Quantum machine learning with canonical variables

Abstract

Ion-trap quantum computers typically utilise electromagnetic fields to confine charged particles and execute quantum operations on qubits. However, gate-based and continuous-variable algorithms encounter challenges in terms of trainability and interpretability. Driven by these limitations, the present work introduces a scheme that integrates supervised learning directly into exactly solvable non-relativistic dynamics of canonical observables, namely position and momentum. The fundamental idea is to regard the time-varying electromagnetic potential as the learning hypotheses, or ansatz, therefore supplanting qubit- or mode-centric manipulations with physically implementable field controls. Consequently, the resulting models possess closed-form solutions for both regression and classification tasks, thereby establishing a transparent framework for quantum machine learning at the observable level.