On Hitting Times for General Quantum Markov Processes

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 Schöning’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 tool such as hitting times can be computed analytically with a formula similar to the one found in the classical theory, which we then apply to known quantum settings such as Grover’s algorithm.