# Out-of-time-ordered correlators and quantum walks

## TL;DR

This paper investigates out-of-time-ordered correlators (OTOC) in quantum walks, revealing algebraic growth patterns and indicating the absence of quantum chaos in these models.

## Contribution

It introduces the analysis of OTOC behavior in quantum walks, showing simple algebraic growth and clarifying the lack of chaos in these systems.

## Key findings

- OTOC behavior is well described by algebraic functions
- Quadratic growth indicates no quantum chaos
- Different operator localizations affect OTOC growth time scales

## Abstract

Out-of time-ordered correlators (OTOC) have recently attracted significant attention from the physics of many-body systems, to quantum black-holes, with an exponential growth of the OTOC indicating quantum chaos. Here we consider OTOC in the context of coined discrete quantum walks, a very well studied model of quantization of classical random walks with applications to quantum algorithms. Three separate cases of operators, variously localized in the coin and walker spaces, are discussed in this context and it is found that the approximated behavior of the OTOCs is well described by simple algebraic functions in all these three cases with different time scale of growth. The quadratic increase of OTOC signals the absence of quantum chaos in these simplest forms of quantum walks.