The paper introduces quantum Hamiltonian embeddings, a supervised learning framework that encodes a classical training dataset into a single parameterized Hamiltonian. Training optimizes the Hamiltonian’s parameters, and its approximate ground state defines the classification rule, enabling inference either classically or quantumly. The authors provide efficient gradient estimation, prove generalization guarantees, and show that, under cryptographic assumptions, the method can realize hypothesis functions beyond efficient classical reach, demonstrating scalability on IBM Heron processors.
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