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| Auteurs principaux: | , , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2403.04980 |
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| _version_ | 1866916267243339776 |
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| author | Li, Jia-Kun Sun, Kai Hao, Ze-Yan Liang, Jia-He Tao, Si-Jing Pachos, Jiannis K. Xu, Jin-Shi Han, Yong-Jian Li, Chuan-Feng Guo, Guang-Can |
| author_facet | Li, Jia-Kun Sun, Kai Hao, Ze-Yan Liang, Jia-He Tao, Si-Jing Pachos, Jiannis K. Xu, Jin-Shi Han, Yong-Jian Li, Chuan-Feng Guo, Guang-Can |
| contents | Jones polynomials were introduced as a tool to distinguish between topologically different links. Recently, they emerged as the central building block of topological quantum computation: by braiding non-Abelian anyons it is possible to realise quantum algorithms through the computation of Jones polynomials. So far, it has been a formidable task to evaluate Jones polynomials through the control and manipulation of non-Abelian anyons. In this study, a photonic quantum system employing two-photon correlations and non-dissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes. The resulting amplitudes are shown to be mathematically equivalent to Jones polynomials at a particular value of their parameter. The high-fidelity of our optical platform allows us to distinguish between a wide range of links, such as Hopf links, Solomon links, Trefoil knots, Figure Eight knots and Borromean rings, through determining their corresponding Jones polynomials. Our photonic quantum simulator represents a significant step towards executing fault-tolerant quantum algorithms based on topological quantum encoding and manipulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Photonic simulation of Majorana-based Jones polynomials Li, Jia-Kun Sun, Kai Hao, Ze-Yan Liang, Jia-He Tao, Si-Jing Pachos, Jiannis K. Xu, Jin-Shi Han, Yong-Jian Li, Chuan-Feng Guo, Guang-Can Quantum Physics Jones polynomials were introduced as a tool to distinguish between topologically different links. Recently, they emerged as the central building block of topological quantum computation: by braiding non-Abelian anyons it is possible to realise quantum algorithms through the computation of Jones polynomials. So far, it has been a formidable task to evaluate Jones polynomials through the control and manipulation of non-Abelian anyons. In this study, a photonic quantum system employing two-photon correlations and non-dissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes. The resulting amplitudes are shown to be mathematically equivalent to Jones polynomials at a particular value of their parameter. The high-fidelity of our optical platform allows us to distinguish between a wide range of links, such as Hopf links, Solomon links, Trefoil knots, Figure Eight knots and Borromean rings, through determining their corresponding Jones polynomials. Our photonic quantum simulator represents a significant step towards executing fault-tolerant quantum algorithms based on topological quantum encoding and manipulation. |
| title | Photonic simulation of Majorana-based Jones polynomials |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.04980 |