A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices

• URL: http://arxiv.org/abs/2504.13232v1
• Date: Thu, 17 Apr 2025 14:51:21 GMT
• Title: A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices
• Authors: Sayed Pouria Talebi, Clive Cheong Took, Danilo P. Mandic,
• Abstract summary: This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines.<n>The division algebra of quaternions is used to derive an effective model for representing computation and measurement operations on qubits.
• Score: 19.714874318004508
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation and measurement operations on qubits. In turn, the derived model, serves as the foundation for formulating an adaptive learning problem on principal quantum learning units, thereby establishing quantum information processing units akin to that of neurons in classical approaches. Then, leveraging the modern HR-calculus, a comprehensive training framework for learning on quantum machines is developed. The quaternion-valued model accommodates mathematical tractability and establishment of performance criteria, such as convergence conditions.

Related papers

• 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)
• Symmetry-invariant quantum machine learning force fields [0.0]
  We design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning.
  arXiv  Detail & Related papers  (2023-11-19T16:15:53Z)
• Variational quantum algorithms for machine learning: theory and applications [0.0]
  This thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning. The discussion then shifts to quantum machine learning, where an introduction to the elements of machine learning and statistical learning theory is followed by a review of the most common quantum counterparts of machine learning models.
  arXiv  Detail & Related papers  (2023-06-16T17:28:35Z)
• Shadows of quantum machine learning [2.236957801565796]
  We introduce a new class of quantum models where quantum resources are only required during training, while the deployment of the trained model is classical. We prove that this class of models is universal for classically-deployed quantum machine learning.
  arXiv  Detail & Related papers  (2023-05-31T18:00:02Z)
• 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)
• A didactic approach to quantum machine learning with a single qubit [68.8204255655161]
  We focus on the case of learning with a single qubit, using data re-uploading techniques. We implement the different proposed formulations in toy and real-world datasets using the qiskit quantum computing SDK.
  arXiv  Detail & Related papers  (2022-11-23T18:25:32Z)
• Generative model for learning quantum ensemble via optimal transport loss [0.9404723842159504]
  We propose a quantum generative model that can learn quantum ensemble. The proposed model paves the way for a wide application such as the health check of quantum devices.
  arXiv  Detail & Related papers  (2022-10-19T17:35:38Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Quantum-tailored machine-learning characterization of a superconducting qubit [50.591267188664666]
  We develop an approach to characterize the dynamics of a quantum device and learn device parameters. This approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task.
  arXiv  Detail & Related papers  (2021-06-24T15:58:57Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)

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.