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.
Authors 11
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Leiden University · IBM (United States)
Affiliation as printed
Applied Quantum Algorithms ⟨aQa L ⟩ , Leiden University , The Netherlands
IBM Research
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IBM (United States) · University of Oxford
Affiliation as printed
Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , United Kingdom
IBM Research
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Affiliation as printed
IBM Research
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Affiliation as printed
IBM Research
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Affiliation as printed
Applied Quantum Algorithms ⟨aQa L ⟩ , Leiden University , The Netherlands
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IBM (United States) · University of Chicago
Affiliation as printed
IBM Research
The University of Chicago
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IBM (United States) · University of Chicago
Affiliation as printed
IBM Research
The University of Chicago
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Affiliation as printed
IBM Research
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Affiliation as printed
IBM Research
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Affiliation as printed
IBM Research
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Affiliation as printed
IBM Research