integral is evaluated by efficient system-specific quadratures in most regimes of parameter space, although some cases are handled by grid Monte Carlo sampling. Exploiting the finite span of nonlocal influence functional interactions characteristic of broad condensed phase spectra leads to an iterative scheme for calculating the path integral over arbitrary time lengths. No uncontrolled approximations are introduced, and the resulting methodology converges to the exact quantum result with modest amounts of computational power. Applications to tunneling dynamics in the condensed phase are described.
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.