Network Function Virtualization (NFV) has enabled scalable deployment of novel user service requests in current and future communication networks (sixth generation (6G)). However, virtualization also introduces down functioning of certain Key Performance Indicator (KPI)s such as latency. Novel technology like quantum computing has potential to surpass these limitations. One of the problems to tackle in NFV based systems, is decision making for Virtual Network Function (VNF) migration. Classical and quantum solutions are proposed for this problem. It is observed that both solutions ensure anonymity; however lesser overhead is required in the quantum solution. Further, future research directions are discussed as well to inculcate quantum technology into broader class of problems in 6G communication networks.