The prime concern in data communication over a transmission channel is the security of the data which is being exchanged amongst the sender and the receiver. Of late DNA based cryptography has emerged as an alternative to data encryption in the research of secure communications. In contrast, the axioms of quantum computation have greatly impacted the study of cryptoanalysis and network security according to recent trends. The idea of using quantum computing using DNA encoding to perform the quantum session key exchange is that each cipher-text pattern has its own unique properties and so, using a scheme that applies both is more secured than using any one alone. Message exchange amongst the two participants is established through quantum channels with non-orthogonal superposition states. The experimental setup is also discussed. Various encoding schemes, such as use of super-increasing Knapsack sequences, Fermat Number and Gödel Code have also been explored to protect the quantum key distribution procedure from different types of security concerns. The significant advantage of this technique lies in the ease of detection of any malicious intervention in the communication channel and how by computing the bit error rate which is a function of the noise on the communication network is discussed in my work.