Higher-Order Topological Kernels via Quantum Computation

Incudini, Massimiliano; Martini, Francesco; Di Pierro, Alessandra

doi:10.1109/qce57702.2023.00076

2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 2023

DOI: 10.1109/qce57702.2023.00076

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Higher-Order Topological Kernels via Quantum Computation

Massimiliano Incudini,

Francesco Martini,

Alessandra Di Pierro

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2024

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Cited by 2 publications

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Toward Useful Quantum Kernels

Incudini,

Martini,

Pierro

2024

Adv Quantum Tech

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Supervised machine learning is a popular approach to the solution of many real‐life problems. This approach is characterized by the use of labeled datasets to train algorithms for classifying data or predicting outcomes accurately. The question of the extent to which quantum computation can help improve existing classical supervised learning methods is the subject of intense research in the area of quantum machine learning. The debate centers on whether an advantage can be achieved already with current noisy quantum computer prototypes or it is strictly dependent on the full power of a fault‐tolerant quantum computer. The current proposals can be classified into methods that can be suitably implemented on near‐term quantum computers but are essentially empirical, and methods that use quantum algorithms with a provable advantage over their classical counterparts but only when implemented on the still unavailable fault‐tolerant quantum computer.It turns out that, for the latter class, the benefit offered by quantum computation can be shown rigorously using quantum kernels, whereas the approach based on near‐term quantum computers is very unlikely to bring any advantage if implemented in the form of hybrid algorithms that delegate the hard part (optimization) to the far more powerful classical computers.

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Toward Useful Quantum Kernels

Incudini,

Martini,

Pierro

2024

Adv Quantum Tech

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Enhancing the Vietoris–Rips simplicial complex for topological data analysis: applications in cancer gene expression datasets

Mashatola,

Kader,

Abdulla

et al. 2024

Int J Data Sci Anal

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The aim of this study is to enhance the extraction of informative features from complex data through the application of topological data analysis (TDA) using novel topological overlapping measures. Topological data analysis has emerged as a promising methodology for extracting meaningful insights from complex datasets. Existing approaches in TDA often involve extrapolating data points using distance correlation measures, which subsequently constrain downstream predictive tasks. Our objective is to improve the construction of the Vietoris–Rips simplicial complex by introducing topological overlapping measures. These measures take into account the interplay of direct connection strengths and shared neighbours, leading to the identification of persistent topological features. We propose the utilisation of topological overlapping measures to optimise the construction of the Vietoris–Rips simplicial complex, offering a more refined representation of complex data structures. The application of topological overlapping measures results in the identification of plentiful persistent topological features. This enhancement contributes to an improvement of up to 20% in cancer phenotype prediction across different cancer types. Our study demonstrates the effectiveness of utilising topological overlapping measures in optimising the construction of the Vietoris–Rips simplicial complex. The identified persistent topological features significantly enhance the predictive accuracy of cancer phenotypes. This novel approach has the potential to advance the field of topological data analysis and improve our understanding of complex data structures, particularly in the context of cancer research and predictive modelling. Further exploration and application of these measures may yield valuable insights in various domains dealing with intricate datasets.

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Higher-Order Topological Kernels via Quantum Computation

Cited by 2 publications

References 20 publications

Toward Useful Quantum Kernels

Toward Useful Quantum Kernels

Enhancing the Vietoris–Rips simplicial complex for topological data analysis: applications in cancer gene expression datasets

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