Learning quantum states prepared by shallow circuits in polynomial time
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916796091596800 |
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| author | Landau, Zeph Liu, Yunchao |
| author_facet | Landau, Zeph Liu, Yunchao |
| contents | We give a polynomial time algorithm that, given copies of an unknown quantum state $\vertψ\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth quantum circuit that prepares $\vertψ\rangle$. The algorithm extends to the case when the depth of $U$ is $\mathrm{polylog}(n)$, with a quasi-polynomial run-time. The key new idea is a simple and general procedure that efficiently reconstructs the global state $\vertψ\rangle$ from its local reduced density matrices. As an application, we give an efficient algorithm to test whether an unknown quantum state on a lattice has low or high quantum circuit complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning quantum states prepared by shallow circuits in polynomial time Landau, Zeph Liu, Yunchao Quantum Physics Computational Complexity Machine Learning We give a polynomial time algorithm that, given copies of an unknown quantum state $\vertψ\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth quantum circuit that prepares $\vertψ\rangle$. The algorithm extends to the case when the depth of $U$ is $\mathrm{polylog}(n)$, with a quasi-polynomial run-time. The key new idea is a simple and general procedure that efficiently reconstructs the global state $\vertψ\rangle$ from its local reduced density matrices. As an application, we give an efficient algorithm to test whether an unknown quantum state on a lattice has low or high quantum circuit complexity. |
| title | Learning quantum states prepared by shallow circuits in polynomial time |
| topic | Quantum Physics Computational Complexity Machine Learning |
| url | https://arxiv.org/abs/2410.23618 |