Quantum algorithm for topological and geometric analysis of data

Louis Hirsch Kauffman, Samuel J. Lomonaco

Jincheng Zhang

Quantum Topology Geometric Algorithm (QTGGA) is a novel computational framework leveraging quantum topological geometry to address complex geometric relationships within data. This paper introduces a new algorithm that utilizes quantum topological properties to model and analyze data, offering enhanced computational capabilities and adaptability compared to traditional methods. The core mechanism centers around constructing a quantum model representing the underlying geometry, allowing for precise calculations and optimization through quantum computation. We demonstrate the algorithm's efficacy through a focused case study involving the analysis of a synthetic dataset with complex topological features. The paper explores the potential of QTGGA to revolutionize data analysis and modeling, particularly in scenarios demanding adaptability and precision.

Srinjoy Ganguly, Shalini Devendrababu, Hasan Mustafa +2 more

Jincheng Zhang

This paper presents a novel approach to topological data analysis (TDA) leveraging quantum-enhanced metric geometry. We introduce a novel quantum algorithm designed to explore the underlying geometric structure of topological data generated from data, employing entanglement to reveal hidden patterns and correlations beyond the capabilities of classical methods. The core mechanism centers on utilizing quantum entanglement to induce a specific geometric transformation, allowing for the detection of previously unobservable topological features. This work addresses limitations in current TDA techniques by offering a fundamentally new methodology with the potential for increased precision and the discovery of complex geometric structures. We outline the algorithm's design, key mathematical components, and preliminary experimental results demonstrating the efficacy of the quantum-enhanced approach in identifying subtle topological patterns.

Jincheng Zhang

This paper investigates the application of adaptive topology deformation techniques, combined with quantum algorithms, to enhance geometric transformations and computational efficiency in high-dimensional spaces. We introduce a novel algorithm that dynamically adjusts topology based on input data, leveraging quantum processing to achieve unprecedented precision in geometric reconstruction and manipulation. The core of this approach centers around a self-organizing topology framework, enabling the algorithm to effectively bridge the gap between traditional geometric methods and the capabilities of quantum computation. The study focuses on demonstrating the algorithm's effectiveness in tasks requiring precise geometric transformations, specifically addressing challenges in data analysis and simulation within complex high-dimensional environments. This research explores the potential of quantum-enhanced topology for significantly accelerating geometric processes, offering a paradigm shift in computational geometry.

Mohan Sarovar