  In this note we show how the Quantum Information Metric can be computed
holographically using a perturbative approach. In particular when the
deformation of the conformal field theory state is induced by a scalar operator
the corresponding bulk configuration reduces to a scalar field perturbatively
probing the unperturbed background. We study two concrete examples: a CFT
ground state deformed by a primary operator and thermofield double state in
$d=2$ deformed by a marginal operator. Finally, we generalize the bulk
construction to the case of a multi dimensional parameter space and show that
the Quantum Information Metric coincides with the metric of the non-linear
sigma model for the corresponding scalar fields.
