Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application, such as detecting anomalies in E-commerce transactions, discerning protein-protein interactions in biology, and refining the efficacy of social network recommendation algorithms. However, the inherent NP-hardness of this problem significantly complicates the matter. The prohibitive time complexity of existing algorithms is the primary bottleneck constraining the application scenarios. Aiming to address this challenge, we present an unprecedented exploration of a quantum computing approach. Efficient quantum algorithms, as a crucial future direction for handling NP-hard problems, are presently under intensive investigation, of which the potential has already been proven in practical arenas such as cybersecurity. However, in the field of quantum algorithms for graph databases, little work has been done due to the challenges presented by the quantum representation of complex graph topologies. In this study, we delve into the intricacies of encoding a bipartite graph on a quantum computer. Given a bipartite graph with n vertices, we propose a ground-breaking algorithm qMBS with time complexity O^*(2^(n/2)), illustrating a quadratic speed-up in terms of complexity compared to the state-of-the-art. Furthermore, we detail two variants tailored for the maximum vertex biclique problem and the maximum balanced biclique problem. To corroborate the practical performance and efficacy of our proposed algorithms, we have conducted proof-of-principle experiments utilizing IBM quantum simulators, of which the results provide a substantial validation of our approach to the extent possible to date.

翻译：识别具有最大边数的二部团在众多应用领域具有重要意义，例如检测电子商务交易中的异常、识别生物学中的蛋白质相互作用以及优化社交网络推荐算法的效能。然而，该问题固有的NP难度使得这一任务极为复杂。现有算法的高时间复杂度是制约其应用场景的主要瓶颈。为应对这一挑战，我们首次探索了量子计算方法。高效的量子算法作为处理NP难问题的重要未来方向，目前正处于深入研究中，其潜力已在网络安全等实际领域得到验证。然而，在图数据库量子算法领域，由于复杂图拓扑结构的量子表示存在挑战，相关研究尚显不足。在本研究中，我们深入探讨了在量子计算机上编码二部图的复杂性。针对具有n个顶点的二部图，我们提出了一种突破性算法qMBS，其时间复杂度为O^*(2^(n/2))，与现有最优算法相比实现了复杂度上的二次加速。此外，我们还详细介绍了针对最大顶点二部图问题和最大平衡二部图问题而设计的两种变体算法。为验证所提出算法的实际性能与有效性，我们利用IBM量子模拟器进行了原理验证实验，实验结果在现有条件下充分证实了我们的方法。