4,448 research outputs found
Quantum search algorithms on a regular lattice
Quantum algorithms for searching one or more marked items on a d-dimensional
lattice provide an extension of Grover's search algorithm including a spatial
component. We demonstrate that these lattice search algorithms can be viewed in
terms of the level dynamics near an avoided crossing of a one-parameter family
of quantum random walks. We give approximations for both the level-splitting at
the avoided crossing and the effectively two-dimensional subspace of the full
Hilbert space spanning the level crossing. This makes it possible to give the
leading order behaviour for the search time and the localisation probability in
the limit of large lattice size including the leading order coefficients. For
d=2 and d=3, these coefficients are calculated explicitly. Closed form
expressions are given for higher dimensions
Quantum Mechanics helps in searching for a needle in a haystack
Quantum mechanics can speed up a range of search applications over unsorted
data. For example imagine a phone directory containing N names arranged in
completely random order. To find someone's phone number with a probability of
50%, any classical algorithm (whether deterministic or probabilistic) will need
to access the database a minimum of O(N) times. Quantum mechanical systems can
be in a superposition of states and simultaneously examine multiple names. By
properly adjusting the phases of various operations, successful computations
reinforce each other while others interfere randomly. As a result, the desired
phone number can be obtained in only O(sqrt(N)) accesses to the database.Comment: Postscript, 4 pages. This is a modified version of the STOC paper
(quant-ph/9605043) and is modified to make it more comprehensible to
physicists. It appeared in Phys. Rev. Letters on July 14, 1997. (This paper
was originally put out on quant-ph on June 13, 1997, the present version has
some minor typographical changes
Observation of tunable exchange bias in SrYbRuO
The double perovskite compound, SrYbRuO, displays reversal in the
orientation of magnetic moments along with negative magnetization due to an
underlying magnetic compensation phenomenon. The exchange bias (EB) field below
the compensation temperature could be the usual negative or the positive
depending on the initial cooling field. This EB attribute has the potential of
getting tuned in a preselected manner, as the positive EB field is seen to
crossover from positive to negative value above .Comment: 4 Pages, 4 Figure
Noise in Grover's Quantum Search Algorithm
Grover's quantum algorithm improves any classical search algorithm. We show
how random Gaussian noise at each step of the algorithm can be modelled easily
because of the exact recursion formulas available for computing the quantum
amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness
when no quantum correction codes are used, and evaluate how much noise the
algorithm can bear with, in terms of the size of the phone book and a desired
probability of finding the correct result. The algorithm loses efficiency when
noise is added, but does not slow down. We also study the maximal noise under
which the iterated quantum algorithm is just as slow as the classical
algorithm. In all cases, the width of the allowed noise scales with the size of
the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA,
December 199
Energy and Efficiency of Adiabatic Quantum Search Algorithms
We present the results of a detailed analysis of a general, unstructured
adiabatic quantum search of a data base of items. In particular we examine
the effects on the computation time of adding energy to the system. We find
that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it
temporarily} to a maximum of , it is possible to do the
calculation in constant time. This leads us to derive the general theorem which
provides the adiabatic analogue of the bound of conventional quantum
searches. The result suggests that the action associated with the oracle term
in the time dependent Hamiltonian is a direct measure of the resources required
by the adiabatic quantum search.Comment: 6 pages, Revtex, 1 figure. Theorem modified, references and comments
added, sections introduced, typos corrected. Version to appear in J. Phys.
Optimization of Partial Search
Quantum Grover search algorithm can find a target item in a database faster
than any classical algorithm. One can trade accuracy for speed and find a part
of the database (a block) containing the target item even faster, this is
partial search. A partial search algorithm was recently suggested by Grover and
Radhakrishnan. Here we optimize it. Efficiency of the search algorithm is
measured by number of queries to the oracle. The author suggests new version of
Grover-Radhakrishnan algorithm which uses minimal number of queries to the
oracle. The algorithm can run on the same hardware which is used for the usual
Grover algorithm.Comment: 5 page
New Samarium and Neodymium based admixed ferromagnets with near zero net magnetization and tunable exchange bias field
Rare earth based intermetallics, SmScGe and NdScGe, are shown to exhibit near
zero net magnetization with substitutions of 6 to 9 atomic percent of Nd and 25
atomic percent of Gd, respectively. The notion of magnetic compensation in them
is also elucidated by the crossover of zero magnetization axis at low magnetic
fields (less than 103 Oe) and field-induced reversal in the orientation of the
magnetic moments of the dissimilar rare earth ions at higher magnetic fields.
These magnetically ordered materials with no net magnetization and appreciable
conduction electron polarization display an attribute of an exchange bias
field, which can be tuned. The attractively high magnetic ordering temperatures
of about 270 K, underscore the importance of these materials for potential
applications in spintronics.Comment: 6 page text + 5 figure
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