  We present a new perspective on bulk reconstruction using Berry phases in the
boundary CFT. Our parallel transport of modular Hamiltonians is associated to a
trajectory in the space of states, which we obtain from the insertion of a
source in the Euclidean path integral. Using a modular version of the
extrapolate dictionary and the equivalence between modular flow in the boundary
and the bulk, we show that the expectation value of the modular Berry curvature
on the boundary agrees with an appropriately defined bulk symplectic form
associated to the entanglement wedge. In addition, we derive a quantum
information metric on the space of density matrices from the Berry curvature,
which is related to the canonical energy in the bulk. We also explore the case
where a state change reduces to a shape change, uncovering the coadjoint orbit
structure of kinematic space in higher dimensions.
