14,265 research outputs found
A lower bound on the quantum query complexity of read-once functions
We establish a lower bound of on the bounded-error
quantum query complexity of read-once Boolean functions, providing evidence for
the conjecture that is a lower bound for all Boolean
functions. Our technique extends a result of Ambainis, based on the idea that
successful computation of a function requires ``decoherence'' of initially
coherently superposed inputs in the query register, having different values of
the function. The number of queries is bounded by comparing the required total
amount of decoherence of a judiciously selected set of input-output pairs to an
upper bound on the amount achievable in a single query step. We use an
extension of this result to general weights on input pairs, and general
superpositions of inputs.Comment: 12 pages, LaTe
Limits in PMF of Teichmuller geodesics
We consider the limit set in Thurston's compactification PMF of Teichmueller
space of some Teichmueller geodesics defined by quadratic differentials with
minimal but not uniquely ergodic vertical foliations. We show that a) there are
quadratic differentials so that the limit set of the geodesic is a unique
point, b) there are quadratic differentials so that the limit set is a line
segment, c) there are quadratic differentials so that the vertical foliation is
ergodic and there is a line segment as limit set, and d) there are quadratic
differentials so that the vertical foliation is ergodic and there is a unique
point as its limit set. These give examples of divergent Teichmueller geodesics
whose limit sets overlap and Teichmueller geodesics that stay a bounded
distance apart but whose limit sets are not equal. A byproduct of our methods
is a construction of a Teichmueller geodesic and a simple closed curve
so that the hyperbolic length of the geodesic in the homotopy class of gamma
varies between increasing and decreasing on an unbounded sequence of time
intervals along the geodesic.Comment: 39 pages, 4 figure
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