Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations
<|reference_start|>Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations: Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian Learning (HL) problem-inferring quantum dynamics from many-body state trajectories-using Neural Differential Equations combined with an Ansatz Hamiltonian. Our method is reliably convergent, experimentally friendly, and interpretable, making it a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin-1/2 chain proof of concept.<|reference_end|>
@article{heightman2024solving,
    title={Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural
  Differential Equations},
    author={Timothy Heightman, Edward Jiang, Antonio Ac'in},
    journal={arXiv preprint arXiv:2408.08639},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08639},
    primaryClass={quant-ph cond-mat.str-el cs.LG}
}