Dynamics of Complex Quantum Systems

Jincheng Zhang

Quantum Complexity Theory represents a paradigm shift in our understanding of complex quantum systems, moving beyond static models to embrace dynamic, hybrid dynamical systems. This paper proposes a novel framework for analyzing quantum complexity by integrating quantum dynamics with hybrid dynamical systems, aiming to unveil hidden patterns and provide deeper insights into the behavior of these systems. The core mechanism involves a closed-loop simulation that continuously updates the system's state, driving a dynamic evolution guided by quantum principles. This approach offers a more complete and nuanced understanding of complexity compared to traditional approaches.

Xiang Ying Sun

Noboru Watanabe

In Ref. 27, Ohya proposed the information dynamics synthesizing several ways of studying complex systems. In information dynamics, there are two types of complexities, one is a complexity of state representing system itself and another is a transmitted complexity between two systems. Entropies in classical and quantum systems are examples of these complexities of information dynamics. Transmitted complexity is an important tool to analyze the efficiency of information transmission in communication processes. In order to treat a flow of dynamical process, dynamical entropies were introduced in not only classical but also quantum systems. Based on the transition expectation introduced by Accardi to study quantum Markov process, the KOW entropy for completely positive (CP) maps was defined in Ref. 17. The generalized AOW and the AF entropies was constructed by the KOW entropy. The compound states are important tool to define the transmitted entropy 43,44. The transmitted complexity associated with the separable compound states is defined by using the generalized AOW entropy in Refs. 36 and 45. In this paper, we define a transmitted complexity (quantum dynamical mutual entropy) by means of the modified compound states and we prove the fundamental inequalities of the transmitted complexity for the independent quantum dynamical systems.

Gernot Schaller

Jincheng Zhang

Abstract: Quantum-enhanced simulation of complex dynamical systems presents a significant challenge in scientific research and engineering. Traditional computational methods often struggle to effectively model and analyze intricate systems exhibiting nonlinear behavior. This paper introduces the Quantum-Enhanced Simulation of Complex Dynamical Systems (QESCS) methodology, a novel approach leveraging quantum computing to accelerate the simulation of these systems. We detail the fundamental principles behind the QESCS, outlining its architecture, computational steps, and potential benefits in terms of speed and accuracy. This research aims to provide a viable pathway for tackling computationally intensive dynamical systems simulations, offering a dramatic reduction in time and resource requirements.

Ángel S. Sanz, Salvador Miret-Artés