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：随机游走（或称马尔可夫链）是理论计算机科学中广泛使用的模型。包括分析命中时间和混合时间在内的多种工具，有助于设计随机化算法。一个著名的例子是Schöning算法用于可满足性（SAT）问题。本文利用密度矩阵形式化定义了一种直接推广经典游走的量子马尔可夫链模型，并证明命中时间等通用工具可通过与经典理论中类似的公式进行计算。我们将此方法应用于已知量子场景，例如Grover算法。