Related papers: Towards quantum topological data analysis: torsion…

Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…

We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…

We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…

In an era where data underpins decision-making across science, politics, and economics, ensuring high data quality is of paramount importance. Conventional computing algorithms for enhancing data quality, including anomaly detection, demand…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure…

A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…

Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…

Spectral methods are a leading approach for tensor PCA with a ``spiked" Gaussian tensor. The methods use the spectrum of a linear operator in a vector space with exponentially high dimension and in Ref. 1 it was shown that quantum…

We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize…

Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…