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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.15544 |
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| _version_ | 1866908998202032128 |
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| author | Jorquera, Zackary Kolla, Alexandra Kordonowy, Steven Sandhu, Juspreet Singh Wayland, Stuart |
| author_facet | Jorquera, Zackary Kolla, Alexandra Kordonowy, Steven Sandhu, Juspreet Singh Wayland, Stuart |
| contents | We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares proofs. Algorithmically, we show that a simple matching-based algorithm approximates the maximum energy to at least $1/d$ for general graphs and to at least $1/d + Θ(1/D)$ for graphs with bounded degree, $D$. This outperforms random assignment, which, in expectation, achieves energy of only $1/d^2$ of the maximum energy for general graphs. Notably, on $D$-regular graphs with degree, $D \leq 5$, and for any local dimension, $d$, we show that this simple matching-based algorithm has an approximation guarantee of $1/2$. Lastly, when $d=2$, we present an algorithm achieving an approximation guarantee of $0.595$, beating that of [PT22, arXiv:2206.08342], which gave an approximation ratio of $1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians Jorquera, Zackary Kolla, Alexandra Kordonowy, Steven Sandhu, Juspreet Singh Wayland, Stuart Quantum Physics We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares proofs. Algorithmically, we show that a simple matching-based algorithm approximates the maximum energy to at least $1/d$ for general graphs and to at least $1/d + Θ(1/D)$ for graphs with bounded degree, $D$. This outperforms random assignment, which, in expectation, achieves energy of only $1/d^2$ of the maximum energy for general graphs. Notably, on $D$-regular graphs with degree, $D \leq 5$, and for any local dimension, $d$, we show that this simple matching-based algorithm has an approximation guarantee of $1/2$. Lastly, when $d=2$, we present an algorithm achieving an approximation guarantee of $0.595$, beating that of [PT22, arXiv:2206.08342], which gave an approximation ratio of $1/2$. |
| title | Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.15544 |