A train--prune--readout--rewrite workflow for interpretable quantum learning

Abstract:AI for Science aims not only to predict complex physical systems from data, but also to extract mathematical structure and physically testable representations from learned models. Here, a train--prune--readout--rewrite workflow is developed that separates physical-domain grounding from three increasingly stringent analysis claims: algebraically equivalent readout of a trained predictor, compact teacher-faithful symbolic rewriting on the sampled physical domain, and transformation-based tests of learned internal representations. The workflow is implemented with complex-valued Kolmogorov--Arnold networks, whose explicit edge functions enable post-pruning analytic readout of the retained computation. In analytically controlled single-qubit tasks, rewriting recovered the quadratic structure of purity, whereas von Neumann entropy yielded only a domain-bounded symbolic surrogate; physics-aligned variable grouping preserved symbolic fidelity. For two-qubit entanglement-related tasks, shared learning exposed a common internal representation whose physical content was interrogated directly. Local-unitary transformations rejected a direct invariant-coordinate interpretation, while fixed-decoder transfer showed that the shared activation carries Pauli-correlation information in a transformation-consistent form. Task-related invariant spectral features were subsequently recovered through low-order nonlinear readouts. Separate predictive tests retained high accuracy for three-qubit classification and controlled ten-qubit purity regression with over one million complex inputs. These results establish an evidence-resolved framework for distinguishing physical grounding, readable computation, faithful symbolic compression and transformation-tested physical structure in constrained complex-valued scientific learning.

arXiv:2609.15139 [quant-ph]

(or arXiv:2609.15139v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.15139 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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