13,282 research outputs found
Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls
We present an algebraic framework to study the time-optimal synthesis of
arbitrary unitaries in SU(2), when the control set is restricted to rotations
around two non-parallel axes in the Bloch sphere. Our method bypasses commonly
used control-theoretical techniques, and easily imposes necessary conditions on
time-optimal sequences. In a straightforward fashion, we prove that
time-optimal sequences are solely parametrized by three rotation angles and
derive general bounds on those angles as a function of the relative rotation
speed of each control and the angle between the axes. Results are substantially
different whether both clockwise and counterclockwise rotations about the given
axes are allowed, or only clockwise rotations. In the first case, we prove that
any finite time-optimal sequence is composed at most of five control
concatenations, while for the more restrictive case, we present scaling laws on
the maximum length of any finite time-optimal sequence. The bounds we find for
both cases are stricter than previously published ones and severely constrain
the structure of time-optimal sequences, allowing for an efficient numerical
search of the time-optimal solution. Our results can be used to find the
time-optimal evolution of qubit systems under the action of the considered
control set, and thus potentially increase the number of realizable unitaries
before decoherence
Network service chaining with efficient network function mapping based on service decompositions
Network Service Chaining (NSC) is a service concept which promises increased flexibility and cost-efficiency for future carrier networks. The two recent developments, Network Function Virtualization (NFV) and Software-Defined Networking (SDN), are opportunities for service providers to simplify the service chaining and provisioning process and reduce the cost (in CAPEX and OPEX) while introducing new services as well. One of the challenging tasks regarding NFV-based services is to efficiently map them to the components of a physical network based on the services specifications/constraints. In this paper, we propose an efficient cost-effective algorithm to map NSCs composed of Network Functions (NF) to the network infrastructure while taking possible decompositions of NFs into account. NF decomposition refers to converting an abstract NF to more refined NFs interconnected in form of a graph with the same external interfaces as the higher-level NF. The proposed algorithm tries to minimize the cost of the mapping based on the NSCs requirements and infrastructure capabilities by making a reasonable selection of the NFs decompositions. Our experimental evaluations show that the proposed scheme increases the acceptance ratio significantly while decreasing the mapping cost in the long run, compared to schemes in which NF decompositions are selected randomly
Parallel Graph Decompositions Using Random Shifts
We show an improved parallel algorithm for decomposing an undirected
unweighted graph into small diameter pieces with a small fraction of the edges
in between. These decompositions form critical subroutines in a number of graph
algorithms. Our algorithm builds upon the shifted shortest path approach
introduced in [Blelloch, Gupta, Koutis, Miller, Peng, Tangwongsan, SPAA 2011].
By combining various stages of the previous algorithm, we obtain a
significantly simpler algorithm with the same asymptotic guarantees as the best
sequential algorithm
Degree of separability of bipartite quantum states
We investigate the problem of finding the optimal convex decomposition of a
bipartite quantum state into a separable part and a positive remainder, in
which the weight of the separable part is maximal. This weight is naturally
identified with the degree of separability of the state. In a recent work, the
problem was solved for two-qubit states using semidefinite programming. In this
paper, we describe a procedure to obtain the optimal decomposition of a
bipartite state of any finite dimension via a sequence of semidefinite
relaxations. The sequence of decompositions thus obtained is shown to converge
to the optimal one. This provides, for the first time, a systematic method to
determine the so-called optimal Lewenstein-Sanpera decomposition of any
bipartite state. Numerical results are provided to illustrate this procedure,
and the special case of rank-2 states is also discussed.Comment: 11 pages, 7 figures, submitted to PR
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