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Krylov Complexity
Eliezer Rabinovici, Adri\'an S\'anchez-Garrido, Ruth Shir, Julian Sonner
https://arxiv.org/abs/2507.06286 https://

Krylov Complexity
We introduce and review a new complexity measure, called `Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics, serving as a canonical measure of operator growth and spreading. Krylov complexity, underpinned by the Lanczos algorithm, has since evolved into a highly diverse field of its own right, both because of its attractive features as a complexity, whose definition does not depend on arbitrary control parameters, and whose phenomenology serves as a rich and s…