Quantum Simulation of Chaos- Concepts, Methods, and Contemporary Perspectives

Liang Huang, Ying‐Cheng Lai

Abstract Quantum Chaos has been investigated for about a half century. It is an old yet vigorous interdisciplinary field with new concepts and interesting topics emerging constantly. Recent years have witnessed a growing interest in quantum chaos in relativistic quantum systems, leading to the still developing field of relativistic quantum chaos . The purpose of this paper is not to provide a thorough review of this area, but rather to outline the basics and introduce the key concepts and methods in a concise way. A few representative topics are discussed, which may help the readers to quickly grasp the essentials of relativistic quantum chaos. A brief overview of the general topics in quantum chaos has also been provided with rich references.

André Voros

Michel Paty

The problem of the nature of probability laws in physics is a central one from the epistemologic point of view : perhaps the most central one for twentieth century physics, if we consider, on the one hand, the harsh debates to which it has given rise in the recent past (left unconcluded by the protagonists and most often by their successors) and the vagueness of the answers which are generally proposed by contemporary physicists when asked about this problem ; and, on the other hand, the perspectives of theoretical physics as it is developing under our eyes in the various domains - and, perhaps above all, in the "frontier" domains such as particle symmetry fields and cosmology, or, differently, dynamics of continuous media, turbulences and chaos, where probability is a - if not the - fundamental concept.

Simone Montangero

Jincheng Zhang

Quantum entanglement, a bizarre phenomenon in quantum mechanics, offers a unique perspective for modeling complex systems, particularly those exhibiting chaotic behavior. This paper explores the potential of utilizing quantum entanglement to represent and simulate the dynamics of chaotic systems, proposing a novel framework for investigating the fundamental mechanisms underlying chaos and stability. We delve into the implications of entanglement, focusing on its capacity to represent correlations beyond classical limits and provide a means for probing the underlying structure of chaotic systems. The work outlines the theoretical foundation of this approach, detailing the key mathematical concepts involved and illustrating its potential for advancing our understanding of chaos.

Cole Bernard Cecchetto