Quantum machine learning with canonical variables

Jesús Fuentes

doi:10.1007/s42484-026-00373-w

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Quantum machine learning with canonical variables

2026-02-26

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Jesús Fuentes *

DOI：10.1007/s42484-026-00373-w

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Abstract

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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.

Keywords:

Quantum machine learning

Quantum dynamics

Quantum control

Exact solutions