Dynamical Systems Simulation via Tensor Networks with Adaptive Entanglement

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper proposes a novel approach to simulating complex dynamical systems utilizing tensor networks coupled with adaptive entanglement control. Traditional dynamical systems simulation methods often struggle with accuracy and computational efficiency, particularly when dealing with systems exhibiting intricate dynamics or requiring high precision. We introduce a framework where the system's state is represented as a tensor network, and an intelligent agent, trained via reinforcement learning, dynamically adjusts the entanglement level within the network. This adaptive entanglement control mechanism responds to the simulation's error metrics and computational cost, optimizing the representation for improved accuracy and reduced computational burden. The core claim is that this synergistic combination can achieve significantly higher accuracy and efficiency compared to conventional methods. The method presents a new paradigm for simulating complex systems by dynamically tailoring the computational resources to the system's specific needs. This work lays the groundwork for a more efficient and accurate approach to simulating a wide range of dynamical systems.

DOI: 10.5281/zenodo.22463826

Related papers

Quantum-Inspired Simulation of Complex Systems using Tensor Networks

Jincheng Zhang

The accurate simulation of complex systems, encompassing fields like materials science, quantum chemistry, and finance, often presents a formidable computational challenge. Traditional methods frequently struggle to scale effectively, particularly when dealing with high-dimensionality or intricate correlations. This paper introduces a novel simulation approach leveraging tensor networks (TN) in conjunction with quantum-inspired sampling techniques. The core idea is to approximate the dynamics of these complex systems by exploiting the inherent structure of tensor networks and employing sampling strategies inspired by quantum measurement processes. We demonstrate that this hybrid approach offers a pathway towards scalable simulations, achieving high accuracy while mitigating the computational bottlenecks associated with conventional methods. The key innovations lie in the adaptive construction of TNs based on the system's correlation structure and the utilization of quantum-inspired sampling methods to efficiently capture the relevant dynamics. This work presents a theoretical framework and outlines a methodology for implementing such simulations, paving the way for advancements in the modeling and understanding of complex systems.

Sep 6, 20260 citations

Title: Adaptive Quantum Simulation of Complex Dynamical Systems

Jincheng Zhang

This paper introduces an innovative quantum simulation technique designed to address the challenges of simulating complex dynamical systems. Traditional simulation methods frequently suffer from limitations in accuracy and computational cost, particularly when dealing with intricate dynamics. This work proposes an adaptive quantum simulation framework centered around a neural network that dynamically adjusts simulation parameters based on observed system evolution. The core mechanism leverages a neural network to learn a mapping between simulation parameters and the system's dynamics, enabling the simulation to concentrate computational resources on areas of interest. We demonstrate the effectiveness of this approach through simulations of a simplified, yet representative, dynamical system exhibiting key features of phase transitions and complex behavior. The results highlight the potential for significant improvements in simulation accuracy and efficiency compared to traditional methods, particularly in scenarios involving high dimensionality and non-linear dynamics. The paper concludes with a discussion of future research directions and potential applications of this technology.

Aug 29, 20260 citations

Dynamic Multi-Particle Quantum Simulation: An Adaptive Adjustment Mechanism

Jincheng Zhang

Abstract: This paper introduces a novel dynamic adjustment mechanism for quantum simulation, designed to enhance precision and efficiency through the utilization of quantum entanglement and topology optimization. Traditional quantum simulation often relies on fixed parameters, struggling to accurately represent complex systems exhibiting dynamic changes. This work proposes a mechanism that enables adaptive simulation, allowing the system to respond to changes in the underlying dynamics. We detail the core concept, outline the key algorithmic components, and present preliminary results demonstrating the effectiveness of this approach in simulating a specific multi-particle system.

Sep 6, 20260 citations

Dynamic Quantum Entanglement Resource Allocation

Jincheng Zhang

Quantum entanglement is a fundamental resource in quantum computing, enabling phenomena like super-dense coding and quantum teleportation. However, effectively utilizing this resource is a significant challenge, particularly in large-scale quantum computations. Traditional methods for quantum resource allocation are often static and rely heavily on expert knowledge, which may not adapt well to the dynamic and complex demands of real-world quantum tasks. This paper proposes a novel framework for dynamic quantum entanglement resource allocation, leveraging the power of reinforcement learning (RL). We construct a quantum computing environment simulator and train a reinforcement learning agent to autonomously manage and allocate entanglement resources based on task requirements and current resource availability. The agent learns an optimal policy through trial and error, maximizing the efficiency and potentially enhancing the error resilience of quantum computations. The core of this approach lies in the adaptive nature of the RL agent, allowing it to respond to fluctuating demands and optimize resource allocation in real-time. This work represents a significant step towards more efficient and practical quantum computing by moving away from pre-defined rules and embracing intelligent automation.

Aug 31, 20260 citations

基于自适应的量子纠缠模拟算法

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, is a uniquely fragile phenomenon with profound implications for quantum computing and information processing. Accurate simulation of entangled states is crucial for many quantum algorithms and applications. However, traditional quantum state simulation methods often struggle with the inherent complexity of entangled systems and the difficulty of accurately capturing their dynamics. This paper introduces a novel approach to quantum state simulation, termed "Adaptive Quantum Entanglement Simulation" (AQES), which leverages dynamic parameter adjustment to enhance the precision and efficiency of quantum state simulations. AQES employs a feedback mechanism that continuously monitors and adjusts parameters based on the observed evolution of entangled states, mitigating the limitations of static simulation approaches. We demonstrate the effectiveness of AQES through a series of simulations involving various entangled systems, showcasing significant improvements in fidelity and reduced computational cost compared to traditional methods. The core of the algorithm lies in its ability to dynamically respond to subtle changes in the entanglement network, ensuring a more robust and accurate representation of quantum states.

Sep 5, 20260 citations

Scalable Quantum Simulation of Molecular Dynamics using Tensor Networks

Jincheng Zhang

Quantum simulation offers a pathway to accurately model and understand complex molecular systems, a task often intractable using classical computational methods. However, the computational cost of simulating quantum systems, particularly those involving many particles and complex interactions, remains a significant barrier. This work presents a novel approach leveraging tensor network methods to achieve scalable quantum simulation of molecular dynamics. We demonstrate how tensor networks can efficiently represent the quantum state of a molecular system, allowing for the accurate calculation of its dynamics. The core idea is to utilize the tensor network representation to reduce the computational complexity associated with traditional quantum simulation algorithms. The presented method offers a promising route toward simulating larger and more realistic molecular systems, opening up new possibilities in fields such as drug discovery, materials science, and fundamental physics. This paper details the theoretical framework and provides a conceptual outline, emphasizing the scalability of the approach.

Aug 28, 20260 citations