Title: Non-Standard Geometric Topology for Quantum State Preservation
Jincheng Zhang
Abstract
Abstract: Quantum state preservation is a fundamental challenge in quantum information processing, demanding robust and reliable methods for maintaining quantum coherence over extended time scales. Traditional topological approaches, while offering valuable insights, often struggle with the inherent complexities of quantum systems. This paper proposes a novel geometric topology, termed "Dynamic Entanglement Topology" (DET), designed to intrinsically guarantee the preservation of quantum states across extended time scales. DET leverages dynamically evolving entanglement patterns to achieve continuous state evolution without collapse, offering a robust framework for quantum information processing. The core mechanism involves introducing a self-correcting topology that adapts to maintain quantum coherence. We present a rigorous mathematical framework demonstrating the robustness of DET against various perturbations, highlighting its potential to overcome limitations of existing topological methods.