Improved algorithms for learning quantum Hamiltonians, via flat polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914859621285888 |
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| author | Narayanan, Shyam |
| author_facet | Narayanan, Shyam |
| contents | We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved algorithms for learning quantum Hamiltonians, via flat polynomials Narayanan, Shyam Quantum Physics Data Structures and Algorithms Machine Learning We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24]. |
| title | Improved algorithms for learning quantum Hamiltonians, via flat polynomials |
| topic | Quantum Physics Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2407.04540 |