A Quantum Approach to Walk on Networks

Some interesting findings can be achieved by modeling and visualizing networks which can include complex networks and large scale networks to name a few. These networks have been analyzed with the help of classical stochastic walks before. So, here in our proposed work, we provide the quantum version of the walk which basically involves making use of properties found in quantum computing. These properties can include such as quantum interference, no-cloning theorem, and restriction on intermediate measurement. In this proposed work, we present quantum circuit designs for discrete time random walk algorithms that operate on various networks.To demonstrate our ideas we have considered two different types of networks, the star network and an extended version of the star network.Though there exist a few research works related to quantum approach for random walk on networks, to the best of our knowledge, the ideas and approach we present here are unique. These ideas which we have discussed can be extended to more complex networks and systems as well. As an application of quantum walk we have shown, how results got after performing quantum walk can be used to identify critical nodes in such networks. Therefore, we have also provided some analysis of complex networks. Identification of critical nodes is important for robustness and survivability of the network.