String Theory Seminar

# Path integral optimization as circuit complexity

## by Michal P. Heller (Max Planck Institute for Gravitational Physics (Albert Einstein Institute) / National Centre for Nuclear Research)

Thursday, May 23, 2019 from to (Europe/Berlin)
at SR2
 Description Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations of the Euclidean path integral that prepares a given operator or state may provide an alternative definition, whose connection to the standard notion of complexity is less apparent. In this talk, I will bridge the gap between these two proposals in two-dimensional conformal field theories, by explicitly showing how the latter approach from path integral optimization may be given a concrete realization within the standard gate counting framework. In particular, I will show that when the background geometry is deformed by a Weyl rescaling, a judicious gate counting allows one to recover the Liouville action as a particular choice within a more general class of cost functions. Based on 1904.02713.