Practical Quantum Topological Data Analysis with Applications to High-Dimensional Feature Extraction and Time Series Analysis

• URL: http://arxiv.org/abs/2607.27206v1
• Date: Wed, 29 Jul 2026 17:59:59 GMT
• Title: Practical Quantum Topological Data Analysis with Applications to High-Dimensional Feature Extraction and Time Series Analysis
• Abstract summary: Topological data analysis (TDA) provides a powerful framework for extracting information about the shape of complex, unstructured data.<n>We frame quantum TDA as a feature-extraction method for downstream data analysis by extracting low-order spectral information from the Laplacian.<n>We show that higher-order TDA features improve predictive performance in two time-series applications: functional MRI analysis for neurodegenerative disease classification and financial time-series analysis for identifying market instability.
• Score: 0.32622301272834514
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological data analysis (TDA) provides a powerful framework for extracting information about the shape of complex, unstructured data, but the classical cost of computing high dimensional topological features limits its application. Quantum algorithms for TDA offer a route around this bottleneck, yet existing approaches typically focus on exact or high precision Betti number estimation, making the regime for practical quantum advantage appear narrow. Here, we instead frame quantum TDA as a feature-extraction method for downstream data analysis by extracting low-order spectral information from the combinatorial Laplacian as a proxy for high-dimensional topology. We support this perspective from both the application and algorithmic sides. First, we show that higher-order TDA features improve predictive performance in two time-series applications: functional MRI analysis for neurodegenerative disease classification and financial time-series analysis for identifying market instability. Second, we develop a moment-based quantum algorithm and show that low-order moments, including the relative trace, are strongly correlated with high-dimensional Betti information, even when the relative Betti number is small. Finally, we present circuit constructions, resource estimates, quantum-classical crossover projections, and experimental results from a Barium development system similar to the forthcoming IonQ Tempo line, extracting Laplacian-derived observables from graph instances and quantitatively comparing them with exact Betti information. Together, these results establish quantum TDA as a practical approach for extracting topological features from classically challenging data

Related papers

• Quartic quantum speedups for community detection [84.14713515477784]
  We develop a quantum algorithm for hypergraph community detection that achieves a quartic quantum speedup.<n>Our algorithm is based on the Kikuchi method, which we extend beyond previously considered problems such as PCA and $p$XORSAT.
  arXiv  Detail & Related papers  (2025-10-09T17:35:17Z)
• Towards quantum topological data analysis: torsion detection [0.0]
  We introduce a quantum algorithm for torsion detection, that is, determining whether a given simplicial complex contains torsion.<n>Our algorithm, assisted by a low complexity classical procedure, can succeed with high probability and potentially offer exponential speedup.
  arXiv  Detail & Related papers  (2025-08-27T14:59:44Z)
• Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis [0.7997838571956237]
  Topological data analysis (TDA) is a rapidly growing area that applies techniques from algebraic topology to extract robust features from large-scale data.<n>A key task in TDA is the estimation of (normalized) Betti numbers, which capture essential topological invariants.<n>We explore an alternative direction: combining classical and quantum resources to estimate the Betti numbers of a simplicial complex more efficiently.
  arXiv  Detail & Related papers  (2025-08-02T23:19:11Z)
• New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes [3.2268950104324965]
  We present new quantum algorithms for estimating homological invariants, specifically Betti and persistent Betti numbers.<n>Our approach efficiently block-encodings of constructs (persistent) Laplacians, enabling estimation via exponential rank methods.<n>These results open a new direction in quantum topological data analysis and demonstrate provable quantum advantages in computing topological invariants.
  arXiv  Detail & Related papers  (2025-06-02T08:43:58Z)
• Explainable Spatio-Temporal GCNNs for Irregular Multivariate Time Series: Architecture and Application to ICU Patient Data [7.433698348783128]
  We present XST-CNN (eXG-Temporal Graph Conal Neural Network), a novel architecture for processing heterogeneous and irregular Multi Time Series (MTS) data. Our approach captures temporal and feature within a unifiedtemporal-temporal pipeline by leveraging a GCNN pipeline. We evaluate XST-CNN using real-world Electronic Health Record data to predict Multidrug Resistance (MDR) in ICU patients.
  arXiv  Detail & Related papers  (2024-11-01T22:53:17Z)
• Minimally Supervised Learning using Topological Projections in Self-Organizing Maps [55.31182147885694]
  We introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs) Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are assigned to key best matching units (BMU) Our results indicate that the proposed minimally supervised model significantly outperforms traditional regression techniques.
  arXiv  Detail & Related papers  (2024-01-12T22:51:48Z)
• Higher-order topological kernels via quantum computation [68.8204255655161]
  Topological data analysis (TDA) has emerged as a powerful tool for extracting meaningful insights from complex data. We propose a quantum approach to defining Betti kernels, which is based on constructing Betti curves with increasing order.
  arXiv  Detail & Related papers  (2023-07-14T14:48:52Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Quantum-Enhanced Topological Data Analysis: A Peep from an Implementation Perspective [22.137388773023854]
  This paper presents an implementation of one such algorithm for calculating Betti numbers. The step-by-step instructions for the chosen quantum algorithm and the aspects of how it can be used for machine learning tasks are provided. We provide encouraging results on using Betti numbers for classification and give a preliminary analysis of the effect of the number of shots and precision qubits on the outcome of the quantum algorithm.
  arXiv  Detail & Related papers  (2023-02-19T12:18:13Z)
• Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis [59.545114016224254]
  Quantum algorithms for topological data analysis seem to provide an exponential advantage over the best classical approach. We show that the central task of TDA -- estimating Betti numbers -- is intractable even for quantum computers. We argue that an exponential quantum advantage can be recovered if the input data is given as a specification of simplices.
  arXiv  Detail & Related papers  (2022-09-28T17:53:25Z)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• Quantum Algorithms for Data Representation and Analysis [68.754953879193]
  We provide quantum procedures that speed-up the solution of eigenproblems for data representation in machine learning. The power and practical use of these subroutines is shown through new quantum algorithms, sublinear in the input matrix's size, for principal component analysis, correspondence analysis, and latent semantic analysis. Results show that the run-time parameters that do not depend on the input's size are reasonable and that the error on the computed model is small, allowing for competitive classification performances.
  arXiv  Detail & Related papers  (2021-04-19T00:41:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.