Supervised Learning with Quantum Hamiltonian Embeddings
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.
Related
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BibTeX
@misc{molteni2026supervised,
title = {{Supervised Learning with Quantum Hamiltonian Embeddings}},
author = {Riccardo Molteni and Minjun Jeon and Paolo Braccia and Abhinav Deshpande and Vedran Dunjko and Liang Jiang and Su-un Lee and Swarnadeep Majumder and Javier Robledo Moreno and Parthasarathy Suryanarayanan and Kunal Sharma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26833},
eprint = {2610.26833},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26833},
}
RIS
TY - UNPB
TI - Supervised Learning with Quantum Hamiltonian Embeddings
AU - Riccardo Molteni
AU - Minjun Jeon
AU - Paolo Braccia
AU - Abhinav Deshpande
AU - Vedran Dunjko
AU - Liang Jiang
AU - Su-un Lee
AU - Swarnadeep Majumder
AU - Javier Robledo Moreno
AU - Parthasarathy Suryanarayanan
AU - Kunal Sharma
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.26833
UR - https://arxiv.org/abs/2610.26833
AB - 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.
ER -