Related papers: Demonstration of Topological Data Analysis on a Qu…
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…
The Bott index has become an indispensable tool to probe the topology of quantum matter, particularly in systems lacking translational symmetry. Constructed from a plaquette operator, it retains the phase information while discarding the…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. A solution is…
In this paper, we formalize the notion of lambda-AT-model (where $\lambda$ is a non-null integer) for a given chain complex, which allows the computation of homological information in the integer domain avoiding using the Smith Normal Form…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Existing and near-term quantum computers can only perform two-qubit gates between physically connected qubits. Research has been done on compilers to rewrite quantum programs to match hardware constraints. However, the quantum processor…
In this paper the analysis of the result of numerical simulations of pasta phases using algebraic topology methods is presented. These considerations suggest that some phases can be further split into (sub)phases and therefore should be…
In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
Data generated in the fields of science, technology, business and in many other fields of research are increasing in an exponential rate. The way to extract knowledge from a huge set of data is a challenging task. This paper aims to propose…
A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to…
Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…
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.…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…
Artificial Neural Networks (ANNs) require significant amounts of data and computational resources to achieve high effectiveness in performing the tasks for which they are trained. To reduce resource demands, various techniques, such as…