  We propose a gravity dual description of the path-integral optimization in
conformal field theories arXiv:1703.00456, using Hartle-Hawking wave functions
in anti-de Sitter spacetimes. We show that the maximization of the
Hartle-Hawking wave function is equivalent to the path-integral optimization
procedure. Namely, the variation of the wave function leads to a constraint,
equivalent to the Neumann boundary condition on a bulk slice, whose classical
solutions reproduce metrics from the path-integral optimization in conformal
field theories. After taking the boundary limit of the semi-classical
Hartle-Hawking wave function, we reproduce the path-integral complexity action
in two dimensions as well as its higher and lower dimensional generalizations.
We also discuss an emergence of holographic time from conformal field theory
path-integrals.
