Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example is Sch\"oning's algorithm for the satisfiability (SAT) problem. In this work, we use the density-matrix formalism to define a quantum Markov chain model which directly generalizes classical walks, and we show that a common tools such as hitting times can be computed with a similar formula as the one found in the classical theory, which we then apply to known quantum settings such as Grover's algorithm.

翻译：随机行走( 或 Markov 链条 ) 是在理论计算机科学中广泛使用的模型。 一些工具, 包括诸如打击和混合时间等数量分析, 有助于设计随机化算法。 一个显著的例子就是Sch\“ oning ” 的可坐性( SAT) 问题算法 。 在这项工作中, 我们使用密度矩阵形式主义来定义一个量子 Markov 链条模型, 该模型直接概括了古典行走法, 我们显示, 类似古典理论的公式可以计算出像撞击时间这样的常见工具, 我们然后将其应用到已知量子设置, 比如 Grover 算法 。