Improved machine learning algorithm for predicting ground state properties
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914974716133376 |
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| author | Lewis, Laura Huang, Hsin-Yuan Tran, Viet T. Lehner, Sebastian Kueng, Richard Preskill, John |
| author_facet | Lewis, Laura Huang, Hsin-Yuan Tran, Viet T. Lehner, Sebastian Kueng, Richard Preskill, John |
| contents | Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log(n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n \log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13169 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved machine learning algorithm for predicting ground state properties Lewis, Laura Huang, Hsin-Yuan Tran, Viet T. Lehner, Sebastian Kueng, Richard Preskill, John Quantum Physics Machine Learning Computational Physics Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log(n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n \log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset. |
| title | Improved machine learning algorithm for predicting ground state properties |
| topic | Quantum Physics Machine Learning Computational Physics |
| url | https://arxiv.org/abs/2301.13169 |