Related papers: Complexity-Theoretic Limitations on Quantum Algori…

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…

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…

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…

Quantum computing offers the potential of exponential speedups for certain classical computations. Over the last decade, many quantum machine learning (QML) algorithms have been proposed as candidates for such exponential improvements.…

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…

Topological data analysis (TDA) is a fast-growing field that utilizes advanced tools from topology to analyze large-scale data. A central problem in topological data analysis is estimating the so-called Betti numbers of the underlying…

There is heightened interest in quantum algorithms for Topological Data Analysis (TDA) as it is a powerful tool for data analysis, but it can get highly computationally expensive. Even though there are different propositions and…

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and…

Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned…

Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…

Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. TDA enhances the analysis of objects by embedding them into a simplicial complex and extracting useful global properties…

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…

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 --…

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 offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat.…

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…

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…

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…

Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…

Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…