A Quantum of Learning: Using Quaternion Algebra to Model Learning on Quantum Devices
This work addresses the challenge of training quantum devices for machine learning, which is an incremental step in quantum AI.
The paper tackles the problem of designing adaptation and optimization techniques for training quantum learning machines by using quaternion algebra to model computation and measurement on qubits, resulting in a comprehensive training framework with established convergence conditions.
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.