Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity

TL;DR

This paper investigates how information spreads in discrete-time quantum walks using out-of-time-ordered correlators and Krylov complexity, revealing light-cone structures, effects of disorder, and linear versus sub-linear growth patterns.

Contribution

It introduces a formulation of Krylov complexity for discrete-time quantum walks and analyzes how disorder influences information scrambling and complexity growth.

Findings

OTOC exhibits shell-like light-cone structure

Disorder induces localization effects

K-complexity grows linearly, becomes sub-linear with disorder

Abstract

We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a probe of information scrambling. The OTOC for local spin operators in all directions has a light-cone structure which is ``shell-like''. As the wavefront passes, the OTOC approaches to zero in the long-time limit, showing no signature of scrambling. The introduction of spatial or temporal disorder changes the shape of the light-cone akin to localization of wavefunction. We formulate the K-complexity in system with discrete-time evolution, and show that it grows linearly in discrete-time quantum walk. The presence of disorder modifies this growth to sub-linear. Our study present interesting case to explore many-body phenomenon in a discrete-time quantum walk using scrambling.