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Title: Quantum State-Based Topology as a Quantum Algorithm for Large-Scale Topology Problem

Jincheng Zhang

Published Sep 5, 2026• 0 citations
Publisher

Abstract

This paper presents a novel quantum algorithm for tackling large-scale topology problems, leveraging the principles of quantum state manipulation to achieve computational advantages over classical approaches. The core concept revolves around constructing and manipulating a quantum state representation of the topology of a given problem, allowing for efficient exploration of solution spaces. We introduce a specific quantum algorithm framework centered around the concept of "Quantum Topology Networks" (QTNs), where the topology itself is encoded within the quantum state. This framework allows for efficient traversal and analysis of complex topological structures. The design incorporates a key mechanism involving the application of a specific quantum circuit to induce a particular topological transformation on the input data, which then guides the algorithm towards finding optimal solutions. The novelty of this work lies in the explicit use of quantum state manipulation to represent and process topology, offering a fundamentally different approach compared to existing topological algorithms. We explore the algorithm's performance characteristics through simulations and preliminary testing with simplified topologies, demonstrating its potential for significant speedups in certain scenarios. The paper concludes with a discussion of future research directions, including scaling and broader applicability.

DOI
10.5281/zenodo.22332153

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This paper introduces a novel algorithm for topological information extraction based on quantum entanglement. Traditional methods often struggle with complex topological structures due to computational complexity and the need for extensive mapping. This algorithm leverages the unique properties of quantum entanglement to directly extract relevant information from these structures, offering a potentially transformative approach to data analysis and representation. The core mechanism involves constructing a specialized quantum state representation that encapsulates the topological information, allowing for efficient and accurate extraction via mathematical transformations. The algorithm demonstrates its efficacy through theoretical analysis and preliminary experimental validation, highlighting its potential to unlock new insights from topological data. This research explores the fundamental principles behind this approach and investigates its capacity to address limitations of existing topological information extraction techniques.
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