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We propose an adiabatic quantum algorithm for generating a quantum pure stateencoding of the PageRank vector, the most widely used tool in ranking therelative importance of internet pages. We present extensive numericalsimulations which provide evidence that this algorithm can prepare the quantumPageRank state in a time which, on average, scales polylogarithmically in thenumber of webpages. We argue that the main topological feature of theunderlying web graph allowing for such a scaling is the out-degreedistribution. The top ranked $\log(n)$ entries of the quantum PageRank statecan then be estimated with a polynomial quantum speedup. Moreover, the quantumPageRank state can be used in "q-sampling" protocols for testing properties ofdistributions, which require exponentially fewer measurements than allclassical schemes designed for the same task. This can be used to decidewhether to run a classical update of the PageRank.

Adiabatic quantum algorithm for search engine ranking