  In recent years, photon routing has garnered considerable research activity
due to its key applications in quantum networking and optical communications.
This paper studies the single photon routing scheme in many-emitter disordered
chiral waveguide quantum electrodynamics (wQED) ladders. The wQED ladder
consists of two one-dimensional lossless waveguides simultaneously and chirally
coupled with a chain of dipole-dipole interacting two-level quantum emitters
(QEs) or atoms. In particular, we analyze how a departure from the periodic
placement of the QEs due to temperature-induced position disorder can impact
the routing probability. This involves analyzing how the interplay between the
collective atomic effects originating from the dipole-dipole interaction and
disorder in the atomic location leading to single-photon localization can
change the routing probabilities. As for some key results, we find that the
routing probability exhibits a considerable improvement (more than $90\%$
value) for periodic and disordered wQED ladders when considering lattices
consisting of twenty QEs. This robustness of collective effects against
spontaneous emission loss and weak disorders is further confirmed by examining
the routing efficiency and localization length for up to twenty QE chains.
These results may find applications in quantum networking and distributed
quantum computing under the realistic conditions of imperfect emitter
trappings.
