Modern web applications often rely on complex computational processes that can be time-consuming and resource-intensive. Quantum Computing has emerged as a promising paradigm to accelerate these tasks. However, incorporating quantum computing into current web application architecture poses significant challenges. Also, Quality of Service attributes are crucial for current web applications, these attributes will need to be considered for the deployment of hybrid web applications that leverage quantum and classical computing. This work outlines the general research directions and objectives to be addressed throughout this PhD. thesis. The core objective is to design a workflow for obtaining an optimal deployment configuration that maximizes the Quality of Service attributes. Moreover, a dynamic reconfiguration of the distribution of hybrid web application services in terms of demand fluctuations to ensure performance, resource utilization and responsiveness will be composed. This work lays the foundation for novel tools and methodologies to bridge classical and quantum paradigms in service-oriented computing.