43,504 research outputs found
Quantum Query Complexity of Multilinear Identity Testing
Motivated by the quantum algorithm in \cite{MN05} for testing commutativity
of black-box groups, we study the following problem: Given a black-box finite
ring where is an additive
generating set for and a multilinear polynomial over
also accessed as a black-box function (where we allow the
indeterminates to be commuting or noncommuting), we study the
problem of testing if is an \emph{identity} for the ring . More
precisely, the problem is to test if for all .
We give a quantum algorithm with query complexity assuming . Towards a lower bound,
we also discuss a reduction from a version of -collision to this problem.
We also observe a randomized test with query complexity and constant
success probability and a deterministic test with query complexity.Comment: 12 page
Unified theory of bound and scattering molecular Rydberg states as quantum maps
Using a representation of multichannel quantum defect theory in terms of a
quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering
map to derive a generalized quantum map, that includes the continuum. We show,
that this representation not only simplifies the understanding of the method,
but moreover produces considerable numerical advantages. Finally we show under
what circumstances the usual semi-classical approximations yield satisfactory
results. In particular we see that singularities that cause problems in
semi-classics are irrelevant to the quantum map
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