6,125 research outputs found
From Schr\"odinger's Equation to the Quantum Search Algorithm
The quantum search algorithm is a technique for searching N possibilities in
only sqrt(N) steps. Although the algorithm itself is widely known, not so well
known is the series of steps that first led to it, these are quite different
from any of the generally known forms of the algorithm. This paper describes
these steps, which start by discretizing Schr\"odinger's equation. This paper
also provides a self-contained introduction to the quantum search algorithm
from a new perspective.Comment: Postscript file, 16 pages. This is a pedagogical article describing
the invention of the quantum search algorithm. It appeared in the July, 2001
issue of American Journal of Physics (AJP
Simple Algorithm for Partial Quantum Search
Quite often in database search, we only need to extract portion of the
information about the satisfying item. Recently Radhakrishnan & Grover [RG]
considered this problem in the following form: the database of items was
divided into equally sized blocks. The algorithm has just to find the block
containing the item of interest. The queries are exactly the same as in the
standard database search problem. [RG] invented a quantum algorithm for this
problem of partial search that took about fewer iterations
than the quantum search algorithm. They also proved that the best any quantum
algorithm could do would be to save iterations. The main
limitation of the algorithm was that it involved complicated analysis as a
result of which it has been inaccessible to most of the community. This paper
gives a simple analysis of the algorithm. This analysis is based on three
elementary observations about quantum search, does not require a single
equation and takes less than 2 pages.Comment: 3 pages, 3 figure
Quantum computers can search arbitrarily large databases by a single query
This paper shows that a quantum mechanical algorithm that can query
information relating to multiple items of the database, can search a database
in a single query (a query is defined as any question to the database to which
the database has to return a (YES/NO) answer). A classical algorithm will be
limited to the information theoretic bound of at least O(log N) queries (which
it would achieve by using a binary search).Comment: Several enhancements to the original pape
Quantum computers can search rapidly by using almost any transformation
A quantum computer has a clear advantage over a classical computer for
exhaustive search. The quantum mechanical algorithm for exhaustive search was
originally derived by using subtle properties of a particular quantum
mechanical operation called the Walsh-Hadamard (W-H) transform. This paper
shows that this algorithm can be implemented by replacing the W-H transform by
almost any quantum mechanical operation. This leads to several new applications
where it improves the number of steps by a square-root. It also broadens the
scope for implementation since it demonstrates quantum mechanical algorithms
that can readily adapt to available technology.Comment: This paper is an adapted version of quant-ph/9711043. It has been
modified to make it more readable for physicists. 9 pages, postscrip
Grover's quantum searching algorithm is optimal
I improve the tight bound on quantum searching by Boyer et al.
(quant-ph/9605034) to a matching bound, thus showing that for any probability
of success Grovers quantum searching algorithm is optimal. E.g. for near
certain success we have to query the oracle pi/4 sqrt{N} times, where N is the
size of the search space. I also show that unfortunately quantum searching
cannot be parallelized better than by assigning different parts of the search
space to independent quantum computers. Earlier results left open the
possibility of a more efficient parallelization.Comment: 13 pages, LaTeX, essentially published versio
Hamiltonian and measuring time for analog quantum search
We derive in this study a Hamiltonian to solve with certainty the analog
quantum search problem analogue to the Grover algorithm. The general form of
the initial state is considered. Since the evaluation of the measuring time for
finding the marked state by probability of unity is crucially important in the
problem, especially when the Bohr frequency is high, we then give the exact
formula as a function of all given parameters for the measuring time.Comment: 5 page
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
Realization of generalized quantum searching using nuclear magnetic resonance
According to the theoretical results, the quantum searching algorithm can be
generalized by replacing the Walsh-Hadamard(W-H) transform by almost any
quantum mechanical operation. We have implemented the generalized algorithm
using nuclear magnetic resonance techniques with a solution of chloroform
molecules. Experimental results show the good agreement between theory and
experiment.Comment: 11 pages,3 figure. Accepted by Phys. Rev. A. Scheduled Issue: 01 Mar
200
Scattering quantum random-walk search with errors
We analyze the realization of a quantum-walk search algorithm in a passive,
linear optical network. The specific model enables us to consider the effect of
realistic sources of noise and losses on the search efficiency. Photon loss
uniform in all directions is shown to lead to the rescaling of search time.
Deviation from directional uniformity leads to the enhancement of the search
efficiency compared to uniform loss with the same average. In certain cases
even increasing loss in some of the directions can improve search efficiency.
We show that while we approach the classical limit of the general search
algorithm by introducing random phase fluctuations, its utility for searching
is lost. Using numerical methods, we found that for static phase errors the
averaged search efficiency displays a damped oscillatory behaviour that
asymptotically tends to a non-zero value.Comment: 10 pages, 10 figures. Two figures added for clarity, also made
improvements to the tex
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