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Topological Data Analysis (TDA) is a discipline that applies algebraic topology techniques to analyze complex, multi-dimensional data. Although it is a relatively new field, TDA has been widely and successfully applied across various…

Machine Learning · Computer Science 2024-07-29 Martin Uray , Barbara Giunti , Michael Kerber , Stefan Huber

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Algebraic Topology · Mathematics 2026-02-04 Christian Lentz , Gregory Henselman-Petrusek , Lori Ziegelmeier

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes…

Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…

Quantum Physics · Physics 2025-01-10 Johannes Nokkala , Gian Luca Giorgi , Roberta Zambrini

Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…

Machine Learning · Statistics 2023-07-10 Yueqi Cao , Athanasios Vlontzos , Luca Schmidtke , Bernhard Kainz , Anthea Monod

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…

Machine Learning · Statistics 2025-10-23 Pattravadee de Favereau de Jeneret , Ioannis Diamantis

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

Algebraic Topology · Mathematics 2021-01-20 Bastian Rieck , Markus Banagl , Filip Sadlo , Heike Leitte

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…

Machine Learning · Computer Science 2020-03-31 Shafie Gholizadeh , Ketki Savle , Armin Seyeditabari , Wlodek Zadrozny

Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…

Quantum Physics · Physics 2025-09-23 Christophe Pere

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…

Quantum Physics · Physics 2017-11-08 Iris Cong , Meng Cheng , Zhenghan Wang

Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…

Algebraic Topology · Mathematics 2024-06-26 Cheyne Glass , Elizabeth Vidaurre

I introduce a continuous-variable quantum topological data algorithm. The goal of the quantum algorithm is to calculate the Betti numbers in persistent homology which are the dimensions of the kernel of the combinatorial Laplacian. I…

Quantum Physics · Physics 2019-12-17 George Siopsis

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Algebraic Topology · Mathematics 2025-07-22 Athanasios Andrikopoulos , Nikolaos Sampanis

The accelerated development of quantum technology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of…

Quantum Physics · Physics 2014-05-21 Simon J. Devitt

Quantum data learning (QDL) provides a framework for extracting physical insights directly from quantum states, bypassing the need for any identification of the classical observable of the theory. A central challenge in many-body physics is…

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…

Machine Learning · Computer Science 2023-03-09 Aina Ferrà , Gloria Cecchini , Fritz-Pere Nobbe Fisas , Carles Casacuberta , Ignasi Cos

Anomaly detection is an important problem with applications in various domains such as fraud detection, pattern recognition or medical diagnosis. Several algorithms have been introduced using classical computing approaches. However, using…

Machine Learning · Computer Science 2024-10-10 Robin Frehner , Kurt Stockinger

Our primary objective is to conduct a brief survey of various classical and quantum neural net sequence models, which includes self-attention and recurrent neural networks, with a focus on recent quantum approaches proposed to work with…

Quantum Physics · Physics 2024-02-23 I-Chi Chen , Harshdeep Singh , V L Anukruti , Brian Quanz , Kavitha Yogaraj

In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…

Quantum Physics · Physics 2009-11-11 N. E. Bonesteel , Layla Hormozi , Georgios Zikos , Steven H. Simon

Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…

Quantum Physics · Physics 2025-04-01 Shiwen An , Konstantinos Slavakis