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Supervised Learning with Quantum Hamiltonian Embeddings

Riccardo Molteni, Minjun Jeon, Paolo Braccia, Abhinav Deshpande, Vedran Dunjko, Liang Jiang, Su-un Lee, Swarnadeep Majumder, Javier Robledo Moreno, Parthasarathy Suryanarayanan, Kunal Sharma · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26833 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El aprendizaje de máquinas se considera ampliamente como una aplicación prometedora en la que la computación cuántica puede ofrecer una ventaja computacional. Sin embargo, los modelos generales de aprendizaje de máquinas cuánticas con garantías probables sobre el rendimiento, la capacitación y la inferencia eficiente permanecen limitados. En este trabajo, introducimos las incorporaciones cuánticas de Hamilton, un marco de aprendizaje supervisado en el que un conjunto de datos de capacitación clásico se codifica en un estado cuántico eficaz, parametrizado. El entrenamiento optimiza los parámetros de este Hamilton dependiente de datos, cuyo estado de tierra aproximado define la regla de clasificación. Una vez que el estado de tierra se ha aproximado utilizando un algoritmo cuántico, la inferencia puede ser realizada clásicamente usando una representación clásica del estado aprendido, o con una

Machine translation (Meta M2M100); the English original follows.

Abstract

Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.

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Topics: Hamiltonian (control theory), Quantum, Parameterized complexity, Quantum algorithm, Computer science, Quantum computer

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