1,982 research outputs found
Grover's search with faults on some marked elements
Grover's algorithm is a quantum query algorithm solving the unstructured
search problem of size using queries. It provides a
significant speed-up over any classical algorithm \cite{Gro96}.
The running time of the algorithm, however, is very sensitive to errors in
queries. It is known that if query may fail (report all marked elements as
unmarked) the algorithm needs queries to find a marked element
\cite{RS08}. \cite{AB+13} have proved the same result for the model where each
marked element has its own probability to be reported as unmarked.
We study the behavior of Grover's algorithm in the model where the search
space contains both faulty and non-faulty marked elements. We show that in this
setting it is indeed possible to find one of non-faulty marked items in
queries.
We also analyze the limiting behavior of the algorithm for a large number of
steps and show the existence and the structure of limiting state .Comment: 17 pages, 6 figure
Expected lengths and distribution functions for Young diagrams in the hook
AbstractWe consider ÎČ-Plancherel measures [J. Baik, E. Rains, The asymptotics of monotone subsequences of involutions, Duke Math. J. 109 (2001) 205â281] on subsets of partitionsâand their asymptotics. These subsets are the Young diagrams contained in a (k,â)-hook, and we calculate the asymptotics of the expected shape of these diagrams, relative to such measures. We also calculate the asymptotics of the distribution function of the lengths of the rows and the columns for these diagrams. This might be considered as the restriction to the (k,â)-hook of the fundamental work of Baik, Deift and Johansson [J. Baik, P. Deift, K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999) 1119â1178]. The above asymptotics are given here by ratios of certain Selberg-type multi-integrals
Effects of dissipation in an adiabatic quantum search algorithm
We consider the effect of two different environments on the performance of
the quantum adiabatic search algorithm, a thermal bath at finite temperature,
and a structured environment similar to the one encountered in systems coupled
to the electromagnetic field that exists within a photonic crystal. While for
all the parameter regimes explored here, the algorithm performance is worsened
by the contact with a thermal environment, the picture appears to be different
when considering a structured environment. In this case we show that, by tuning
the environment parameters to certain regimes, the algorithm performance can
actually be improved with respect to the closed system case. Additionally, the
relevance of considering the dissipation rates as complex quantities is
discussed in both cases. More particularly, we find that the imaginary part of
the rates can not be neglected with the usual argument that it simply amounts
to an energy shift, and in fact influences crucially the system dynamics.Comment: 18 pages, 9 figure
Hydrodynamic response of rotationally supported flows in the Small Shearing Box model
The hydrodynamic response of the inviscid small shearing box model of a
midplane section of a rotationally supported astrophysical disk is examined. An
energy functional is formulated for the general nonlinear problem.
It is found that the fate of disturbances is related to the conservation of
this quantity which, in turn, depends on the boundary conditions utilized:
is conserved for channel boundary conditions while it is not
conserved in general for shearing box conditions. Linearized disturbances
subject to channel boundary conditions have normal-modes described by Bessel
Functions and are qualitatively governed by a quantity which is a
measure of the ratio between the azimuthal and vertical wavelengths. Inertial
oscillations ensue if - otherwise disturbances must in general be
treated as an initial value problem. We reflect upon these results and offer a
speculation.Comment: 6 pages, resubmitted to Astronomy and Astrophysics, shortened with
references adde
What are the factors that contribute to road accidents? An assessment of law enforcement views, ordinary driversâ opinions, and road accident records
What are the main contributing factors to road accidents? Factors such as inexperience, lack of skill, and risk-taking behaviors have been associated with the collisions of young drivers. In contrast, visual, cognitive, and mobility impairment have been associated with the collisions of older drivers. We investigated the main causes of road accidents by drawing on multiple sources: expert views of police officers, lay views of the driving public, and official road accident records. In Studies 1 and 2, police officers and the public were asked about the typical causes of road traffic collisions using hypothetical accident scenarios. In Study 3, we investigated whether the views of police officers and the public about accident causation influence their recall accuracy for factors reported to contribute to hypothetical road accidents. The results show that both expert views of police officers and lay views of the driving public closely approximated the typical factors associated with the collisions of young and older drivers, as determined from official accident records. The results also reveal potential underreporting of factors in existing accident records, identifying possible inadequacies in law enforcement practices for investigating driver distraction, drug and alcohol impairment, and uncorrected or defective eyesight. Our investigation also highlights a need for accident report forms to be continuously reviewed and updated to ensure that contributing factor lists reflect the full range of factors that contribute to road accidents. Finally, the views held by police officers and the public on accident causation influenced their memory recall of factors involved in hypothetical scenarios. These findings indicate that delay in completing accident report forms should be minimised, possibly by use of mobile reporting devices at the accident scene
Recommended from our members
Cell-type-specific resolution epigenetics without the need for cell sorting or single-cell biology.
High costs and technical limitations of cell sorting and single-cell techniques currently restrict the collection of large-scale, cell-type-specific DNA methylation data. This, in turn, impedes our ability to tackle key biological questions that pertain to variation within a population, such as identification of disease-associated genes at a cell-type-specific resolution. Here, we show mathematically and empirically that cell-type-specific methylation levels of an individual can be learned from its tissue-level bulk data, conceptually emulating the case where the individual has been profiled with a single-cell resolution and then signals were aggregated in each cell population separately. Provided with this unprecedented way to perform powerful large-scale epigenetic studies with cell-type-specific resolution, we revisit previous studies with tissue-level bulk methylation and reveal novel associations with leukocyte composition in blood and with rheumatoid arthritis. For the latter, we further show consistency with validation data collected from sorted leukocyte sub-types
- âŠ