Frobenius light cone and the shift unitary
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917782499622912 |
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| author | Yin, Chao Lucas, Andrew Stephen, David T. |
| author_facet | Yin, Chao Lucas, Andrew Stephen, David T. |
| contents | We bound the time necessary to implement the shift unitary on a one-dimensional ring, both using local Hamiltonians and those with power-law interactions. This time is constrained by the Frobenius light cone; hence we prove that (for certain power law exponents) shift unitaries cannot be implemented in the same amount of time needed to prepare long-range Bell pairs. We note an intriguing similarity between the proof of our results, and the hardness of preparing symmetry-protected topological states with symmetry-preserving Hamiltonians. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frobenius light cone and the shift unitary Yin, Chao Lucas, Andrew Stephen, David T. Quantum Physics Strongly Correlated Electrons Mathematical Physics We bound the time necessary to implement the shift unitary on a one-dimensional ring, both using local Hamiltonians and those with power-law interactions. This time is constrained by the Frobenius light cone; hence we prove that (for certain power law exponents) shift unitaries cannot be implemented in the same amount of time needed to prepare long-range Bell pairs. We note an intriguing similarity between the proof of our results, and the hardness of preparing symmetry-protected topological states with symmetry-preserving Hamiltonians. |
| title | Frobenius light cone and the shift unitary |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2402.07990 |