Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911991303503872 |
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| author | Heightman, Timothy Jiang, Edward Acín, Antonio |
| author_facet | Heightman, Timothy Jiang, Edward Acín, Antonio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_08639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations Heightman, Timothy Jiang, Edward Acín, Antonio Quantum Physics Strongly Correlated Electrons Machine Learning 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. |
| title | Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations |
| topic | Quantum Physics Strongly Correlated Electrons Machine Learning |
| url | https://arxiv.org/abs/2408.08639 |