  We propose a controllable qubit in a graphene nanobubble with emergent
two-level systems induced by pseudo-magnetic fields. We found that double
quantum dots can be created by the strain-induced pseudo-magnetic fields of a
nanobubble, and that their quantum states can be manipulated by either local
gate potentials or the pseudo-magnetic fields. Graphene qubits clearly exhibit
an avoided crossing behavior via electrical detuning, with energy splittings of
about a few meV. We also show a remarkable tunability of our device design that
allows for the fine control of the Landau--Zener transition probability through
strain engineering of the nanobubble, showing half-and-half splitting at the
avoided crossing point. Further, we demonstrate that the two-level systems in
the nanobubble exhibit Rabi oscillations near the avoided crossing point,
resulting in very fast Rabi cycles of a few ps.
