  We propose an analogue of Dubrovin's conjecture for the case where Fano
manifolds have quantum connections of exponential type. It includes the case
where the quantum cohomology rings are not necessarily semisimple. The
conjecture is described as an isomorphism of two linear algebraic structures,
which we call "mutation systems". Given such a Fano manifold $X$, one of the
structures is given by the Stokes structure of the quantum connection of $X$,
and the other is given by a semiorthogonal decomposition of the derived
category of coherent sheaves on $X$. We also prove the conjecture for a class
of smooth Fano complete intersections in a projective space.
