用四元数建模量子学习，让量子设备像神经元一样自适应训练。
A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices
- 用四元数代数构建量子计算与测量的统一模型。
- 基于该模型提出可收敛的量子学习训练框架。
- 适合研究量子机器学习算法的科研人员参考。
本文研究量子学习机器的自适应与优化方法。利用四元数的除法代数性质，推导出描述量子比特计算与测量操作的有效模型。该模型为量子学习单元上的自适应学习问题提供基础，建立起类似经典神经元的量子信息处理单元。进一步结合现代HR微分学，构建了完整的量子机器学习训练框架。四元数模型具备数学可处理性，并能确立收敛性等性能准则。
原文摘要 · Abstract (English)
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.
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