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Quantum networks are interconnected by nodes, between singlets which areformed to ensure the successful transmission of information with a probabilityof 1. However, in real quantum networks, nodes often share a partiallyentangled state instead of a singlet due to factors such as environmentalnoise. Therefore, it is necessary to convert the partially entangled state intoa singlet for efficient communication. Percolation happens during theconversion of connected edges in the whole network. As a result, when thesinglet conversion probability (SCP) is greater than the percolation threshold,a giant interconnected cluster that meets the basic requirements ofcommunication will appear in the network. The percolation threshold of thenetwork reveals the minimum resources required to carry out large scale quantumcommunication. In this paper, we investigate the effect of different q-swaps onthe percolation threshold in quantum entanglement percolation of small worldnetworks. We show that Quantum Entanglement Percolation (QEP) has a betterpercolation performance than Classical Entanglement Percolation (CEP). By usingdifferent q swaps in Watts Strogatz (WS) small world networks and Kleinbergnetworks for simulation, we also show that the percolation threshold isminimized when SCP is equal to the average degree of the network. Furthermore,we introduce quantum walk as a new scheme to have an extra reduction in thepercolation threshold.

Effects of Different Q-swaps Modes on Percolation Threshold in Small-world Quantum Networks