The challenge is to create an efficient quantum algorithm for the bosonic model capable of calculating the Jones polynomials for a knot resulting from interweaving or interlacing n-vertices. This weave is the construction of braid group representations from nineteen-vertex model. We present eigenbases and eigenvalues for lattice generators and their usefulness for the direct computation of Jones polynomials. The calculation shows that the Temperley-Lieb operators can be used for any braid word. Therefore, we propose a quantum sequence using these singular operators as quantum gates operating on the state of n qubits. We show that quantum calculations give the Jones polynomial for achiral knots and links.

中文翻译：

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19顶点模型与琼斯多项式关系的量子解

挑战在于为玻色子模型创建一种有效的量子算法，能够计算由交织或交错产生的结的琼斯多项式n-顶点。这种编织是十九顶点模型的辫子组表示的构造。我们提出了格子生成器的特征基和特征值及其对于直接计算琼斯多项式的有用性。计算表明，Temperley-Lieb 算子可用于任何辫子词。因此，我们提出了一个量子序列，使用这些奇异算子作为在以下状态下运行的量子门：n量子位。我们证明量子计算给出了非手性结和链接的琼斯多项式。