# Simulating complex quantum networks with time crystals

## TL;DR

This paper introduces a graph-theoretic approach to analyze and simulate complex quantum networks using time crystals, revealing emergent phenomena like scale-free networks during phase transitions.

## Contribution

It presents a novel method to characterize time crystals through graph analysis, enabling simulation of complex quantum networks with new insights into their melting processes.

## Key findings

- Graph analysis visualizes time-crystalline order.
- Melting process shows emergent scale-free network behavior.
- Time crystals can simulate complex quantum networks.

## Abstract

Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and explore the physical phenomena related to this phase of matter using tools from graph theory. The analysis of the graphs allows to visualizing time-crystalline order and to analyze features of the quantum system. For example, we explore in detail the melting process of a minimal model of a period-2 discrete time crystal and describe it in terms of the evolution of the associated graph structure. We show that during the melting process, the network evolution exhibits an emergent preferential attachment mechanism, directly associated with the existence of scale-free networks. Thus, our strategy allows us to propose a previously unexplored far-reaching application of time crystals as a quantum simulator of complex quantum networks.