  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.
