Routing Protocols based on Quantum bunch graphs acquaint an advanced approach to implementing routing in multifarious networks, commercialising principles of quantum computing and graph theory. This chapter discusses quantum bunch graphs, focusing on entanglement-based, degree-based, spectral, path-based, and indirect neighbour-based irregularity measures. These measures are essential for understanding the complexity and behavior of quantum bunch graphs, which are characterized by dynamic weights and entangled edges. The degree-based measure extends the concept of vertex degrees to dynamic quantum graphs by considering the time-averaged degree of each vertex, while the entanglement-based measure leverages the correlation functions of entangled edges. We used the Fuzzy Bunch Graph (FBG) concept to find the uncertain route. Both quantum bunch graphs and fuzzy bunch graph work on uncertainty, but they belong to different framework. The time-averaged adjacency matrix, and the path-based measure considers the variability in the shortest path lengths between all pairs of vertices. The indirect neighbor-based measure examines the influence of indirect neighbors by considering the variability in their weights. These irregularity measures are crucial in the analysis of dynamical networks, such as communication networks, where maintaining consistent performance and reliability is essential. For instance, in a quantum communication network, the degree-based irregularity measure can help identify nodes with fluctuating connectivity, which may affect the overall network stability and efficiency. By applying these measures, network designers can optimize the network structure to minimize irregularities and enhance performance. The result indicates that quantum-based routing guarantees achieving outstanding procure in network performance, flooring the way for a more reliable and efficient communication system in the quantum period.