Quantum circuits can be constructed from Virasoro symmetry transformations in a two-dimensional CFT. Employing the holographic dictionary we realize such circuits in AdS3 as a non-trivial time evolution of the bulk spacetime. This allows us to find holographic duals to CFT cost functionals such as the Fubini-Study metric.
The same transformations we use to construct the circuits also give rise to Berry phases. These Virasoro Berry phases play a pivotal role in realizing the holographic features of bulk wormholes. The holonomy induced by the wormholes can be interpreted in terms of a coupling between Virasoro orbits which become manifest through a Virasoro Berry phase of the coupled orbits. For an eternal black hole in AdS, the coupling parameter, giving rise to a non-trivial Berry phase, is related to the expectation value of the energy-momentum tensor of the holographic CFT.