18,058 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
Sequential Quantum Cloning
Not all unitary operations upon a set of qubits can be implemented by
sequential interactions between each qubit and an ancillary system. We analyze
the specific case of sequential quantum cloning 1->M and prove that the minimal
dimension D of the ancilla grows linearly with the number of clones M. In
particular, we obtain D = 2M for symmetric universal quantum cloning and D =
M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for
the required ancilla-qubit interactions in each step of the sequential
procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical
Review Letter
Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
We determine the existence of critical lines in dimerized quantum spin
ladders in their phase diagram of coupling constants using the finite-size DMRG
algorithm. We consider both staggered and columnar dimerization patterns, and
antiferromagnetic and ferromagnetic inter-leg couplings. The existence of
critical phases depends on the precise combination of these patterns. The
nature of the massive phases separating the critical lines are characterized
with generalized string order parameters that determine their valence bond
solid (VBS) content.Comment: 9 pages 10 figure
Universality Classes of Diagonal Quantum Spin Ladders
We find the classification of diagonal spin ladders depending on a
characteristic integer in terms of ferrimagnetic, gapped and critical
phases. We use the finite algorithm DMRG, non-linear sigma model and
bosonization techniques to prove our results. We find stoichiometric contents
in cuprate planes that allow for the existence of weakly interacting
diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl
Ambiguities of arrival-time distributions in quantum theory
We consider the definition that might be given to the time at which a
particle arrives at a given place, both in standard quantum theory and also in
Bohmian mechanics. We discuss an ambiguity that arises in the standard theory
in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure
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