Adiabatic quantum algorithm for search engine ranking

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of webpages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top ranked $\log(n)$ entries of the quantum PageRank state can then be estimated with a polynomial quantum speedup. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.Comment: 7 pages, 5 figures; closer to published versio

The Local Emergence and Global Diffusion of Research Technologies: An Exploration of Patterns of Network Formation

Grasping the fruits of "emerging technologies" is an objective of many government priority programs in a knowledge-based and globalizing economy. We use the publication records (in the Science Citation Index) of two emerging technologies to study the mechanisms of diffusion in the case of two innovation trajectories: small interference RNA (siRNA) and nano-crystalline solar cells (NCSC). Methods for analyzing and visualizing geographical and cognitive diffusion are specified as indicators of different dynamics. Geographical diffusion is illustrated with overlays to Google Maps; cognitive diffusion is mapped using an overlay to a map based on the ISI Subject Categories. The evolving geographical networks show both preferential attachment and small-world characteristics. The strength of preferential attachment decreases over time, while the network evolves into an oligopolistic control structure with small-world characteristics. The transition from disciplinary-oriented ("mode-1") to transfer-oriented ("mode-2") research is suggested as the crucial difference in explaining the different rates of diffusion between siRNA and NCSC