2,555 research outputs found
Fully-Automated Verification of Linear Systems Using Inner- and Outer-Approximations of Reachable Sets
Reachability analysis is a formal method to guarantee safety of dynamical
systems under the influence of uncertainties. A major bottleneck of all
reachability algorithms is the requirement to adequately tune certain algorithm
parameters such as the time step size, which requires expert knowledge. In this
work, we solve this issue with a fully-automated reachability algorithm that
tunes all algorithm parameters internally such that the reachable set enclosure
satisfies a user-defined accuracy in terms of distance to the exact reachable
set. Knowing the distance to the exact reachable set, an inner-approximation of
the reachable set can be efficiently extracted from the outer-approximation
using the Minkowski difference. Finally, we propose a novel verification
algorithm that automatically refines the accuracy of the outer- and
inner-approximation until specifications given by time-varying safe and unsafe
sets can either be verified or falsified. The numerical evaluation demonstrates
that our verification algorithm successfully verifies or falsifies benchmarks
from different domains without any requirement for manual tuning.Comment: 16 page
Global Control Methods for GHZ State Generation on 1-D Ising Chain
We discuss how to prepare an Ising chain in a GHZ state using a single global
control field only. This model does not require the spins to be individually
addressable and is applicable to quantum systems such as cold atoms in optical
lattices, some liquid- or solid-state NMR experiments, and many nano-scale
quantum structures. We show that GHZ states can always be reached
asymptotically from certain easy-to-prepare initial states using adiabatic
passage, and under certain conditions finite-time reachability can be ensured.
To provide a reference useful for future experimental implementations three
different control strategies to achieve the objective, adiabatic passage,
Lyapunov control and optimal control are compared, and their advantages and
disadvantages discussed, in particular in the presence of realistic
imperfections such as imperfect initial state preparation, system inhomogeneity
and dephasing.Comment: 13 pages, 11 figure
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