  The ability to accurately transfer quantum information through networks is an
important primitive in distributed quantum systems. While perfect quantum state
transfer (PST) can be effected by a single particle undergoing continuous-time
quantum walks on a variety of graphs, it is not known if PST persists for many
particles in the presence of interactions. We show that if single-particle PST
occurs on one-dimensional weighted path graphs, then systems of hard-core
bosons undergoing quantum walks on these paths also undergo PST. The analysis
extends the Tonks-Girardeau ansatz to weighted graphs using techniques in
algebraic graph theory. The results suggest that hard-core bosons do not
generically undergo PST, even on graphs which exhibit single-particle PST.
