Ultimate speed limits to the growth of operator complexity

Abstract In an isolated system, the time evolution of a given observable in Heisenberg picture can be efficiently represented Krylov space. this representation, initial operator becomes increasingly complex as goes by, feature that quantified by complexity. We introduce fundamental and universal limit to growth complexity formulating Robertson uncertainty relation, involving Liouvillian, generator evolution. further show conditions for bound saturated illustrate its validity paradigmatic models quantum chaos.