961 research outputs found
Effects of imperfections for Shor's factorization algorithm
We study effects of imperfections induced by residual couplings between
qubits on the accuracy of Shor's algorithm using numerical simulations of
realistic quantum computations with up to 30 qubits. The factoring of numbers
up to N=943 show that the width of peaks, which frequencies allow to determine
the factors, grow exponentially with the number of qubits. However, the
algorithm remains operational up to a critical coupling strength
which drops only polynomially with . The numerical dependence of
on is explained by analytical estimates that allows to
obtain the scaling for functionality of Shor's algorithm on realistic quantum
computers with a large number of qubits.Comment: 10 pages, 10 figures, 1 table. Added references and new data. Erratum
added as appendix. 1 Figure and 1 Table added. Research is available at
http://www.quantware.ups-tlse.fr
Lautman and the Reality of Mathematics
Working in he 1930s, Albert Lautman described with extraordinary clarity the new understanding of mathematics of that time. He delighted in the multiple manifestations of a common idea in different mathematical fields. However, he took the common idea to belong not to mathematics itself, but to an 'ideal reality' sitting above mathematics. I argue in this paper that now that we have a mathematical language which can characterize these common ideas, we need not follow Lautman to adopt his form of Platonism. On the other hand, Lautman should be much better known than he is for pointing philosophy towards this most important feature of mathematics
Dynamical localization simulated on a few qubits quantum computer
We show that a quantum computer operating with a small number of qubits can
simulate the dynamical localization of classical chaos in a system described by
the quantum sawtooth map model. The dynamics of the system is computed
efficiently up to a time , and then the localization length
can be obtained with accuracy by means of order computer runs,
followed by coarse grained projective measurements on the computational basis.
We also show that in the presence of static imperfections a reliable
computation of the localization length is possible without error correction up
to an imperfection threshold which drops polynomially with the number of
qubits.Comment: 8 pages, 8 figure
Eigenstates of Operating Quantum Computer: Hypersensitivity to Static Imperfections
We study the properties of eigenstates of an operating quantum computer which
simulates the dynamical evolution in the regime of quantum chaos. Even if the
quantum algorithm is polynomial in number of qubits , it is shown that the
ideal eigenstates become mixed and strongly modified by static imperfections
above a certain threshold which drops exponentially with . Above this
threshold the quantum eigenstate entropy grows linearly with but the
computation remains reliable during a time scale which is polynomial in the
imperfection strength and in .Comment: revtex, 4 pages, 4 figure
On function field Mordell-Lang and Manin-Mumford
We present a reduction of the function field Mordell-Lang conjecture to the
function field Manin-Mumford conjecture, in all characteristics, via model
theory, but avoiding recourse to the dichotomy theorems for (generalized)
Zariski structures.
In this version 2, the quantifier elimination result in positive
characteristic is extended from simple abelian varieties to all abelian
varieties, completing the main theorem in the positive characteristic case.
In version 3, some corrections are made to the proof of quantifier
elimination in positive characteristic, and the paper is substantially
reorganized.Comment: 21 page
On function field Mordell-Lang: the semiabelian case and the socle theorem
We here aim to complete our model-theoretic account of the function field
Mordell-Lang conjecture, avoiding appeal to dichotomy theorems for Zariski
geometries, where we now consider the general case of semiabelian varieties.
The main result is a reduction, using model-theoretic tools, of the semiabelian
case to the abelian case.Comment: 43 pages. Some minor corrections and clarifications were made
following a referee's repor
Communities and beyond: mesoscopic analysis of a large social network with complementary methods
Community detection methods have so far been tested mostly on small empirical
networks and on synthetic benchmarks. Much less is known about their
performance on large real-world networks, which nonetheless are a significant
target for application. We analyze the performance of three state-of-the-art
community detection methods by using them to identify communities in a large
social network constructed from mobile phone call records. We find that all
methods detect communities that are meaningful in some respects but fall short
in others, and that there often is a hierarchical relationship between
communities detected by different methods. Our results suggest that community
detection methods could be useful in studying the general mesoscale structure
of networks, as opposed to only trying to identify dense structures.Comment: 11 pages, 10 figures. V2: typos corrected, one sentence added. V3:
revised version, Appendix added. V4: final published versio
Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance
In this paper, we consider the coherent theory of (epistemic) uncertainty of
Walley, in which beliefs are represented through sets of probability
distributions, and we focus on the problem of modeling prior ignorance about a
categorical random variable. In this setting, it is a known result that a state
of prior ignorance is not compatible with learning. To overcome this problem,
another state of beliefs, called \emph{near-ignorance}, has been proposed.
Near-ignorance resembles ignorance very closely, by satisfying some principles
that can arguably be regarded as necessary in a state of ignorance, and allows
learning to take place. What this paper does, is to provide new and substantial
evidence that also near-ignorance cannot be really regarded as a way out of the
problem of starting statistical inference in conditions of very weak beliefs.
The key to this result is focusing on a setting characterized by a variable of
interest that is \emph{latent}. We argue that such a setting is by far the most
common case in practice, and we provide, for the case of categorical latent
variables (and general \emph{manifest} variables) a condition that, if
satisfied, prevents learning to take place under prior near-ignorance. This
condition is shown to be easily satisfied even in the most common statistical
problems. We regard these results as a strong form of evidence against the
possibility to adopt a condition of prior near-ignorance in real statistical
problems.Comment: 27 LaTeX page
Early aspects: aspect-oriented requirements engineering and architecture design
This paper reports on the third Early Aspects: Aspect-Oriented Requirements Engineering and Architecture Design Workshop, which has been held in Lancaster, UK, on March 21, 2004. The workshop included a presentation session and working sessions in which the particular topics on early aspects were discussed. The primary goal of the workshop was to focus on challenges to defining methodical software development processes for aspects from early on in the software life cycle and explore the potential of proposed methods and techniques to scale up to industrial applications
Strategic Insider Trading with Imperfect Information: A Trading Volume Analysis
A model of insider trading is used to analyze the behaviour of trading volume in financial markets characterized by asymmetric information. This model extends the one in Bhattacharya and Nicodano (2001) by introducing competition among informed traders and imperfection of their private information. Contrary to the broad implications of adverse selection models and according to some empirical studies, this paper shows that trading volume is higher when the insiders are active in the market. A higher level of outsidersâ risky investment, due to an improved ĂąâŹĆrisk sharingù⏠among them, leads to a higher level of trading.
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