8,111 research outputs found
Complete methods set for scalable ion trap quantum information processing
Large-scale quantum information processors must be able to transport and
maintain quantum information, and repeatedly perform logical operations. Here
we demonstrate a combination of all the fundamental elements required to
perform scalable quantum computing using qubits stored in the internal states
of trapped atomic ions. We quantify the repeatability of a multi-qubit
operation, observing no loss of performance despite qubit transport over
macroscopic distances. Key to these results is the use of different pairs of
beryllium ion hyperfine states for robust qubit storage, readout and gates, and
simultaneous trapping of magnesium re-cooling ions along with the qubit ions.Comment: 9 pages, 4 figures. Accepted to Science, and thus subject to a press
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Classification and nondegeneracy of Toda system with singular sources
We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n
a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb
R^2}e^{u_i} dx -1\delta_0a_{ij}\gamma_i=0\forall \;1\leq i\leq n\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z1\leq i\leq
j\leq nu_i$ is \textit{radially symmetric} w.r.t. 0.
(iii) We prove that the linearized equation at any solution is
\textit{non-degenerate}. These are fundamental results in order to understand
the bubbling behavior of the Toda system.Comment: 28 page
Euclidean versus hyperbolic congestion in idealized versus experimental networks
This paper proposes a mathematical justification of the phenomenon of extreme
congestion at a very limited number of nodes in very large networks. It is
argued that this phenomenon occurs as a combination of the negative curvature
property of the network together with minimum length routing. More
specifically, it is shown that, in a large n-dimensional hyperbolic ball B of
radius R viewed as a roughly similar model of a Gromov hyperbolic network, the
proportion of traffic paths transiting through a small ball near the center is
independent of the radius R whereas, in a Euclidean ball, the same proportion
scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at
the center of the hyperbolic ball scales as the square of the volume, whereas
the same traffic load scales as the volume to the power (n+1)/n in the
Euclidean ball. This provides a theoretical justification of the experimental
exponent discrepancy observed by Narayan and Saniee between traffic loads in
Gromov-hyperbolic networks from the Rocketfuel data base and synthetic
Euclidean lattice networks. It is further conjectured that for networks that do
not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of
maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure
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