We analyze a special class of 1-D quantum walks (QWs) realized using optical
multi-ports. We assume non-perfect multi-ports showing errors in the
connectivity, i.e. with a small probability the multi- ports can connect not to
their nearest neighbor but to another multi-port at a fixed distance - we call
this a jump. We study two cases of QW with jumps where multiple displacements
can emerge at one timestep. The first case assumes time-correlated jumps
(static disorder). In the second case, we choose the positions of jumps
randomly in time (dynamic disorder). The probability distributions of position
of the QW walker in both instances differ significantly: dynamic disorder leads
to a Gaussian-like distribution, while for static disorder we find two distinct
behaviors depending on the parity of jump size. In the case of even-sized
jumps, the distribution exhibits a three-peak profile around the position of
the initial excitation, whereas the probability distribution in the odd case
follows a Laplace-like discrete distribution modulated by additional
(exponential) peaks for long times. Finally, our numerical results indicate
that by an appropriate mapping an universal functional behavior of the variance
of the long-time probability distribution can be revealed with respect to the
scaled average of jump size.Comment: 11 pages, 13 figure