Topological Data Analysis with Quantum-Enhanced Feature Extraction

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

This paper investigates the integration of Topological Data Analysis (TDA) with quantum algorithms to enhance feature extraction processes. Traditional feature extraction methods often struggle with noisy data and limited representation, while TDA offers a powerful framework for identifying inherent patterns and structures within complex datasets. We propose a novel approach that leverages the topological properties of data to generate robust and informative features, ultimately improving the performance of machine learning models. The paper explores the potential of quantum algorithms, specifically Quantum Feature Extraction (QFE), to accelerate and refine this process. We present a preliminary implementation demonstrating the efficacy of this combined technique, showcasing improved accuracy in a simulated dataset. The research explores the benefits of using quantum algorithms to discover hidden patterns that classical methods miss, offering a pathway toward more accurate and resilient machine learning.

DOI: 10.5281/zenodo.22635518

Related papers

Quantum-Enhanced Topological Data Analysis for Image Recognition

Jincheng Zhang

This paper explores the potential of quantum computing to revolutionize topological data analysis (TDA) techniques, specifically within image recognition. Traditional TDA methods often struggle with the computational complexity of analyzing high-dimensional data, limiting their applicability to complex image datasets. We propose a quantum-enhanced approach that leverages quantum feature extraction and pattern recognition to accelerate the identification of subtle correlations, ultimately improving the speed and accuracy of image classification. This work investigates the feasibility of quantum algorithms to address these computational bottlenecks, demonstrating a promising pathway for enhanced image recognition capabilities.

Sep 4, 20260 citations

Quantum-Enhanced Topological Data Analysis (QTDDA)

Jincheng Zhang

Abstract: Quantum-Enhanced Topological Data Analysis (QTDDA) explores the potential of quantum computation to revolutionize data representation and pattern discovery within topological data analysis (TDA). This paper introduces a novel algorithm, Quantum-Guided Topological Feature Extraction (QGTE), designed to leverage quantum properties – specifically superposition and entanglement – to enhance the representation of topological features. We demonstrate the efficacy of QGTE through a series of experiments, showcasing improvements in data quality and pattern identification compared to existing TDA techniques. This work provides a foundational basis for future research into utilizing quantum mechanics to enhance the capabilities of TDA.

Sep 4, 20260 citations

Quantum-Inspired Algorithms for Topological Data Analysis

Jincheng Zhang

Topological data analysis (TDA) has emerged as a powerful tool for uncovering hidden patterns and structures within complex datasets. However, traditional TDA algorithms can be computationally intensive, particularly when dealing with high-dimensional data. This paper explores the application of quantum-inspired algorithms to enhance TDA, aiming to improve both efficiency and accuracy. We propose a framework that leverages concepts from quantum mechanics, such as entanglement and superposition, to simulate and manipulate topological data structures. The core mechanism involves the use of quantum-inspired simulation techniques to represent and process persistent homology calculations, resulting in a potential acceleration of the algorithm. We demonstrate the theoretical feasibility and outline a potential implementation strategy, suggesting that this approach could unlock new insights within TDA and provide a pathway toward more scalable and robust topological analysis methods. The primary focus is on developing a computational model that mimics aspects of quantum computation without requiring actual quantum hardware, focusing instead on algorithmic design inspired by quantum principles. This work establishes a foundational approach for integrating quantum-inspired techniques into the domain of TDA, paving the way for future research and development in this exciting area.

Aug 31, 20260 citations

Quantum-Inspired Algorithms for Topological Data Analysis

Jincheng Zhang

Quantum-inspired algorithms are emerging as a promising approach to analyze complex topological data, offering potential advantages over classical methods. This paper explores the design of such algorithms inspired by quantum mechanics, aiming to enhance robustness and scalability through novel representations and processing techniques. We propose a framework centered on quantum state representations, demonstrating their efficacy in identifying intricate patterns within topological data. The core mechanism hinges on leveraging quantum properties to facilitate enhanced analysis and insight extraction. The research presents a preliminary investigation into this approach, highlighting potential improvements in data comprehension and robustness.

Aug 31, 20260 citations

Quantum-Driven Topological Data Analysis for Sparse Data

Jincheng Zhang

Quantum-driven Topological Data Analysis (Q-TDA) offers a fundamentally different approach to analyzing sparse data compared to traditional methods. This paper investigates the potential of leveraging quantum mechanics to identify patterns and relationships within these datasets, with the goal of significantly reducing the computational burden associated with data preprocessing and enhancing the detection of hidden structure. We introduce a novel quantum algorithm designed to efficiently explore topological spaces, which are inherently structured and provide a powerful framework for understanding data. This work explores the theoretical foundations and preliminary implementation of this quantum approach, highlighting its potential to revolutionize the field of topological data analysis. The core claim is that Q-TDA can achieve superior performance and efficiency for sparse data, offering a paradigm shift in the analysis of complex datasets.

Sep 1, 20260 citations

Topological Quantum Machine Learning Algorithm (TQMA)

Jincheng Zhang

This paper introduces the Topological Quantum Machine Learning Algorithm (TQMA), a novel approach to machine learning that leverages the inherent properties of topology and quantum mechanics to enhance model identification and prediction capabilities. Traditional machine learning methods often rely on extensive parameter tuning, hindering model adaptability and robustness. TQMA overcomes this limitation by incorporating a dynamically evolving, topologically structured representation within the model, enabling it to better capture complex relationships within data. We present a framework that integrates a quantum-inspired optimization process within a topological graph, allowing for exploration of intricate feature spaces and improved generalization. The algorithm's core mechanism centers around the construction and application of a quantum-enhanced topological graph, which facilitates the identification of subtle patterns and correlations often missed by conventional methods. We demonstrate the efficacy of TQMA through a series of benchmark datasets, showcasing significant improvements in classification accuracy and predictive performance compared to existing state-of-the-art techniques. This paper provides a comprehensive investigation into the potential of TQMA as a paradigm shift in machine learning, offering a pathway towards more intelligent and adaptable models.

Sep 4, 20260 citations