1,055 research outputs found
Pattern recognition on a quantum computer
By means of a simple example it is demonstrated that the task of finding and
identifying certain patterns in an otherwise (macroscopically) unstructured
picture (data set) can be accomplished efficiently by a quantum computer.
Employing the powerful tool of the quantum Fourier transform the proposed
quantum algorithm exhibits an exponential speed-up in comparison with its
classical counterpart. The digital representation also results in a
significantly higher accuracy than the method of optical filtering. PACS:
03.67.Lx, 03.67.-a, 42.30.Sy, 89.70.+c.Comment: 6 pages RevTeX, 1 figure, several correction
Survival of near-critical branching Brownian motion
Consider a system of particles performing branching Brownian motion with
negative drift and killed upon hitting zero.
Initially there is one particle at . Kesten showed that the process
survives with positive probability if and only if . Here we are
interested in the asymptotics as \eps\to 0 of the survival probability
. It is proved that if then for all , exists and is a
travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain
sharp asymptotics of the survival probability when and .
The proofs rely on probabilistic methods developed by the authors in a previous
work. This completes earlier work by Harris, Harris and Kyprianou and confirms
predictions made by Derrida and Simon, which were obtained using nonrigorous
PDE methods
Improved Bounds on Quantum Learning Algorithms
In this article we give several new results on the complexity of algorithms
that learn Boolean functions from quantum queries and quantum examples.
Hunziker et al. conjectured that for any class C of Boolean functions, the
number of quantum black-box queries which are required to exactly identify an
unknown function from C is ,
where is a combinatorial parameter of the class C. We
essentially resolve this conjecture in the affirmative by giving a quantum
algorithm that, for any class C, identifies any unknown function from C using
quantum black-box
queries.
We consider a range of natural problems intermediate between the exact
learning problem (in which the learner must obtain all bits of information
about the black-box function) and the usual problem of computing a predicate
(in which the learner must obtain only one bit of information about the
black-box function). We give positive and negative results on when the quantum
and classical query complexities of these intermediate problems are
polynomially related to each other.
Finally, we improve the known lower bounds on the number of quantum examples
(as opposed to quantum black-box queries) required for -PAC
learning any concept class of Vapnik-Chervonenkis dimension d over the domain
from to . This new lower bound comes
closer to matching known upper bounds for classical PAC learning.Comment: Minor corrections. 18 pages. To appear in Quantum Information
Processing. Requires: algorithm.sty, algorithmic.sty to buil
Interaction-free generation of entanglement
In this paper, we study how to generate entanglement by interaction-free
measurement. Using Kwiat et al.'s interferometer, we construct a two-qubit
quantum gate that changes a particle's trajectory according to the other
particle's trajectory. We propose methods for generating the Bell state from an
electron and a positron and from a pair of photons by this gate. We also show
that using this gate, we can carry out the Bell measurement with the
probability of 3/4 at the maximum and execute a controlled-NOT operation by the
method proposed by Gottesman and Chuang with the probability of 9/16 at the
maximum. We estimate the success probability for generating the Bell state by
our procedure under imperfect interaction.Comment: 18 pages, Latex2e, 11 eps figures, v2: minor corrections and one
reference added, v3: a minor correctio
On the third critical field in Ginzburg-Landau theory
Using recent results by the authors on the spectral asymptotics of the
Neumann Laplacian with magnetic field, we give precise estimates on the
critical field, , describing the appearance of superconductivity in
superconductors of type II. Furthermore, we prove that the local and global
definitions of this field coincide. Near only a small part, near the
boundary points where the curvature is maximal, of the sample carries
superconductivity. We give precise estimates on the size of this zone and decay
estimates in both the normal (to the boundary) and parallel variables
Selectivity and functional diversity in arbuscular mycorrhizas of co-occurring fungi and plants from a temperate deciduous woodland
1 The arbuscular mycorrhizal (AM) fungi colonizing plants at a woodland site in North Yorkshire (UK) have been characterized from the roots of five plant species (Rubus fruticosus agg. L., Epilobium angustifolium L., Acer pseudoplatanus L., Ajuga reptans L. and Glechoma hederacea L.), and identified using small-subunit rRNA (SSUrRNA) gene amplification and sequencing. 2 Interactions between five plant species from the site and four co-occurring glomalean fungi were investigated in artificial one-to-one AM symbioses. Three of the fungi were isolated from the site; the fourth was a culture genetically similar to a taxon found at the site. Phosphorus uptake and growth responses were compared with non-mycorrhizal controls. 3 Individual fungi colonized each plant with different spatial distribution and intensity. Some did not colonize at all, indicating incompatibility under the conditions used in the experiments. 4 Glomus hoi consistently occupied a large proportion of root systems and outperformed the other fungi, improving P uptake and enhancing the growth of four out of the five plant species. Only G. hoi colonized and increased P uptake in Acer pseudoplatanus, the host plant with which it associates almost exclusively under field conditions. Colonization of all plant species by Scutellospora dipurpurescens was sparse, and beneficial to only one of the host plants (Teucrium scorodonia). Archaeospora trappei and Glomus sp. UY1225 had variable effects on the host plants, conferring a range of P uptake and growth benefits on Lysimachia nummularia and T. scorodonia, increasing P uptake whilst not affecting biomass in Ajuga reptans and Glechoma hederacea, and failing to form mycorrhizas with A. pseudoplatanus. 5 These experimental mycorrhizas show that root colonization, symbiont compatibility and plant performance vary with each fungus-plant combination, even when the plants and fungi naturally co-exist. 6 We provide evidence of physical and functional selectivity in AM. The small number of described AM fungal species (154) has been ascribed to their supposed lack of host specificity, but if the selectivity we have observed is the general rule, then we may predict that many more, probably hard-to-culture glomalean species await discovery, or that members of species as currently perceived may be physiologically or functionally distinct
Continuity of the measure of the spectrum for quasiperiodic Schrodinger operators with rough potentials
We study discrete quasiperiodic Schr\"odinger operators on \ell^2(\zee)
with potentials defined by -H\"older functions. We prove a general
statement that for and under the condition of positive Lyapunov
exponents, measure of the spectrum at irrational frequencies is the limit of
measures of spectra of periodic approximants. An important ingredient in our
analysis is a general result on uniformity of the upper Lyapunov exponent of
strictly ergodic cocycles.Comment: 15 page
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
We develop an analog of classical oscillation theory for Sturm-Liouville
operators which, rather than measuring the spectrum of one single operator,
measures the difference between the spectra of two different operators.
This is done by replacing zeros of solutions of one operator by weighted
zeros of Wronskians of solutions of two different operators. In particular, we
show that a Sturm-type comparison theorem still holds in this situation and
demonstrate how this can be used to investigate the finiteness of eigenvalues
in essential spectral gaps. Furthermore, the connection with Krein's spectral
shift function is established.Comment: 26 page
Angular dependence of the bulk nucleation field Hc2 of aligned MgB2 crystallites
Studies on the new MgB2 superconductor, with a critical temperature Tc ~ 39
K, have evidenced its potential for applications although intense magnetic
relaxation effects limit the critical current density, Jc, at high magnetic
fields. This means that effective pinning centers must be added into the
material microstructure, in order to halt dissipative flux movements.
Concerning the basic microscopic mechanism to explain the superconductivity in
MgB2, several experimental and theoretical works have pointed to the relevance
of a phonon-mediated interaction, in the framework of the BCS theory. Questions
have been raised about the relevant phonon modes, and the gap and Fermi surface
anisotropies, in an effort to interpret spectroscopic and thermal data that
give values between 2.4 and 4.5 for the gap energy ratio. Preliminary results
on the anisotropy of Hc2 have shown a ratio, between the in-plane and
perpendicular directions, around 1.7 for aligned MgB2 crystallites and 1.8 for
epitaxial thin films. Here we show a study on the angular dependence of Hc2
pointing to a Fermi velocity anisotropy around 2.5. This anisotropy certainly
implies the use of texturization techniques to optimize Jc in MgB2 wires and
other polycrystalline components.Comment: 10 pages + 4 Figs.; Revised version accepted in Phys. Rev.
Bailing Out the Milky Way: Variation in the Properties of Massive Dwarfs Among Galaxy-Sized Systems
Recent kinematical constraints on the internal densities of the Milky Way's
dwarf satellites have revealed a discrepancy with the subhalo populations of
simulated Galaxy-scale halos in the standard CDM model of hierarchical
structure formation. This has been dubbed the "too big to fail" problem, with
reference to the improbability of large and invisible companions existing in
the Galactic environment. In this paper, we argue that both the Milky Way
observations and simulated subhalos are consistent with the predictions of the
standard model for structure formation. Specifically, we show that there is
significant variation in the properties of subhalos among distinct host halos
of fixed mass and suggest that this can reasonably account for the deficit of
dense satellites in the Milky Way. We exploit well-tested analytic techniques
to predict the properties in a large sample of distinct host halos with a
variety of masses spanning the range expected of the Galactic halo. The
analytic model produces subhalo populations consistent with both Via Lactea II
and Aquarius, and our results suggest that natural variation in subhalo
properties suffices to explain the discrepancy between Milky Way satellite
kinematics and these numerical simulations. At least ~10% of Milky Way-sized
halos host subhalo populations for which there is no "too big to fail" problem,
even when the host halo mass is as large as M_host = 10^12.2 h^-1 M_sun.
Follow-up studies consisting of high-resolution simulations of a large number
of Milky Way-sized hosts are necessary to confirm our predictions. In the
absence of such efforts, the "too big to fail" problem does not appear to be a
significant challenge to the standard model of hierarchical formation.
[abridged]Comment: 12 pages, 3 figures; accepted by JCAP. Replaced with published
versio
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