  In this work we introduce, test and discuss three quantum methods for
computing hub and authority centrality scores in directed networks. The methods
are based on unitary, continuous-time quantum walks; the construction of a
suitable Hermitian Hamiltonian is achieved by performing a quantum walk on the
associated bipartite graph.
  Two methods, called CQAu and CQAw, use the same evolution operator, inspired
by the classical HITS algorithm, but with different initial states; the
computation of hub and authority scores is performed simultaneously. The third
method, called CQG and inspired by classical PageRank, requires instead two
separate runs with different evolution operators, one for hub and one for
authority scores.
  The methods are tested on several directed graphs with different sizes and
properties; a comparison with other well-established ranking algorithms is
provided. CQAw emerges as the most reliable of the three methods and yields
rankings that are largely compatible with results from HITS, although CQAu and
CQG also present interesting features and potential for applications.
