  Coherent manipulation of binary degrees of freedom is at the heart of modern
quantum technologies. Graphene offers two binary degrees: the electron spin and
the valley. Efficient spin control has been demonstrated in many solid state
systems, while exploitation of the valley has only recently been started, yet
without control on the single electron level. Here, we show that van-der Waals
stacking of graphene onto hexagonal boron nitride offers a natural platform for
valley control. We use a graphene quantum dot induced by the tip of a scanning
tunneling microscope and demonstrate valley splitting that is tunable from -5
to +10 meV (including valley inversion) by sub-10-nm displacements of the
quantum dot position. This boosts the range of controlled valley splitting by
about one order of magnitude. The tunable inversion of spin and valley states
should enable coherent superposition of these degrees of freedom as a first
step towards graphene-based qubits.
