QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems

Abstract

A simulation of the non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye toward moving to larger systems and more complicated descriptions of solvents. Many of these methods, however, are quite difficult to implement and debug. Furthermore, trying to make the individual algorithms work together through a modular application programming interface can be quite difficult as well. We present a new, open-source software framework, QuantumDynamics.jl, designed to address these challenges. It provides implementations of a variety of perturbative and non-perturbative methods for simulating the dynamics of these systems. Most prominently, QuantumDynamics.jl supports hierarchical equations of motion and methods based on path integrals. An effort has been made to ensure maximum compatibility of the interface between the various methods. Additionally, QuantumDynamics.jl, being built on a high-level programming language, brings a host of modern features to explorations of systems, such as the usage of Jupyter notebooks and high level plotting, the possibility of leveraging high-performance machine learning libraries for further development. Thus, while the built-in methods can be used as end-points in themselves, the package provides an integrated platform for experimentation, exploration, and method development.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna–Matthews–Olson Complex

“…The transfer tensor method (TTM) has demonstrated the possibility of using the augmented forward–backward system propagators as dynamical maps to simplify the propagation in the iterative regime. While the TEMPO with the analytical influence functional MPO allows us to access unprecedented memory lengths for large systems like the FMO, the TTM allows us to speed up the propagation beyond the memory length without incurring further numerical errors from the filtering involved in the tensor network simulations …”

“…While the TEMPO with the analytical influence functional MPO allows us to access unprecedented memory lengths for large systems like the FMO, the TTM allows us to speed up the propagation beyond the memory length without incurring further numerical errors from the filtering involved in the tensor network simulations. 63 Crucial to an exploration of EET dynamics is an understanding of the pathway-dependent population transfer for each of the cases. Baker and Habershon 64 have explored these pathways in FMO using the Lindblad master equation.…”

Real-Time Simulation of Open Quantum Spin Chains with the Inchworm Method

“…Another method, called transfer tensor method (TTM), − has similar time convolution form as SMatPI. Some software packages have been developed for these algorithms. , In recent years, the application of tensor networks is also popular in the simulation of an open quantum systems. − The method of time-evolving matrix product operator (TEMPO) represents the non-Markovian process with a finite memory length. The pairwise connected tensor network path integral (PC-TNPI) is applied in blip-summed path integrals , and has been proved highly efficient.…”

Incorporation of Empirical Gain and Loss Mechanisms in Open Quantum Systems through Path Integral Lindblad Dynamics

“…They showed that, from the dynamical maps that relate the time-evolved density matrix ρ( t ) to the initial density matrix ρ(0) under the influence of the environment, ρ ( t ) = scriptE ( t ) ρ ( 0 ) , one can derive the transfer tensors, T k , that satisfy ρ ( t n ) = prefix∑ k = 1 L T k ρ ( t n − k ) The dynamical maps, including the environment effects, can be simulated using eq by not contracting the initial reduced density matrix. The transfer tensor method (TTM) has already been used with path-integral-based simulations. , It has also been shown that, for short time steps, the transfer tensors can be related to the memory kernel by T k = ( 1 − i L 0 Δ t ) δ k , 1 + scriptK k normalΔ t 2 For longer time steps, this would break down because it is based on a discretization of the time derivative of ρ( t ) correct to scriptO ( Δ t ) . A better mapping can be obtained by converting to the reduced density matrix to the interaction picture with respect to the bare system Hamiltonian, H 0 , in terms of the bare dynamical map, …”

“…The base dynamics without the Lindblad jump operators was first calculated with a time step of Δ t = 3 fs. The dynamical maps, scriptE ( t ) , were generated using the time-evolving matrix product state (TEMPO) algorithm , as implemented in the QuantumDynamics.jl package up to a maximum time of 300 fs. For these calculations, the full path simulation was done up to a memory length of τ mem = K Δ t = 150 fs, beyond which an iterative algorithm was used to generate scriptE ( t ) (a naïve calculation of this problem would need to sum over 25 50 ≈ 7.9 × 10 69 , and the tensor network approach manages to make this computation totally feasible).…”