Simulations of the dynamics of dissipative quantum systems utilize many methods such as physics-based quantum, semiclassical, and quantum-classical as well as machine learning-based approximations, development and testing of which requires diverse data sets. Here we present a new database QD3SET-1 containing eight data sets of quantum dynamical data for two systems of broad interest, spin-boson (SB) model and the Fenna–Matthews–Olson (FMO) complex, generated with two different methods solving the dynamics, approximate local thermalizing Lindblad master equation (LTLME) and highly accurate hierarchy equations of motion (HEOM). One data set was generated with the SB model which is a two-level quantum system coupled to a harmonic environment using HEOM for 1,000 model parameters. Seven data sets were collected for the FMO complex of different sizes (7- and 8-site monomer and 24-site trimer with LTLME and 8-site monomer with HEOM) for 500–879 model parameters. Our QD3SET-1 database contains both population and coherence dynamics data and part of it has been already used for machine learning-based quantum dynamics studies
Simulations of the dynamics of dissipative quantum systems utilize many methods such as physics-based quantum, semiclassical, and quantum-classical as well as machine learning-based approximations, development and testing of which requires diverse data sets. Here we present a new database QD3SET-1 containing eight data sets of quantum dynamical data for two systems of broad interest, spin-boson (SB) model and the Fenna–Matthews–Olson (FMO) complex, generated with two different methods solving the dynamics, approximate local thermalizing Lindblad master equation (LTLME) and highly accurate hierarchy equations of motion (HEOM). One data set was generated with the SB model which is a two-level quantum system coupled to a harmonic environment using HEOM for 1,000 model parameters. Seven data sets were collected for the FMO complex of different sizes (7- and 8-site monomer and 24-site trimer with LTLME and 8-site monomer with HEOM) for 500–879 model parameters. Our QD3SET-1 database contains both population and coherence dynamics data and part of it has been already used for machine learning-based quantum dynamics studies
Machine learning has emerged as a promising paradigm to study the quantum dissipative dynamics of open quantum systems. To facilitate the use of our recently published ML-based approaches for quantum dissipative dynamics, here we present an open-source Python package MLQD (https://github.com/Arif-PhyChem/MLQD), which currently supports the three ML-based quantum dynamics approaches: (1) the recursive dynamics with kernel ridge regression (KRR) method, (2) the non-recursive artificial-intelligence-based quantum dynamics (AIQD) approach and (3) the blazingly fast one-shot trajectory learning (OSTL) approach, where both AIQD and OSTL use the convolutional neural networks (CNN). This paper describes the features of the MLQD package, the technical details, optimization of hyperparameters, visualization of results, and the demonstration of the MLQD's applicability for two widely studied systems, namely the spin-boson model and the Fenna--Matthews--Olson (FMO) complex. To make MLQD more user-friendly and accessible, we have made it available on the XACS cloud computing platform (https://XACScloud.com) via the interface to the MLatom package (http://MLatom.com).
Machine learning has emerged as a promising paradigm to study the quantum dissipative dynamics of open quantum systems. To facilitate the use of our recently published ML-based approaches for quantum dissipative dynamics, here we present an open-source Python package MLQD (https://github.com/Arif-PhyChem/MLQD), which currently supports the three ML-based quantum dynamics approaches: (1) the recursive dynamics with kernel ridge regression (KRR) method, (2) the non-recursive artificial-intelligence-based quantum dynamics (AIQD) approach and (3) the blazingly fast one-shot trajectory learning (OSTL) approach, where both AIQD and OSTL use the convolutional neural networks (CNN). This paper describes the features of the MLQD package, the technical details, optimization of hyperparameters, visualization of results, and the demonstration of the MLQD's applicability for two widely studied systems, namely the spin-boson model and the Fenna--Matthews--Olson (FMO) complex. To make MLQD more user-friendly and accessible, we have made it available on the Python Package Index (PyPi) platform and it can be installed via pip install mlqd. In addition, it is also available on the XACS cloud computing platform (https://XACScloud.com) via the interface to the MLATOM package (http://MLatom.com)
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task in quantum science. While several algorithms have been designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative schemes. Most recently, deep neural networks have been used for quantum dynamics, but current architectures are highly dependent on the physics of the particular system and usually limited to population dynamics. Here we introduce an artificial-intelligence-based surrogate model that solves dissipative quantum dynamics by parametrizing quantum propagators as Fourier neural operators, which we train using both data set and physics-informed loss functions. Compared with conventional algorithms, our quantum neural propagator avoids time-consuming iterations and provides a universal superoperator that can be used to evolve any initial quantum state for arbitrarily long times. To illustrate the wide applicability of the approach, we employ our quantum neural propagator to compute the population dynamics and time-correlation functions of the Fenna-Matthews-Olson complex.
Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most existing models employ real-valued neural networks (RVNNs) that inherently mismatch the complex-valued nature of quantum mechanics. By decoupling the real and imaginary parts of the density matrix, RVNNs can obscure essential amplitude-phase correlations, compromising physical consistency. Here, we introduce complex-valued neural networks (CVNNs) as a physics-consistent framework for learning quantum dissipative dynamics. CVNNs operate directly on complex-valued inputs, preserve the algebraic structure of quantum states, and naturally encode quantum coherences. Through numerical benchmarks on the spin-boson model and few variants of the Fenna-Matthews-Olson complex, we demonstrate that CVNNs outperform RVNNs in convergence speed, training stability, and physical fidelity-including significantly improved trace conservation and Hermiticity. These advantages increase with system size and coherence complexity, establishing CVNNs as a robust, scalable, quantum-aware classical approach for simulating open quantum systems in the pre-fault-tolerant quantum era.
Simulating open quantum systems remains one of the most demanding problems in quantum dynamics, as environmental interactions lead to non-unitary evolution that challenges standard quantum simulation techniques. Variational quantum algorithms (VQAs) offer a practical way forward by combining classical optimization with quantum hardware, making them well suited for near-term devices. Here, in Part V of the QFlux implementation series, we introduce adaptive variational-ansatz methods for solving the Lindblad master equation. This tutorial presents the Python-based qmad module of the QFlux toolkit, which is designed to help students and researchers easily build and explore adaptive VQA strategies. The tutorial walks through each step of the workflow and applies the methods to two illustrative examples. The first is the amplitude-damping channel, which models spontaneous emission in a two-level system. The second is the Fenna-Matthews-Olson (FMO) complex, a prominent model for excitonic energy transfer in photosynthesis. The two workflows utilizing adaptive variational approaches implemented here are the unrestricted adaptive variational quantum dynamics (UAVQD) scheme and the stochastic Schrödinger equation (SSE) based trajectory method. By working through these examples, readers gain both intuition and hands-on experience with variational techniques for simulating dissipative quantum dynamics.
Simulating open quantum systems remains one of the most demanding problems in quantum dynamics, as environmental interactions lead to non-unitary evolution that challenges standard quantum simulation techniques. Variational quantum algorithms (VQAs) offer a practical way forward by combining classical optimization with quantum hardware, making them well suited for near-term devices. Here, in Part V of the QFlux implementation series, we introduce adaptive variational-ansatz methods for solving the Lindblad master equation. This tutorial presents the Python-based qmad module of the QFlux toolkit, which is designed to help students and researchers easily build and explore adaptive VQA strategies. The tutorial walks through each step of the workflow and applies the methods to two illustrative examples. The first is the amplitude-damping channel, which models spontaneous emission in a two-level system. The second is the Fenna-Matthews-Olson (FMO) complex, a prominent model for excitonic energy transfer in photosynthesis. The two workflows utilizing adaptive variational approaches implemented here are the unrestricted adaptive variational quantum dynamics (UAVQD) scheme and the stochastic Schrödinger equation (SSE) based trajectory method. By working through these examples, readers gain both intuition and hands-on experience with variational techniques for simulating dissipative quantum dynamics.