Identifying community structures in complex networks is foundational to graph theory, but classical algorithms struggle with scalability and the "curse of dimensionality" in high-dimensional embedding, while existing quantum methods lack unified architectures or compatibility with practical hardware. Here we present Embedded Quantum Density-based Spatial Clustering (EQDSC), an end-to-end quantum framework for community detection with key theoretical and technical advances over state-of-the-art approaches: it integrates discrete-time quantum walks (DTQW) augmented with Grover diffusion operators for efficient topological feature extraction, and adopts quantum fidelity to quantify similarity—mitigating dimensionality issues inherently. We validated EQDSC on 11 real-world and synthetic datasets via Qiskit simulations. It achieved up to 0.855 modularity and 0.887 NMI (DBLP), outperforming classical methods by 18–35% on large networks. The achieved gains stem from quantum superposition and accelerated quantum walk diffusion, with small-dataset performance restricted by constrained parameter optimization. Simulated performance confirms practical applicability, laying the groundwork for future deployment on real NISQ devices.
Identifying community structures in complex networks is foundational to graph theory, but classical algorithms struggle with scalability and the "curse of dimensionality" in high-dimensional embedding, while existing quantum methods lack unified architectures or compatibility with practical hardware. Here we present Embedded Quantum Density-based Spatial Clustering (EQDSC), an end-to-end quantum framework for community detection with key theoretical and technical advances over state-of-the-art approaches: it integrates discrete-time quantum walks (DTQW) augmented with Grover diffusion operators for efficient topological feature extraction, and adopts quantum fidelity to quantify similarity—mitigating dimensionality issues inherently. We validated EQDSC on 11 real-world and synthetic datasets via Qiskit simulations. It achieved up to 0.855 modularity and 0.887 NMI (DBLP), outperforming classical methods by 18–35% on large networks. The achieved gains stem from quantum superposition and accelerated quantum walk diffusion, with small-dataset performance restricted by constrained parameter optimization. Simulated performance confirms practical applicability, laying the groundwork for future deployment on real NISQ devices.
Abstract The problem of detecting communities in real-world networks has been extensively studied in the past, but most of the existing approaches work on single-domain networks, i.e. they consider only one type of relationship between nodes. Single-domain networks may contain noisy edges and they may lack some important information. Thus, some authors have proposed to consider the multiple relationships that connect the nodes of a network, thus obtaining multi-domain networks. However, most community detection approaches are limited to multi-layer networks, i.e. networks generated from the superposition of several single-domain networks (called layers) that are regarded as independent of each other. In addition to being computationally expensive, multi-layer approaches might yield inaccurate results because they ignore potential dependencies between layers. This paper proposes a multi-domain discrete-time quantum walks (MDQW) model for multi-domain networks. First, the walking space of network nodes in multi-domain network is constructed. Second, the quantum permutation circuit of the coin state is designed based on the coded particle state. Then, using different coin states, the shift operator performs several quantum walks on the particles. Finally, the corresponding update rule is selected to move the node according to the measurement result of the quantum state. With continuous update iteration, the shift operator automatically optimizes the discovered community structure. We experimentally compared our MDQW method with four state-of-the-art competitors on five real datasets. We used the normalized mutual information (NMI) to compare clustering quality, and we report an increase in NMI of up to 3.51 of our MDQW method in comparison with the second-best performing competitor. The MDQW method is much faster than its competitors, allowing us to conclude that MDQW is a useful tool in the analysis of large real-life multi-domain networks. Finally, we illustrate the usefulness of our approach on two real-world case studies.
The article introduces Q-ClusterSim, a resource-efficient hybrid quantum-classical framework designed to accelerate clustering operations on large-scale and high-dimensional datasets. The proposed model combines quantum-enhanced k-means and density-based clustering within a unified quantum simulation environment to achieve improved computational efficiency and scalability. By leveraging the parallelism of quantum circuits and the adaptability of classical optimization, Q-ClusterSim significantly reduces execution time while maintaining clustering accuracy. Simulations are conducted using IBM Qiskit and TensorFlow Quantum on benchmark datasets, where the proposed model consistently outperforms classical clustering algorithms in terms of convergence speed, precision, and resource consumption. Results validate the model’s effectiveness in managing complex data structures under limited qubit resources, making it suitable for real-world large data applications. This study highlights the transformative potential of quantum-assisted clustering in reshaping future data analytics and computational intelligence paradigms..
Many systems such as social networks and biological networks take the form of complex networks, which have a community structure.Community detection in complex networks is of great interest to many researchers in statistical physics and mathematical physics.There have been studies on community detection that use the classical random walk.The present study utilizes the discrete-time quantum walk instead.The quantum walk plays an important role in various fields, especially in research on quantum computers, and attracts much attention from mathematical physics too.The discrete-time quantum walk has two properties: it linearly spreads on a flat space, and it localizes in some cases because of quantum coherence.We demonstrate that these properties of the quantum walk are useful for community detection on complex networks.We define the discrete-time quantum walk on complex networks and utilize it for community detection.We numerically show that the quantum walk with a Fourier coin is localized in a community to which the initial node belongs.Meanwhile, the quantum walk with a Grover coin tends to be localized around the initial node, not over a community.The probability of a classical random walk on the same network converges to a uniform distribution with a relaxation time generally unknown a priori.We thus claim that the time average of the probability of a Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of a Grover-coin quantum walk and a snapshot of the classical random walk.We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping.We then apply our method to two real-world networks, namely, Zachary's karate club and the U.S. Airport network.We successfully reveal the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.
High-dimensional data presents significant challenges to traditional clustering algorithms due to the "curse of dimensionality," leading to sparsity issues, increased computational complexity, and reduced cluster quality. This research investigates the application of quantum-inspired algorithms to enhance clustering performance in these scenarios. We propose a novel clustering framework leveraging concepts from quantum annealing and quantum walks to efficiently explore the feature space and identify clusters. The core idea is to mimic the probabilistic and superposition properties of quantum systems within the clustering process, allowing for more nuanced exploration of potential cluster configurations. The algorithms are designed to mitigate the effects of dimensionality by introducing stochastic search strategies and exploiting correlations between features. We evaluate the effectiveness of these algorithms on benchmark datasets, demonstrating improved clustering accuracy and reduced computational cost compared to established classical methods. The research highlights the potential of quantum-inspired approaches as a viable solution for high-dimensional clustering problems.
Community recognition continues to be a significant difficulty in the analysis of complex networks, especially in dynamic and stochastic contexts where communities change over time. Conventional spectral clustering and Markovian models either include structural regularities or temporal dependencies, although frequently lack the ability to amalgamate both within a cohesive theoretical framework. This study presents a Fourier operator framework inspired by quantum walks that integrates spectral graph theory, Markov processes, and quantum brain dynamics for the discovery of modular structures. We specifically build Fourier-Markov operators based on quantum walk principles to encapsulate both global frequency components and local transition dynamics of evolving networks. Our system utilizes superposition and interference effects by mapping random walks into a quantum-inspired Hilbert space, therefore uncovering latent modular structures with enhanced resolution. The resultant operator family facilitates interpretable community partitions, scalable computation using hybrid classicalquantum methodologies, and resilient detection across temporal snapshots. Experimental assessments on benchmark dynamic networks—encompassing social, biological, and financial graphs—indicate that our approach attains enhanced modularity optimization, temporal stability, and uncertainty calibration relative to leading community detection benchmarks. This study emphasizes the promise of quantum-spectral operators as a novel basis for examining Markovian community dynamics in intricate systems.
In this research, the computational efficiency of large-scale social network analysis is enhanced by the use of quantum random walk algorithms. The goal of this project is to address the need for high-efficiency centralized analysis of large-scale, heterogeneous social networks, community discovery, and dynamic effect mapping. In a theoretically sound framework of quantum random walks, amplitude superposition and unitary evolution principles have been used to improve both the sensitivity to local and global aspects. The solution uses real social network data with up to 5,000 nodes and more than 60,000 edges, and the testing results demonstrate its excellent scalability and fast convergence. Quantum algorithms have discovered community divisions and cut the mixing time by roughly 2.3 times after multiple optimizations. The performance indicators demonstrate that the above method has greatly improved key node detection accuracy and computation time as compared to the conventional baseline model in noisy situations. According to the aforementioned research, quantum-inspired algorithms have been used to expedite the analysis of large-scale data and reveal hidden structures that are challenging to identify using conventional techniques, such as bridge nodes and core-periphery distributions. The research assist data-driven choices in digital social ecosystems and lay the groundwork for in-depth network analysis.