2,165 research outputs found
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
Nested quantum search and NP-complete problems
A quantum algorithm is known that solves an unstructured search problem in a
number of iterations of order , where is the dimension of the
search space, whereas any classical algorithm necessarily scales as . It
is shown here that an improved quantum search algorithm can be devised that
exploits the structure of a tree search problem by nesting this standard search
algorithm. The number of iterations required to find the solution of an average
instance of a constraint satisfaction problem scales as , with
a constant depending on the nesting depth and the problem
considered. When applying a single nesting level to a problem with constraints
of size 2 such as the graph coloring problem, this constant is
estimated to be around 0.62 for average instances of maximum difficulty. This
corresponds to a square-root speedup over a classical nested search algorithm,
of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure
Out Where The Billows Roll High : Baritone or Contralto
https://digitalcommons.library.umaine.edu/mmb-vp/4489/thumbnail.jp
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.
Fatigue Strength and Related Characteristics of Joints in 24s-t Alclad Sheet
Report includes tension fatigue test results on the following types of samples of 0.040-inch alclad 24s-t: (1) monoblock sheet samples as received and after a post-aging heat treatment, (2) "sheet efficiency" samples (two equally stressed sheets joined by a single transverse row of spot welds) both as received and after post-aging, (3) spot-welded lap-joint samples as received and after post-aging, and (4) roll-welded lap-joint samples. (author
Quantum Portfolios
Quantum computation holds promise for the solution of many intractable
problems. However, since many quantum algorithms are stochastic in nature they
can only find the solution of hard problems probabilistically. Thus the
efficiency of the algorithms has to be characterized both by the expected time
to completion {\it and} the associated variance. In order to minimize both the
running time and its uncertainty, we show that portfolios of quantum algorithms
analogous to those of finance can outperform single algorithms when applied to
the NP-complete problems such as 3-SAT.Comment: revision includes additional data and corrects minor typo
Quantum complexities of ordered searching, sorting, and element distinctness
We consider the quantum complexities of the following three problems:
searching an ordered list, sorting an un-ordered list, and deciding whether the
numbers in a list are all distinct. Letting N be the number of elements in the
input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm
uses a quantum routine for traversing through a binary search tree faster than
classically, and it is of a nature very different from a faster algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some
of the results have previously been presented at QIP '01. This paper subsumes
the papers quant-ph/0009091 and quant-ph/000903
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