3,076 research outputs found
Entangled Quantum States Generated by Shor's Factoring Algorithm
The intermediate quantum states of multiple qubits, generated during the
operation of Shor's factoring algorithm are analyzed. Their entanglement is
evaluated using the Groverian measure. It is found that the entanglement is
generated during the pre-processing stage of the algorithm and remains nearly
constant during the quantum Fourier transform stage. The entanglement is found
to be correlated with the speedup achieved by the quantum algorithm compared to
classical algorithms.Comment: 7 pages, 4 figures submitted to Phys. Rev.
Online Pattern Matching for String Edit Distance with Moves
Edit distance with moves (EDM) is a string-to-string distance measure that
includes substring moves in addition to ordinal editing operations to turn one
string to the other. Although optimizing EDM is intractable, it has many
applications especially in error detections. Edit sensitive parsing (ESP) is an
efficient parsing algorithm that guarantees an upper bound of parsing
discrepancies between different appearances of the same substrings in a string.
ESP can be used for computing an approximate EDM as the L1 distance between
characteristic vectors built by node labels in parsing trees. However, ESP is
not applicable to a streaming text data where a whole text is unknown in
advance. We present an online ESP (OESP) that enables an online pattern
matching for EDM. OESP builds a parse tree for a streaming text and computes
the L1 distance between characteristic vectors in an online manner. For the
space-efficient computation of EDM, OESP directly encodes the parse tree into a
succinct representation by leveraging the idea behind recent results of a
dynamic succinct tree. We experimentally test OESP on the ability to compute
EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International
Symposium on String Processing and Information Retrieval (SPIRE2014
A Minimum-Labeling Approach for Reconstructing Protein Networks across Multiple Conditions
The sheer amounts of biological data that are generated in recent years have
driven the development of network analysis tools to facilitate the
interpretation and representation of these data. A fundamental challenge in
this domain is the reconstruction of a protein-protein subnetwork that
underlies a process of interest from a genome-wide screen of associated genes.
Despite intense work in this area, current algorithmic approaches are largely
limited to analyzing a single screen and are, thus, unable to account for
information on condition-specific genes, or reveal the dynamics (over time or
condition) of the process in question. Here we propose a novel formulation for
network reconstruction from multiple-condition data and devise an efficient
integer program solution for it. We apply our algorithm to analyze the response
to influenza infection in humans over time as well as to analyze a pair of ER
export related screens in humans. By comparing to an extant, single-condition
tool we demonstrate the power of our new approach in integrating data from
multiple conditions in a compact and coherent manner, capturing the dynamics of
the underlying processes.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Algebraic analysis of quantum search with pure and mixed states
An algebraic analysis of Grover's quantum search algorithm is presented for
the case in which the initial state is an arbitrary pure quantum state of n
qubits. This approach reveals the geometrical structure of the quantum search
process, which turns out to be confined to a four-dimensional subspace of the
Hilbert space. This work unifies and generalizes earlier results on the time
evolution of the amplitudes during the quantum search, the optimal number of
iterations and the success probability. Furthermore, it enables a direct
generalization to the case in which the initial state is a mixed state,
providing an exact formula for the success probability.Comment: 13 page
Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
The Groverian entanglement measure, G(psi), is applied to characterize a
variety of pure quantum states |psi> of multiple qubits. The Groverian measure
is calculated analytically for certain states of high symmetry, while for
arbitrary states it is evaluated using a numerical procedure. In particular, it
is calculated for the class of Greenberger-Horne-Zeilinger states, the W states
as well as for random pure states of n qubits. The entanglement generated by
Grover's algorithm is evaluated by calculating G(psi) for the intermediate
states that are obtained after t Grover iterations, for various initial states
and for different sets of the marked states.Comment: 28 pages, 5 figure
Quantum and approximation algorithms for maximum witnesses of Boolean matrix products
The problem of finding maximum (or minimum) witnesses of the Boolean product
of two Boolean matrices (MW for short) has a number of important applications,
in particular the all-pairs lowest common ancestor (LCA) problem in directed
acyclic graphs (dags). The best known upper time-bound on the MW problem for
n\times n Boolean matrices of the form O(n^{2.575}) has not been substantially
improved since 2006. In order to obtain faster algorithms for this problem, we
study quantum algorithms for MW and approximation algorithms for MW (in the
standard computational model). Some of our quantum algorithms are input or
output sensitive. Our fastest quantum algorithm for the MW problem, and
consequently for the related problems, runs in time
\tilde{O}(n^{2+\lambda/2})=\tilde{O}(n^{2.434}), where \lambda satisfies the
equation \omega(1, \lambda, 1) = 1 + 1.5 \, \lambda and \omega(1, \lambda, 1)
is the exponent of the multiplication of an n \times n^{\lambda}$ matrix by an
n^{\lambda} \times n matrix. Next, we consider a relaxed version of the MW
problem (in the standard model) asking for reporting a witness of bounded rank
(the maximum witness has rank 1) for each non-zero entry of the matrix product.
First, by adapting the fastest known algorithm for maximum witnesses, we obtain
an algorithm for the relaxed problem that reports for each non-zero entry of
the product matrix a witness of rank at most \ell in time
\tilde{O}((n/\ell)n^{\omega(1,\log_n \ell,1)}). Then, by reducing the relaxed
problem to the so called k-witness problem, we provide an algorithm that
reports for each non-zero entry C[i,j] of the product matrix C a witness of
rank O(\lceil W_C(i,j)/k\rceil ), where W_C(i,j) is the number of witnesses for
C[i,j], with high probability. The algorithm runs in
\tilde{O}(n^{\omega}k^{0.4653} +n^2k) time, where \omega=\omega(1,1,1).Comment: 14 pages, 3 figure
Surface states in nearly modulated systems
A Landau model is used to study the phase behavior of the surface layer for
magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz
point marking the boundary between modulated and homogeneous bulk phases. The
model incorporates surface and bulk fields and includes a term in the free
energy proportional to the square of the second derivative of the order
parameter in addition to the usual term involving the square of the first
derivative. In the limit of vanishing bulk field, three distinct types of
surface ordering are possible: a wetting layer, a non-wet layer having a small
deviation from bulk order, and a different non-wet layer with a large deviation
from bulk order which decays non-monotonically as distance from the wall
increases. In particular the large deviation non-wet layer is a feature of
systems at the Lifshitz point and also those having only homogeneous bulk
phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.
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