Operator Delocalization in Quantum Networks

TL;DR

This paper explores how operator delocalization in non-chaotic quantum networks depends on network connectivity, using Krylov complexity to analyze delocalization speed and implications for quantum battery performance.

Contribution

It introduces a network connectivity-dependent analysis of operator delocalization using Krylov complexity, linking network topology to quantum information spreading and battery efficiency.

Findings

Efficient operator delocalization requires sufficiently connected networks.

Krylov complexity effectively captures operator delocalization dynamics.

Network topology influences quantum charging advantages in SYK-like systems.

Abstract

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