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Diffusion models have emerged as preeminent contenders in the realm of generative models. Distinguished by their distinctive sequential generative processes, characterized by hundreds or even thousands of timesteps, diffusion models…
We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit…
Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the…
Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME)…
We derive a completely positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological…
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…
The high numerical demands for simulating non-Markovian open quantum systems motivate a line of research where short-time dynamical maps are extrapolated to predict long-time behavior. The transfer tensor method (TTM) has emerged as a…
Driven two-level system is a useful model to describe many quantum objects, particularly in quantum information processing. However, the exact master equation for such a system is barely explored. Making use of the Feynman-Vernon influence…
The master equation describing the non-equilibrium dynamics of a quantum dot coupled to metallic leads is considered. Employing a superoperator approach, we derive an exact time-convolutionless master equation for the probabilities of dot…
Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
There exist two canonical approaches to describe open quantum systems by a time-evolution equation: the Nakajima-Zwanzig quantum master equation, featuring a time-nonlocal memory kernel $\mathcal{K}$, and the time-convolutionless equation…
Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig…
The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath…
We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures [M. Hairer, A theory of…
The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration $\tau$. Recent work suggested that DQS is typically characterized by a…
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori-Zwanzig (MZ) formalism provides a mathematically formal…
Quantization of the parameters of machine learning models, such as deep neural networks, requires solving constrained optimization problems, where the constraint set is formed by the Cartesian product of many simple discrete sets. For such…
We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems governed by generalized quantum master equations with non-Markovian effects. Building upon the memory kernel…
Memory effects play a key role in the dynamics of strongly correlated systems driven out of equilibrium. In the present study, we explore the nature of memory in the nonequilibrium Anderson impurity model. The Nakajima--Zwanzig--Mori…