Simulating the dynamics of open quantum systems coupled to non-Markovian
environments remains an outstanding challenge due to exponentially scaling
computational costs. We present an artificial intelligence strategy to overcome
this obstacle by integrating the neural quantum states approach into the
dissipaton-embedded quantum master equation in second quantization (DQME-SQ).
Our approach utilizes restricted Boltzmann machines (RBMs) to compactly
represent the reduced density tensor, explicitly encoding the combined effects
of system-environment correlations and nonMarkovian memory. Applied to model
systems exhibiting prominent effects of system-environment correlation and
non-Markovian memory, our approach achieves comparable accuracy to conventional
hierarchical equations of motion, while requiring significantly fewer dynamical
variables. The novel RBM-based DQME-SQ approach paves the way for investigating
non-Markovian open quantum dynamics in previously intractable regimes, with
implications spanning various frontiers of modern science.

利用神经量子态的方法，我们提供了一种人工智能策略来模拟耦合非马尔可夫环境的开放量子系统的动力学，通过将神经量子态方法与含衰减耦合的二次量化量子主方程（DQME-SQ）结合起来，我们能够在显著减少动力学变量的同时实现与传统的层次方程相当的精度，为研究以前难以处理的非马尔可夫开放量子动力学在各个现代科学前沿领域提供了新的思路。

多体开放量子系统的非马尔可夫耗散动力学的神经网络方法

Neural Network Approach for Non-Markovian Dissipative Dynamics of  Many-Body Open Quantum Systems

Reinforcement learning (RL) problems are often phrased in terms of Markov
decision processes (MDPs). In this thesis we go beyond MDPs and consider RL in
environments that are non-Markovian, non-ergodic and only partially observable.
Our focus is not on practical algorithms, but rather on the fundamental
underlying problems: How do we balance exploration and exploitation? How do we
explore optimally? When is an agent optimal? We follow the nonparametric
realizable paradigm.
We establish negative results on Bayesian RL agents, in particular AIXI. We
show that unlucky or adversarial choices of the prior cause the agent to
misbehave drastically. Therefore Legg-Hutter intelligence and balanced Pareto
optimality, which depend crucially on the choice of the prior, are entirely
subjective. Moreover, in the class of all computable environments every policy
is Pareto optimal. This undermines all existing optimality properties for AIXI.
However, there are Bayesian approaches to general RL that satisfy objective
optimality guarantees: We prove that Thompson sampling is asymptotically
optimal in stochastic environments in the sense that its value converges to the
value of the optimal policy. We connect asymptotic optimality to regret given a
recoverability assumption on the environment that allows the agent to recover
from mistakes. Hence Thompson sampling achieves sublinear regret in these
environments.
Our results culminate in a formal solution to the grain of truth problem: A
Bayesian agent acting in a multi-agent environment learns to predict the other
agents' policies if its prior assigns positive probability to them (the prior
contains a grain of truth). We construct a large but limit computable class
containing a grain of truth and show that agents based on Thompson sampling
over this class converge to play Nash equilibria in arbitrary unknown
computable multi-agent environments.

本文提出了在非 Markovian、非 ergodic 且只部分可观察的环境下进行强化学习的问题。作者建立了贝叶斯强化学习代理的负面结果，并证明 Thompson 采样在随机环境中是渐进最优的。此外，作者构建了一个大但可计算的类，展示了基于 Thompson 采样的代理在这个类中收敛于任意未知可计算多智能体环境中的纳什均衡。