Related papers: Path Integral Solution for Dissipative Generative …
Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…
In designing generative models, it is commonly believed that in order to learn useful latent structure, we face a fundamental tension between expressivity and structure. In this paper we challenge this view by proposing a new approach to…
In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
Recent work has studied the emergence of language among deep reinforcement learning agents that must collaborate to solve a task. Of particular interest are the factors that cause language to be compositional -- i.e., express meaning by…
We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean…
These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…
Consider the finite state graph that results from a simple, discrete, dynamical system in which an agent moves in a rectangular grid picking up and dropping packages. Can the state variables of the problem, namely, the agent location and…
Large Language Models (LLMs), such as the Generative Pretrained Transformer (GPT), have achieved tremendous success in various language tasks, but their emergent abilities have also raised many questions, concerns, and challenges that need…
Semantic communication is poised to play a pivotal role in shaping the landscape of future AI-driven communication systems. Its challenge of extracting semantic information from the original complex content and regenerating semantically…
Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant…
Quantum information can be encoded in the set of steady-states (SSS) of a driven-dissipative system. Non steady-states are separated by a large dissipative gap that adiabatically decouples them way while the dynamics inside the SSS is…
Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time…
This study is focused on the quantum dynamics of a nitrogen-vacancy (NV) center coupled to a nonlinear, periodically driven mechanical oscillator. For a continuous periodic driving that depends on the position of the oscillator, the…
We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and…
Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary…
In this work, we present a generalized formulation of the Transformer algorithm by reinterpreting its core mechanisms within the framework of Path Integral formalism. In this perspective, the attention mechanism is recast as a process that…
Dissipative systems with decoherence free subspaces, a.k.a. dark spaces (DSs), can be used to protect quantum information. At the same time, dissipation is expected to give rise to coherent information degradation outside the DS. Employed…
Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…