  Quantum transport across discrete structures is a relevant topic of solid
state physics and quantum information science, which can be suitably studied in
the context of continuous-time quantum walks. The addition of phases degrees of
freedom, leading to chiral quantum walks, can also account for directional
transport on graphs with loops. We discuss criteria for quantum transport and
study the enhancement that can be achieved with chiral quantum walks on
chain-like graphs, exploring different topologies for the chain units and
optimizing over the phases. We select three candidate structures with optimal
performance and investigate their transport behaviour with Krylov reduction.
While one of them can be reduced to a weighted line with minor couplings
modulation, the other two are truly chiral quantum walks, with enhanced
transport probability over long chain structures.
