Related papers: Quantum spectroscopy of topological dynamics via a…
We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying…
We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a structured classical input. At the core of our algorithm lies…
Topological data analysis (TDA) is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA are limited if we want to learn from high-dimensional…
We provide a quantum protocol to perform topological data analysis (TDA) via the distillation of quantum thermal states. Recent developments of quantum thermal state preparation algorithms reveal their characteristic scaling defined by…
Topological data analysis (TDA) is a rapidly growing area that applies techniques from algebraic topology to extract robust features from large-scale data. A key task in TDA is the estimation of (normalized) Betti numbers, which capture…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for…
Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to infer the topology of a hypothetical manifold from which…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
In a novel application of the tools of topological data analysis (TDA) to nonperturbative quantum gravity, we introduce a new class of observables that allows us to assess whether quantum spacetime really resembles a ``quantum foam" near…
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…
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…
Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two…
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…
A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…