Discrete-time quantum walk algorithm for ranking nodes on a network
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Abstract
We present a quantum algorithm for ranking the nodes of a network in their order of importance. The algorithm is based on a directed discrete-time quantum walk and works on all directed networks. This algorithm can theoretically be applied to the entire internet and thus can function as a quantum PageRank algorithm. Our analysis shows that the hierarchy of quantum ranks matches well with the hierarchy of classical ranks for directed trees and other acyclic networks. For cyclic networks, however, the hierarchy of quantum ranks does not exactly match the hierarchy of the classical ranks. This highlights the role of quantum interference and fluctuations in networks and the importance of using quantum algorithms to rank nodes in quantum networks. Another application this algorithm can envision is to model the dynamics on networks mimicking chemical complexes and rank active centres in the order of reactivities. Since discrete-time quantum walks are implementable on current quantum processing systems, this algorithm will also be of practical relevance in the analysis of quantum architecture.