A Relation between Krylov and Nielsen Complexity.

Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by quantum chaos and quantum computation, respectively, while the relevant mathematics is as different as matrix diagonalization algorithms and geodesic flows on curved manifolds. We demonstrate that, despite these differences, there is a relation between the two quantities.