37 research outputs found
Quantum Google in a Complex Network
We investigate the behavior of the recently proposed quantum Google
algorithm, or quantum PageRank, in large complex networks. Applying the quantum
algorithm to a part of the real World Wide Web, we find that the algorithm is
able to univocally reveal the underlying scale-free topology of the network and
to clearly identify and order the most relevant nodes (hubs) of the graph
according to their importance in the network structure. Moreover, our results
show that the quantum PageRank algorithm generically leads to changes in the
hierarchy of nodes. In addition, as compared to its classical counterpart, the
quantum algorithm is capable to clearly highlight the structure of secondary
hubs of the network, and to partially resolve the degeneracy in importance of
the low lying part of the list of rankings, which represents a typical
shortcoming of the classical PageRank algorithm. Complementary to this study,
our analysis shows that the algorithm is able to clearly distinguish scale-free
networks from other widespread and important classes of complex networks, such
as Erd\H{o}s-R\'enyi networks and hierarchical graphs. We show that the ranking
capabilities of the quantum PageRank algorithm are related to an increased
stability with respect to a variation of the damping parameter that
appears in the Google algorithm, and to a more clearly pronounced power-law
behavior in the distribution of importance among the nodes, as compared to the
classical algorithm. Finally, we study to which extent the increased
sensitivity of the quantum algorithm persists under coordinated attacks of the
most important nodes in scale-free and Erd\H{o}s-R\'enyi random graphs
Generalized quantum PageRank algorithm with arbitrary phase rotations
CAM/FEDER Project [S2018/TCS-4342]; Spanish MINECO/FEDER Project [PGC2018-099169- B-I00FIS2018]; MCIN; European Union NextGenerationEU [PRTR-C17.I1]; Ministry of Economic Affairs Quantum ENIA project; U.S. Army Research Office [W911NF-14-1-0103]; QUITEMAD grant; Universidad Complutense de Madrid-Banco Santander [CT58/21-CT59/21]The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank, introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We define three different APR schemes with only one phase as a degree of freedom. We have analyzed the behavior of these algorithms in a small generic graph, observing that a decrease of the phase reduces the standard deviation of the instantaneous PageRank, so the nodes of the network can be distinguished better. However, the algorithm takes more time to converge, so the phase cannot be decreased arbitrarily. With these results we choose a concrete value for the phase to later apply the algorithm to complex scale-free graphs. In these networks, the original quantum PageRank is able to break the degeneracy of the residual nodes and detect secondary hubs that the classical algorithm suppresses. Nevertheless, not all of the detected secondary hubs are real according to the PageRank's definition. Some APR schemes can overcome this problem, restoring the degeneration of the residual nodes and highlighting the truly secondary hubs of the networks. Finally, we have studied the stability of the new algorithms. The original quantum algorithm was known to be more stable than the classical. We have found that one of our algorithms, whose PageRank distribution resembles the classical one, has a stability similar to the original quantum algorithm.Depto. de Física TeóricaFac. de Ciencias FísicasTRUEMinisterio de Economia y Competitividad (MINECO)/FEDERMinisterio de Ciencia e Innovación (MICINN)/AEIMinisterio de Economía y Competitividad (MINECO)Comunidad de Madrid/FEDERU.S. Army Research Office W911NF-14-1-0103Universidad Complutense de Madrid/Banco de Santanderpu
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 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
Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
The quantum walk formalism is a widely used and highly successful framework
for modeling quantum systems, such as simulations of the Dirac equation,
different dynamics in both the low and high energy regime, and for developing a
wide range of quantum algorithms. Here we present the circuit-based
implementation of a discrete-time quantum walk in position space on a
five-qubit trapped-ion quantum processor. We encode the space of walker
positions in particular multi-qubit states and program the system to operate
with different quantum walk parameters, experimentally realizing a Dirac
cellular automaton with tunable mass parameter. The quantum walk circuits and
position state mapping scale favorably to a larger model and physical systems,
allowing the implementation of any algorithm based on discrete-time quantum
walks algorithm and the dynamics associated with the discretized version of the
Dirac equation.Comment: 8 pages, 6 figure