Quantum Hamiltonian Embedding

The paper proposes the Quantum Hamiltonian Embeddings framework, which encodes a classical training dataset into a parameterized effective Hamiltonian and defines classification rules via the approximate ground state obtained by optimizing the parameters.

The paper establishes an efficient gradient estimation method and proves favorable generalization guarantees.

The authors prove, under standard cryptographic assumptions, that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms.

The inference stage of Hamiltonian embeddings has two options: classical inference using the classical representation of the learned state, or quantum inference using the quantum representation directly.

Hamiltonian embeddings circumvent some inherent training difficulties in parameterized quantum circuit design while providing a fallback to classical inference.

The practical advantages of this framework still need to be validated on more datasets and hardware platforms.

The paper positions this framework as a new direction for quantum machine learning, combining theoretical guarantees with the feasibility of scaled experimental research on quantum hardware.

Mapping a machine learning dataset to a Hamiltonian means that a classification problem can be transformed into a problem of finding the ground state.