Complex Networks and Quantum Systems

Complex networks provide a universal language for describing the interconnectivity of elements across domains such as social systems, biology and engineered infrastructures. When quantum phenomena are introduced, classical topological methods must be adapted to capture non-classical correlations and coherence. Quantum systems embedded in network frameworks enable the study of entanglement distribution, quantum transport and information processing on a large scale. Rigorous analysis employs tools such as adjacency and Laplacian matrices enriched by quantum amplitudes, while modularity measures are generalised to account for state fidelity and transport probabilities. This interdisciplinary approach reveals that quantum networked structures can exhibit enhanced resilience, novel phase transitions and non-intuitive transport effects, with potential applications in quantum communication, energy harvesting and materials design. The synergy between network topology and quantum mechanics continues to generate both fundamental insights and pathways towards scalable quantum technologies.

Research from Nature Portfolio

Recent studies have demonstrated a fruitful integration of network science and quantum information. A comprehensive review of developments in complex networks traced how classical network concepts have been extended to the quantum domain, highlighting novel phenomena in random graphs with entangled links, and the design of quantum algorithms to accelerate community detection and network centrality tasks. This work showcased the prediction of unique quantum-induced effects in transport and entanglement distribution, and outlined how quantum-inspired metrics can inform the design of robust, scalable quantum architectures.

Research from all publishers

Advances in statistical physics have led to a reappraisal of connectivity thresholds in quantum networks, where classical percolation frameworks are contrasted with an emergent concurrence percolation theory. This new perspective uncovers a quantum advantage in entanglement resilience and suggests guidelines for network-scale quantum repeater placement. In parallel, models of disordered quantum dot arrays cast nodes as spatially constrained elements of a weighted geometric graph, revealing that optimal inter-dot distances minimise electron localisation and enhance coherent transport, with implications for next-generation solar cells. Seminal work in community detection applied quantum transport probabilities and state fidelity to partition quantum complexes, uncovering structures that elude classical modularity approaches and offering a powerful lens on natural light-harvesting assemblies and artificial quantum materials.

Complex Networks and Quantum Systems publication trend

The graph below shows the total number of articles in complex networks and quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Complex network: A mathematical representation of a system composed of nodes interconnected by edges, used to model relationships or interactions across diverse fields.

Quantum entanglement: A non-classical correlation between quantum states of distinct particles or nodes, enabling phenomena such as superposition across the network.

Quantum transport: The movement of quantum excitations or particles through a network, governed by coherence, interference and quantum probabilities.

Percolation: A statistical physics framework describing the emergence of large-scale connectivity in random networks as links are occupied or fail.

Concurrence percolation: A quantum generalisation of percolation theory, using entanglement concurrence as a metric for effective connectivity and robustness in quantum networks.

References

1. Community Detection in Quantum Complex Networks. Physical Review X (2014).
2. Complex networks from classical to quantum. Communications Physics (2019).
3. Percolation Theories for Quantum Networks. Entropy (2023).
4. Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints. Nanomaterials (2021).