A bstract Continuing the previous initiatives [1, 2], we pursue the exploration of operator
growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort …

We present a framework for investigating wave function spreading in PT-symmetric quantum
systems using spread complexity and spread entropy. We consider a tight-binding chain …

Building upon recent research in spin systems with nonlocal interactions, this study
investigates operator growth using the Krylov complexity in different nonlocal versions of the …

A bstract Using spread complexity and spread entropy, we study non-unitary quantum
dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the …

A bstract Krylov complexity characterizes the operator growth in the quantum many-body
systems or quantum field theories. The existing literatures have studied the Krylov …

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of
certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate …

The operator growth hypothesis (OGH) is a technical conjecture about the behavior of
operators—specifically, the asymptotic growth of their Lanczos coefficients—under repeated …

A bstract Recently, the concept of spread complexity, Krylov complexity for states, has been
introduced as a measure of the complexity and chaoticity of quantum systems. In this paper …

We ask whether Krylov complexity is mutually compatible with the circuit and Nielsen
definitions of complexity. We show that the Krylov complexities between three states fail to …

The dynamics of quantum systems unfolds within a subspace of the state space or operator
space, known as the Krylov space. This review presents the use of Krylov subspace …