Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Control Landscapes Are Almost Always Trap Free   A proof that almost all quantum systems have trap free (that is, free from
local optima) landscapes is presented for a large and physically general class
of quantum system. This result offers an explanation for why gradient methods
succeed so frequently in quantum control in both theory and practice. The role
of singular controls is analyzed using geometric tools in the case of the
control of the propagator of closed finite dimension systems. This type of
control field has been implicated as a source of landscape traps. The
conditions under which singular controls can introduce traps, and thus
interrupt the progress of a control optimization, are discussed and a
geometrical characterization of the issue is presented. It is shown that a
control being singular is not sufficient to cause a control optimization
progress to halt and sufficient conditions for a trap free landscape are
presented. It is further shown that the local surjectivity axiom of landscape
analysis can be refined to the condition that the end-point map is transverse
to each of the level sets of the fidelity function. This novel condition is
shown to be sufficient for a quantum system's landscape to be trap free. The
control landscape for a quantum system is shown to be trap free for all but a
null set of Hamiltonians using a novel geometric technique based on the
parametric transversality theorem. Numerical evidence confirming this is also
presented. This result is the analogue of the work of Altifini, wherein it is
shown that controllability holds for all but a null set of quantum systems in
the dipole approximation. The presented results indicate that by-and-large
limited control resources are the most physically relevant source of landscape
traps.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci