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This research demonstrates a specific class of quantum machine learning tasks where state space fragmentation allows for efficient classification on quantum hardware while resisting classical dequantization. The work establishes a rare benchmark for physically motivated QML problems that maintain a genuine computational advantage over classical methods under defined conditions.
Fragmentation is Efficiently Learnable by Quantum Neural Networks
arXiv:2512.00751v4 Announce Type: replace-cross Abstract: In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.
Abstract:In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.
Quantum Physics (quant-ph); Machine Learning (cs.LG)
arXiv:2512.00751 [quant-ph]
(or arXiv:2512.00751v4 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.00751 Focus to learn more arXiv-issued DOI via DataCite
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