# Percolation Transition Control in Quantum Networks

## TL;DR

This paper introduces a model for quantum networks that allows precise control over the percolation transition, enabling the design of networks with desired connectivity properties at any occupation probability, even in simple one-dimensional structures.

## Contribution

It proposes a novel model combining classical and quantum resources to achieve customizable percolation transitions in simple networks.

## Key findings

- Enables continuous or discontinuous percolation transitions on demand.
- Works in the simplest one-dimensional network structures.
- Provides a method to design networks with specific percolation properties.

## Abstract

Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the percolation transition for a chosen occupation probability has been an open problem. At the same time, the task to find a structurally simple network having the desired property seemed to be impossible. I suggest a model, where the combination of the classical and the quantum resources creates a percolation transition, continuous or discontinuous on demand, for any pre-selected occupation probability and already in the simplest possible one-dimensional network.