论文标题
部分可观测时空混沌系统的无模型预测
Discrete Quantum Walks on the Symmetric Group
论文作者
论文摘要
在有限图上随机步行的理论通过众多应用开发得很好。在量子步行中，传播受量子机械规则的约束；将随机步行概括为量子设置。它们已成功地应用于量子算法的开发中。特别是解决可以映射到某些特定图表上搜索或属性测试的问题。在本文中，我们使用非共同傅立叶分析中的工具研究了离散时间创造的量子步行（DTCQW）模型。 Specifically, we are interested in characterizing the DTCQW on Cayley graphs generated by the symmetric group ($\sym$) with appropriate generating sets. The lack of commutativity makes it challenging to find an analytical description of the limiting behavior with respect to the spectrum of the walk-operator.我们使用$ \ sym $的字符的路径积分方法来确定这些步行的某些特征。
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been successfully applied in the development of quantum algorithms. In particular, to solve problems that can be mapped to searching or property testing on some specific graph. In this paper we investigate the discrete time coined quantum walk (DTCQW) model using tools from non-commutative Fourier analysis. Specifically, we are interested in characterizing the DTCQW on Cayley graphs generated by the symmetric group ($\sym$) with appropriate generating sets. The lack of commutativity makes it challenging to find an analytical description of the limiting behavior with respect to the spectrum of the walk-operator. We determine certain characteristics of these walks using a path integral approach over the characters of $\sym$.
