Title: Topological Quantum Field Theory for Unconstrained Complexity

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper explores the potential of Topological Quantum Field Theory (TQFT) for representing and manipulating quantum states with dynamic, continuous evolution. Traditional approaches often rely on mapping quantum states to classical fields, which can be cumbersome and limited in their ability to capture complex phenomena. We propose a novel framework centered around a 'topological state vector', dynamically updating this vector through a series of interwoven, non-local operations to represent the evolving quantum field. This approach eliminates the need for explicit mapping, offering a fundamentally different and potentially more powerful methodology for constructing topological quantum field theories. This work aims to demonstrate the feasibility and advantages of this new approach in exploring complex quantum systems and computational paradigms.

DOI: 10.5281/zenodo.22185163

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