Title: Dynamical Topology in Tensor Networks

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper explores the potential of extending tensor network methods to incorporate continuous topology, a crucial element in representing and analyzing complex, non-linear dynamical systems. Traditional tensor network representations are limited in their ability to capture the intricate interplay of topological defects and their dynamics. We propose a novel tensor network structure that explicitly encodes topological features, enabling a more comprehensive understanding of evolving systems. This work will focus on developing a framework for representing and analyzing topological defects within the context of tensor network analysis. The core mechanism involves introducing a dynamic 'twist' parameter that governs the formation and evolution of topological features, offering a significant advancement over existing approaches. This research will investigate the practical implications of this new approach, providing a foundation for studying diverse dynamical systems and highlighting the potential for enhanced modeling capabilities.

DOI: 10.5281/zenodo.22481939

Related papers

Title: Topological Phase Transitions in Non-Equilibrium Systems

Jincheng Zhang

This paper investigates the emergence of topological phase transitions in non-equilibrium systems, proposing a novel method for quantifying and predicting these transitions through the dynamic analysis of network topology. Traditional approaches often rely on static measurements, lacking the ability to capture the intricate, evolving nature of these phenomena. We introduce a computational framework based on graph neural networks to model and analyze the fractal properties of network topology, providing a fundamentally different perspective on identifying and predicting topological phase transitions. The core mechanism centers on continuous, dynamic network representations, offering enhanced predictive capabilities compared to existing methods. This work presents a rigorous investigation of the impact of temperature and disorder on network topology, demonstrating a significant improvement in prediction accuracy.

Sep 2, 20260 citations

Title: Dynamical Quantum Simulation of Complex Topological Defects

Jincheng Zhang

This research investigates a novel dynamical quantum simulation technique designed to accurately model the formation and dynamics of complex topological defects within materials. The core claim is to develop a quantum algorithm that captures the intricate interplay between quantum fluctuations and topological order, offering a fundamentally more accurate approach compared to existing simulation methods. This work will explore the application of quantum mechanics to simulate the evolution of topological defects, focusing on their interactions with quantum fluctuations. We outline a theoretical framework incorporating elements of quantum field theory and topological phase transitions to achieve this goal. The research will demonstrate the potential for this technique to provide valuable insights into the behavior of these critical defects, with implications for materials science and condensed matter physics.

Sep 6, 20260 citations

Title: Geometric Phase Field Analysis for Non-Linear Tensor Networks

Jincheng Zhang

This paper explores a novel framework for analyzing and manipulating tensor networks, centered around the geometric properties of phase fields. Traditional tensor network analysis often overlooks the inherent geometric structure of these networks, hindering effective manipulation and understanding. We propose a "phase-field gradient" – a dynamically evolving field representing the phase relationships within a tensor network – that explicitly incorporates differential geometry to provide a more precise and insightful method for analyzing and manipulating network topology. This approach allows for the direct manipulation of network structure, opening avenues for new research in areas such as graph theory, optimization, and machine learning. The paper details the mathematical foundations of the phase-field gradient, provides a concrete implementation demonstrating its utility, and discusses potential applications and future directions.

Sep 4, 20260 citations

Title: Topological Information Extraction via Dynamic Quantum State Modeling

Jincheng Zhang

This paper introduces a novel algorithm for extracting richer topological information from quantum states. Traditional topological analysis often relies on static representations, limiting the ability to fully characterize complex quantum systems. Our approach leverages the inherent dynamism of quantum states to construct a dynamic quantum state model and utilize it for information extraction. The core mechanism involves establishing a model based on quantum state evolution, enabling the identification and representation of intricate topological structures. This innovation promises a more flexible and insightful understanding of quantum phenomena, potentially offering significant advancements in quantum information processing and analysis. We demonstrate the effectiveness of this method through theoretical analysis and preliminary experimental validation, highlighting its potential to unlock new insights into quantum systems.

Sep 5, 20260 citations

Title: Quantum Topological Computing Models

Jincheng Zhang

The current limitations of traditional information theory often restrict the ability to accurately model and simulate complex systems. Quantum topological computing offers a potential paradigm shift, leveraging the unique properties of topological quantum systems to provide a fundamentally different approach to computation. This paper explores the application of quantum topological computing models, specifically focusing on the development of a novel computational framework built upon topological structures. We propose a new method for precisely calculating quantum states, particularly high-dimensional ones, by exploiting the inherent properties of these structures. The core claim of this research is that incorporating quantum topological structures into computation will enable more detailed and accurate modeling of complex systems, and a deeper understanding of the intricate connection between quantum information and topological structures. The development of this framework promises a significant advancement in computational capabilities for various fields, particularly those involving quantum systems.

Sep 5, 20260 citations

Title: Topological Entanglement Dynamics – Beyond Classical Correlation

Jincheng Zhang

Topological entanglement, a fundamental concept in quantum mechanics, exhibits unique properties that challenge classical intuition. This research explores a novel framework for quantifying and controlling the dynamic evolution of topological entanglement, predicting and mitigating decoherence in complex quantum systems. We propose a dynamically evolving, multi-scale topology based on a 'self-organizing' entanglement graph, utilizing adaptive feedback loops to minimize dissipation. This approach significantly expands the scope of entanglement analysis, offering predictive capabilities exceeding existing methods. The core mechanism involves modeling entanglement structure through a graph-based approach, incorporating adaptive control to ensure stability and coherence. This work presents a theoretical foundation and preliminary experimental validation demonstrating the framework's ability to predict and counteract decoherence patterns, thereby advancing our understanding of topological entanglement dynamics.

Sep 6, 20260 citations