TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.007
TI  - Random circuits in the black hole interior
PY  - 2025/07/03
UR  - https://www.scipost.org/SciPostPhys.19.1.007
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 007
A1  - Magan, Javier
AU  - Sasieta, Martin
AU  - Swingle, Brian
AB  - We present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We 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, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_{\Delta}$ and matter correlation scale $\ell_{\Delta}$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.
ER  -

@Article{10.21468/SciPostPhys.19.1.007,
	title={{Random circuits in the black hole interior}},
	author={Javier M. Magan and Martin Sasieta and Brian Swingle},
	journal={SciPost Phys.},
	volume={19},
	pages={007},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.007},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.007},
}