Complexity in Dynamics and Computation

Masanori Ohya

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.

Daniel Klaus Burgarth, Paolo Facchi A, Vittorio Giovannetti +3 more

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

Jincheng Zhang

This paper presents a novel theoretical framework for dynamic complexity computation, leveraging the unique properties of quantum entanglement to enhance the assessment of complex system computational complexity. We propose a method that establishes a direct link between complexity metrics and entanglement, enabling the precise evaluation of computational stability and guiding algorithm optimization based on this understanding. The core mechanism involves associating complexity with entanglement's inherent characteristics, utilizing entanglement for stability assessment and algorithmic optimization. This approach offers a fundamentally different perspective on complexity, moving beyond traditional statistical methods and embracing the subtle yet powerful interplay of quantum mechanics. This research aims to provide a robust and potentially transformative tool for computational complexity analysis, particularly in the design and optimization of complex algorithms.