Operator delocalization in quantum networks

We investigate the delocalization of operators in non-chaotic quantum systems whose interactions are encoded an underlying graph or network. In particular, we study how fast different sizes delocalize as network connectivity is varied. argue that these properties well captured by Krylov complexity and show, numerically, efficient large can only happen within sufficiently connected topologies. Finally, demonstrate this be used to furnish a deeper understanding charging advantage class SYK-like batteries.