论文标题
将有限和无限的Hadamard量子步行映射到一个随机步行过程的独特情况下
Mapping a finite and an infinite Hadamard quantum walk onto a unique case of a random walk process
论文作者
论文摘要
提出了一种新的模型，该模型将Hadamard Operator描述的量子随机步行映射到随机行走的特定情况下。该模型由带有随机基质的马尔可夫链表示，即所有过渡速率均为正，尽管Hadamard操作员包含负条目。使用适当的转换，该转换在n步骤之后应用于随机步行分布，揭示了两个量子状态| 1>，| 0>的概率分布。这些表明，量子步行可以完全映射到随机步行模型的较高维度的特定情况下。随机步行模型及其与Hadamard Walk的等效性可以扩展到其他情况下，例如有两个反射点的有限链
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are positive, although the Hadamard operator contains negative entries. Using a proper transformation that is applied to the random walk distribution after n steps, the probability distributions in space of the two quantum states |1>, |0> are revealed. These show that a quantum walk can be entirely mapped to a particular case of a higher dimension of a random walk model. The random walk model and its equivalence to a Hadamard walk can be extended for other cases, such as a finite chain with two reflecting points
