  We present a reconstruction theorem for Fano vector bundles on projective
space which recovers the small quantum cohomology for the projectivisation of
the bundle from a small number of low-degree Gromov--Witten invariants. We
provide an extended example in which we calculate the quantum cohomology of a
certain Fano 9-fold and deduce from this, using the quantum Lefschetz theorem,
the quantum period sequence for a Fano 3-fold of Picard rank 2 and degree 24.
This example is new, and is important for the Fanosearch programme.
