A Geometric-Aware Perspective and Beyond: Hybrid Quantum-Classical Machine Learning Methods

• URL: http://arxiv.org/abs/2504.06328v1
• Date: Tue, 08 Apr 2025 13:24:55 GMT
• Title: A Geometric-Aware Perspective and Beyond: Hybrid Quantum-Classical Machine Learning Methods
• Authors: Azadeh Alavia, Hossein Akhoundib, Fatemeh Kouchmeshkib, Mojtaba Mahmoodianc, Sanduni Jayasinghec, Yongli Rena, Abdolrahman Alavi,
• Abstract summary: Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions.<n> Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages superposition, entanglement, and interference within quantum state manifold for learning tasks.<n>This paper offers a unifying perspective by casting QML as a specialized yet more expressive branch of GML.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages superposition, entanglement, and interference within quantum state manifolds for learning tasks. This paper offers a unifying perspective by casting QML as a specialized yet more expressive branch of GML. We argue that quantum states, whether pure or mixed, reside on curved manifolds (e.g., projective Hilbert spaces or density-operator manifolds), mirroring how covariance matrices inhabit the manifold of symmetric positive definite (SPD) matrices or how image sets occupy Grassmann manifolds. However, QML also benefits from purely quantum properties, such as entanglement-induced curvature, that can yield richer kernel structures and more nuanced data embeddings. We illustrate these ideas with published and newly discussed results, including hybrid classical -quantum pipelines for diabetic foot ulcer classification and structural health monitoring. Despite near-term hardware limitations that constrain purely quantum solutions, hybrid architectures already demonstrate tangible benefits by combining classical manifold-based feature extraction with quantum embeddings. We present a detailed mathematical treatment of the geometrical underpinnings of quantum states, emphasizing parallels to classical Riemannian geometry and manifold-based optimization. Finally, we outline open research challenges and future directions, including Quantum Large Language Models (LLMs), quantum reinforcement learning, and emerging hardware approaches, demonstrating how synergizing GML and QML principles can unlock the next generation of machine intelligence.

Related papers

• Exploring Tensor Network Algorithms as a Quantum-Inspired Method for Quantum Extreme Learning Machine [0.26013878609420266]
  Quantum Extreme Learning Machine (QELM) has emerged as a promising hybrid quantum machine learning (QML) method. We explore how quantum-inspired techniques like tensor networks (TNs) can be used for the QELM algorithm. This study also underscores the potential of tensor networks as quantum-inspired algorithms to enhance the capability of quantum machine learning algorithms to study datasets with large numbers of features.
  arXiv  Detail & Related papers  (2025-03-07T16:03:24Z)
• Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuits [48.33631905972908]
  We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC) This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions. Our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach.
  arXiv  Detail & Related papers  (2024-11-13T12:03:39Z)
• Quantum Geometric Machine Learning [0.6526824510982799]
  We present state-of-the-art machine learning methods with techniques from differential geometry and topology. We demonstrate the use of deep learning greybox machine learning techniques for estimating approximate time-optimal unitary sequences. We present novel techniques utilising Cartan decompositions and variational methods for analytically solving quantum control problems.
  arXiv  Detail & Related papers  (2024-09-08T02:55:19Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning [1.0984331138780683]
  Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives.<n>In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services.<n>QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources.
  arXiv  Detail & Related papers  (2023-01-22T15:17:12Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Representation Theory for Geometric Quantum Machine Learning [0.0]
  Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Geometric Quantum Machine Learning (GQML) will play a crucial role in developing problem-specific and quantum-aware models. We present an introduction to representation theory tools from the optics of quantum learning, driven by key examples involving discrete and continuous groups.
  arXiv  Detail & Related papers  (2022-10-14T17:25:36Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Recent Advances for Quantum Neural Networks in Generative Learning [98.88205308106778]
  Quantum generative learning models (QGLMs) may surpass their classical counterparts. We review the current progress of QGLMs from the perspective of machine learning. We discuss the potential applications of QGLMs in both conventional machine learning tasks and quantum physics.
  arXiv  Detail & Related papers  (2022-06-07T07:32:57Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies [0.0]
  We show that a new approach to optimization with constraints can be applied to complex quantum systems. The developed approach together with the provided open source software can be applied to the optimal control of noisy quantum systems.
  arXiv  Detail & Related papers  (2020-07-02T17:53:01Z)

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.