  We propose a tunable macroscopic quantum system based on two fractional
vortices. Our analysis shows that two coupled fractional vortices pinned at two
artificially created \kappa\ discontinuities of the Josephson phase in a long
Josephson junction can reach the quantum regime where coherent quantum
oscillations arise. For this purpose we map the dynamics of this system to that
of a single particle in a double-well potential. By tuning the \kappa\
discontinuities with injector currents we are able to control the parameters of
the effective double-well potential as well as to prepare a desired state of
the fractional vortex molecule. The values of the parameters derived from this
model suggest that an experimental realisation of this tunable macroscopic
quantum system is possible with today's technology.
