Random Circuits in the Black Hole Interior

 In this talk, I will consider perturbing an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. I will use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, I will show that there is a precise relationship between the amount of microscopic randomness defining the ensemble of states and the average geometric length of the wormhole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. I will comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.