  In graphene superlattices, bulk topological currents can lead to long-range
charge-neutral flow and non-local resistance near Dirac points. A ballistic
version of these phenomena has never been explored. Here, we report transport
properties of ballistic graphene superlattices. This allows us to study and
exploit giant non-local resistances with a large valley Hall angle without a
magnetic field. In the low-temperature regime, a crossover occurs toward a new
state of matter, referred to as a quantum valley Hall state (qVHS), which is an
analog of the quantum Hall state without a magnetic field. Furthermore, a
non-local resistance plateau, implying rigidity of the qVHS, emerges as a
function of magnetic field, and the collapse of this plateau is observed, which
is considered as a manifestation of valley/pseudospin magnetism.
