  In this paper we obtain a system of flat coordinates on the monodromy
manifold of each of the Painlev\'e equations. This allows us to quantise such
manifolds. We produce a quantum confluence procedure between cubics in such a
way that quantisation and confluence commute. We also investigate the
underlying cluster algebra structure and the relation to the versal
deformations of singularities of type $D_4,A_3,A_2$, and $A_1$.
