Quantum Walk Circuits to Analyze Networks

Quantum walks are studied extensively using various networks. The quantum version of the walk involves using the properties found in quantum computing. These properties can include quantum interference, no-cloning theorem, and restriction on an intermediate measurement. Here, in the proposed work, we focus on finding out the properties associated with the networks using quantum walks while also verifying its findings. One of the properties includes identifying critical nodes in a network vital for its robustness and survivability. So, the results related to this and some other properties are analyzed. The proposed work requires the implementation of quantum walk on different networks. Therefore, this research paper presents an algorithm that takes an undirected network, $G$, as input and constructs the quantum circuit to perform quantum walk on $G$. The working of the proposed algorithm is shown using various networks, from simple to complex.