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arXiv · 2403.04980

Photonic simulation of Majorana-based Jones polynomials

Jia-Kun Li·Kai Sun·Ze-Yan Hao·Jia-He Liang·Si-Jing Tao·Jiannis K. Pachos·Jin-Shi Xu·Yong-Jian Han·Chuan-Feng Li·Guang-Can Guo
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Abstract

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.

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Jia-Kun Li, Kai Sun, Ze-Yan Hao, Jia-He Liang, Si-Jing Tao, Jiannis K. Pachos, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo. 2024-05-31. Photonic simulation of Majorana-based Jones polynomials. https://arxiv.org/abs/2403.04980

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