Reducing computational scaling for simulating non-Markovian dissipative dynamics using artificial neural networks is both a major focus and formidable challenge in open quantum systems. To enable neural quantum states (NQSs), we encode environmental memory in dissipatons (quasiparticles with characteristic lifetimes), yielding the dissipaton-embedded quantum master equation (DQME). The resulting NQS-DQME framework achieves compact representation of many-body correlations and non-Markovian memory. Benchmarking against numerically exact hierarchical equations of motion confirms NQS-DQME maintains comparable accuracy while enhancing scalability and interpretability. This methodology opens new paths to explore non-Markovian open quantum dynamics in previously intractable systems.
Reducing computational scaling for simulating non-Markovian dissipative dynamics using artificial neural networks is both a major focus and formidable challenge in open quantum systems. To enable neural quantum states (NQSs), we encode environmental memory in dissipatons (quasiparticles with characteristic lifetimes), yielding the dissipaton-embedded quantum master equation (DQME). The resulting NQS-DQME framework achieves compact representation of many-body correlations and non-Markovian memory. Benchmarking against numerically exact hierarchical equations of motion confirms NQS-DQME maintains comparable accuracy while enhancing scalability and interpretability. This methodology opens new paths to explore non-Markovian open quantum dynamics in previously intractable systems.
Non-Markovianity, the intricate dependence of an open quantum system on its temporal evolution history, holds tremendous implications across various scientific disciplines. However, accurately characterizing the complex non-Markovian effects has posed a formidable challenge for numerical simulations. While quantum computing technologies show promise, a universal theory enabling practical quantum algorithm implementation has been elusive. We address this gap by introducing the dissipaton-embedded quantum master equation in second quantization (DQME-SQ). This exact and compact theory offers two key advantages: representability by quantum circuits and universal applicability to any Gaussian environment. We demonstrate these capabilities through digital quantum simulations of non-Markovian dissipative dynamics in both bosonic and fermionic environments. The DQME-SQ framework opens a new horizon for the efficient exploration of complex open quantum systems by leveraging the rapidly advancing quantum computing technologies.
This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics, to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.
This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics and to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.
Condensed-phase quantum dynamics are strongly shaped by vibrational, solvent, and protein environments, yet their nonperturbative, non-Markovian description requires a rapidly growing high-dimensional representation as environmental complexity increases. Here, we extend neural quantum states (NQS) to the dissipaton-embedded quantum master equation (DQME) for bosonic environments using a complex-valued restricted Boltzmann machine adapted to nonbinary bosonic occupations. An explicit filtering scheme further concentrates the neural representation on dynamically relevant dissipaton configurations. The resulting NQS-DQME approach reproduces representative quantum dissipative dynamics while effectively compressing the reduced density tensor (RDT). For an anharmonic model of condensed-phase hydrogen transfer, the method also reproduces weak-coupling tunneling dynamics. At stronger system-bath coupling, however, errors become localized in a small subset of RDT elements, showing that a small global variational residual does not necessarily ensure accurate chemically relevant observables. This limitation identifies observable-level error control as a key challenge for reliable long-time NQS propagation.
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges have been introduced, originating from different fields, such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations. This diversity, while indicative of the field's relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? Here we give a systematic overview and concise discussion addressing these questions. We make use of a unified framework which very conveniently allows to link different schemes and, this way, may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space which in a minimal fashion includes effective reservoir modes. This in turn offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.
Simulating many-body open quantum systems (OQSs) is challenging due to the intricate interplay between the system and its environment, resulting in strong quantum correlations in both space and time. This Perspective presents an overview of recently developed theoretical methods using artificial intelligence (AI) and quantum computing (QC) to simulate the dynamics of these systems. We briefly introduce the dissipaton-embedded quantum master equation in second quantization, which provides a single master equation suitable for representation by neural quantum states or quantum circuits. The promising performance of AI- and QC-based approaches is demonstrated through preliminary research on simulating the quantum dissipative dynamics of many-body OQSs. We also discuss the limitations and future developments of these methods, which hold promise for overcoming the computational challenges associated with many-body OQS dynamics.