Scale-free network reveals relations between quantum computing and Barrow entropy

Abstract

The scale-free network in the black hole horizon gives rise to Barrow entropy behavior, which can be visualized geometrically through the Farey diagram. We perform a detailed analysis to demonstrate the quantified values of Barrow entropy. We calculate the black hole entropy by using the Mertens function with the Farey sequence. We use the black hole network to create a register of quantum computers by applying controlled-NOT gates and use quantum entanglement for data transmission and retrieval. We propose a scenario of Hawking radiation according to the Farey background.