Complex networks from classical to quantum

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial cross-over. 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. Quantum communication and computing is now in a data-intensive domain where a classical network describing a quantum system seems no longer sufficient to yield a generalization of complex networks methods to the quantum domain. The authors review recent progress into this paradigm shift that drives the creation of a network theory based fundamentally on quantum effects.