Photonic simulation of Majorana-based Jones polynomials

• Main Authors: 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
• Format: Journal Article
• Language: English
• Published: 07.03.2024
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2403.04980

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.