Learning conservation laws in unknown quantum dynamics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912000310771712 |
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| author | Zhan, Yongtao Elben, Andreas Huang, Hsin-Yuan Tong, Yu |
| author_facet | Zhan, Yongtao Elben, Andreas Huang, Hsin-Yuan Tong, Yu |
| contents | We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a $\mathbb{Z}_2$-gauge theory and in many-body localized spin-chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00774 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning conservation laws in unknown quantum dynamics Zhan, Yongtao Elben, Andreas Huang, Hsin-Yuan Tong, Yu Quantum Physics We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a $\mathbb{Z}_2$-gauge theory and in many-body localized spin-chains. |
| title | Learning conservation laws in unknown quantum dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.00774 |