Dubrovin type conjecture holds. More precisely, we have the following.

Let $X$ be a smooth Fano complete intersection in a projective space. If Fano index of $X$ is larger than $1$, then $X$ satisfies Dubrovin type conjecture.

Plan of the paper
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In §2, we introduce the notion of mutation systems, and define the mutation on mutation systems. We also relate it with Stokes filtered local systems, and recall some general facts on the Riemann-Hilbert correspondence for meromorphic connections on a germ of complex plane at the origin. In §3, we give a definition of A-mutation systems. In §4, we give a definition of B-mutation systems. In §5, we formulate an analogue of Dubrovin’s conjecture, which we call \`\` Dubrovin type conjecture”. In §6, we show some properties, which are used to prove the main theorem, of quantum connections of Fano manifolds. In §7, we show the main theorem. That is, we give a class of examples which satisfies Dubrovin type conjecture.

Acknowledgments
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Both of the authors would like to thank Hiroshi Iritani for discussions and encouragement in many occasions, Masahiro Futaki and Yuuki Shiraishi for informal seminar. The first author would like to thank Tatsuki Kuwagaki and Kohei 