  We investigate novel transport properties of chiral continuous-time quantum
walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate
that CTQWs on chiral chains are equivalent to those on non-chiral chains, but
with additional momenta from initial wave packets. This explains the novel
transport phenomenon numerically studied in [New J. Phys. 23, 083005(2021)].
Building on this, we delve deeper into the analysis of chiral CTQWs on the
Y-junction graph, introducing phases to account for the chirality. The phase
plays a key role in controlling both asymmetric transport and directed complete
transport among the chains in the Y-junction graph. We systematically analyze
these features through a comprehensive examination of the chiral
continuous-time quantum walk (CTQW) on a Y-junction graph. Our analysis shows
that the CTQW on Y-junction graph can be modeled as a combination of three wave
functions, each of which evolves independently on three effective open chains.
By constructing a lattice scattering theory, we calculate the phase shift of a
wave packet after it interacts with the potential-shifted boundary. Our results
demonstrate that the interplay of these phase shifts leads to the observed
enhancement and suppression of quantum transport. The explicit condition for
directed complete transport or 100% efficiency is analytically derived. Our
theory has applications in building quantum versions of binary tree search
algorithms.

Quantum Physics