Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations

• URL: http://arxiv.org/abs/2408.08639v1
• Date: Fri, 16 Aug 2024 10:09:45 GMT
• Title: Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations
• Authors: Timothy Heightman, Edward Jiang, Antonio Acín,
• Abstract summary: We propose a novel method to solve the Hamiltonian Learning problem-inferring quantum dynamics from many-body state trajectories. Our method is reliably convergent, experimentally friendly, and interpretable, making it a stable solution for HL on a set of Hamiltonians previously unlearnable. 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.
• Score: 0.716879432974126
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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