Abstract
Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here, we use the all-round framework of discrete-time quantum walks to study the onset of those events due to a random phase modulation, unveiling its long-tailed statistics, distribution profile, and dependence upon the degree of randomness. We find that those rogue waves belong the Gumbel family of extreme value distributions.