  We consider a symmetric 0-pi Josephson junction of length $L$, which
classically can be in one of two degenerate ground states up or down,
corresponding to supercurrents circulating clockwise or counterclockwise around
the 0-pi boundary. When the length $L$ of the junction becomes smaller than the
Josephson penetration depth $\lambda_J$, the system can switch from one state
to the other due to thermal fluctuations or quantum tunneling. We map this
problem to the dynamics of a single particle in a periodic double well
potential and estimate parameters for which macroscopic quantum coherence may
be observed. We conclude that this system is not very promising to build a
qubit because (a) it requires very low temperatures to reach the quantum
regime, (b) its tiny flux is hard to read out and (c) it is very sensitive to
the asymmetries between the 0 and pi parts of the junction.
