相关论文: Learning Volterra Kernels for Non-Markovian Open Q…
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum…
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…
By revising the application of the open quantum system approach to the early universe and extending it to the conditions beyond the Markovian approximation, we obtain a new non-Markovian quantum Boltzmann equation. Throughout the paper, we…
The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of…
As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework…
We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a…
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master…
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in…
On the basis of the dynamical-quantization approach to open quantum systems, we can derive a non-Markovian Caldeira-Leggett quantum master equation as well as a non-Markovian quantum Smoluchowski equation in phase space. On the one hand, we…
We define an ensemble of projection operators, each of which has an exact associated Nakajima-Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields, for an…
Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of…
Models for open quantum systems, which play important roles in electron transport problems and quantum computing, must take into account the interaction of the quantum system with the surrounding environment. Although such models can be…
The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced…
This paper presents detailed insights of embedding Carleman linearization into nonlinear systems for designing Volterra model-based control technique. Volterra series method is a competent mathematical tool, which extends the convolution…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify…
Memory effects arise in many complex systems, from protein folding, to the spreading of epidemics and financial decisions. While so-called non-Markovian dynamics is common in larger systems with interacting components, observations in…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where…
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…