By braiding non-Abelian anyons it is possible to realize fault-tolerant quantum algorithms through the computation of Jones polynomials. So far, this has been an experimentally formidable task. In this Letter, a photonic quantum system employing two-photon correlations and nondissipative 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. 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. Published by the American Physical Society 2024

中文翻译：

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基于 Majorana 的 Jones 多项式的光子仿真


通过编织非 Abelian anyon，可以通过计算 Jones 多项式来实现容错量子算法。到目前为止，这是一项实验性的艰巨任务。在这封信中，利用采用双光子相关和非耗散虚时间演化的光子量子系统来模拟马约拉零模式的两个不等价编织操作。结果振幅在数学上等同于 Jones 多项式。我们的光学平台的高保真度使我们能够通过确定相应的琼斯多项式来区分各种链接，例如 Hopf 链接、Solomon 链接、Trefoil 结、Figure Eight 结和 Borromean 环。我们的光子量子模拟器代表了朝着执行基于拓扑量子编码和操作的容错量子算法迈出的重要一步。 美国物理学会 2024 年出版