# Complex Networks from Classical to Quantum

## TL;DR

This paper reviews the intersection of complex network theory and quantum information, highlighting recent advances, novel quantum effects in networks, and quantum algorithm applications for network problems.

## Contribution

It provides a comprehensive overview of how complex network methods are applied to quantum information problems and discusses new quantum-induced effects and algorithms.

## Key findings

- Quantum effects predicted in entangled random graphs
- Quantum algorithms proposed for network problem enhancement
- Insights into similarities and differences between classical and quantum networks

## Abstract

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.