The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.
翻译:网络结构分析对许多科学领域至关重要,从生物学到社会学。由于将这些网络分组成分区的计算任务(即解决社区探测问题)一般是NP-硬性的,因此,黑奴主义解决办法是不可或缺的。快速超常主义的探索导致在新兴量子计算技术中开发出特别有希望的方法。受所有既有量子群检测方法大量硬件需求驱动,我们采用了新型的基于QUBO的办法,该办法仅需要许多节点数,并有QUBO-矩阵代表的QUBO-矩阵,如输入图的相邻矩阵一样稀少。QUBO-matrix对于QUBO-matrix的宽广性是不可或缺的。 QUBO-matrix通常在相关工作中非常密集,通过新颖的分离点计算技术开发出特别有希望的办法。这种方法不是直接将每一个节点分配给一个社区,而是依靠确定一个分离节点集,在从图表中删除后产生一组相关组成部分,代表着社区的核心组成部分。 将这种贪婪的先入式的先入式的系统,随后的实验性测试阶段的系统,在随后的实验性测试阶段的实验性测试结果显示一个可展式的系统。