Out-of-time-ordered correlators and quantum walks

Area of Science:

• Quantum physics
• Quantum information theory
• Condensed matter physics

Background:

• Out-of-time-ordered correlators (OTOCs) are crucial for detecting quantum chaos.
• Quantum walks are a quantum analogue of classical random walks with applications in quantum algorithms.

Purpose of the Study:

• Investigate OTOCs in coined discrete quantum walks.
• Analyze the behavior of OTOCs in different operator localizations.
• Determine the presence or absence of quantum chaos in these systems.

Main Methods:

• Studied OTOCs within the framework of coined discrete quantum walks.
• Examined three distinct cases of operators localized in coin and walker spaces.
• Analyzed the growth behavior of OTOCs using mathematical approximations.

Main Results:

• OTOCs in quantum walks are approximated by simple algebraic functions.
• Different timescales of growth were observed for different operator localizations.
• A quadratic increase in OTOCs was identified, differing from the exponential growth indicative of chaos.

Conclusions:

• The studied quantum walks do not exhibit quantum chaos.
• The observed quadratic growth of OTOCs suggests a simpler dynamical behavior.
• OTOCs provide a valuable tool for characterizing quantum dynamics in various systems.