  As consequences of disruptions in railway traffic affect passenger
experience/satisfaction, appropriate rerouting and/or rescheduling is
necessary. These problems are known to be NP-hard, given the numerous
restrictions of traffic nature. With the recent advances in quantum
technologies, quantum annealing has become an alternative method to solve such
optimization problems. To use quantum annealing, the problem needs to be
encoded in QUBO (quadratic unconstrained binary optimization) or HOBO
(higher-order binary optimization) formulation that can be recast as a QUBO.
This paper introduces QUBO and HOBO representations for rescheduling problems
of railway traffic management; the latter is a new approach up to our
knowledge. This new approach takes into account not only the single-track lines
but also the double- and multi-track lines, as well as stations composed of
tracks and switches. We consider the conditions of minimal headway between
trains, minimal stay on stations, track occupation, and rolling stock
circulation. Furthermore, a hybrid quantum-classical procedure is presented
that includes rerouting. We demonstrate the proof of concept implementation on
the D-Wave Quantum Processing Unit and D-Wave hybrid solver.
