Related papers: From Betti Numbers to Persistence Diagrams: A Hybr…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
As the availability of imagery data continues to swell, so do the demands on transmission, storage and processing power. Processing requirements to handle this plethora of data is quickly outpacing the utility of conventional processing…
Predictive maintenance in aerospace heavily relies on accurate estimation of the remaining useful life of jet engines. In this paper, we introduce a Hybrid Quantum Recurrent Neural Network framework, combining Quantum Long Short-Term Memory…
Sampling from high-dimensional and structured probability distributions is a fundamental challenge in computational physics, particularly in the context of lattice field theory (LFT), where generating field configurations efficiently is…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
We present a new method for the statistical process control of lattice structures using tools from Topological Data Analysis. Motivated by applications in additive manufacturing, such as aerospace components and biomedical implants, where…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…
Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
Particle-based simulations and point-cloud applications generate massive, irregular datasets that challenge storage, I/O, and real-time analytics. Traditional compression techniques struggle with irregular particle distributions and GPU…
A persistence diagram provides a compact summary of persistent homology, which captures the topological features of a space at different scales. However, due to its nature as a set, incorporating it as a feature into a machine learning…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Classical persistent homology is a powerful mathematical tool for shape comparison. Unfortunately, it is not tailored to study the action of transformation groups that are different from the group Homeo(X) of all self-homeomorphisms of a…
Hybrid quantum-classical machine learning offers a promising direction for advancing automated quality control in industrial settings. In this study, we investigate two hybrid quantum-classical approaches for classifying defects in…
Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…