学习的量子：利用四元数代数对量子设备上的学习进行建模
A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices
AI总结：
本文利用四元数代数建模量子比特上的计算与测量，提出类似神经元的量子学习单元，并结合HR-微积分构建可分析收敛性的量子机器学习训练框架。
摘要：
本文考虑为训练量子学习机设计适配与优化技术的问题。为此，利用四元数除法代数推导出一个有效模型，用于表示量子比特上的计算与测量操作。随后，该推导模型作为在主要量子学习单元上表述自适应学习问题的基础，从而建立起类似于经典方法中神经元的量子信息处理单元。接着，借助现代HR-微积分，开发了一个用于量子机器学习的综合训练框架。该四元数值模型具备数学可处理性，并能够建立性能准则，例如收敛条件。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
