论文标题
绘制量子随机步行到马尔可夫链上,通过将统一转换映射到不可还原矩阵的更高维度
Mapping quantum random walks onto a Markov chain by mapping a unitary transformation to a higher dimension of an irreducible matrix
论文作者
论文摘要
在这里,引入了一个新的二维过程,即时间和空间的离散,从而引入了随机步行和量子随机步行的结果。该模型描述了四个硬币状态| 1>, - | 1>,| 0> - | 0>在没有干扰的空间中的种群分布,而不是两个硬币状态| 1>,| 0>。对于没有边界条件的情况,模型类似于具有随机矩阵的马尔可夫链,即通过量子的分布量| 1个量子的分布,并在两次>量子的种群分布中,|在probers的分布中,|在| probertion | prom的分布中,| tresition | tress的分布| | | | | | 0>。空间,类似于统一操作员。引入了无限线和有限线的量子随机步行的数值结果。
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0> in space without interference, instead of two coin states |1>, |0> .For the case of no boundary conditions, the model is similar to a Markov chain with a stochastic matrix, i.e., it conserves the population distribution of the four coin states, and by using a proper transformation, yield probability distributions of the two quantum states |1>, |0> in space, similar to a unitary operator. Numerical results for a quantum random walk on infinite and finite lines are introduced.