1,646 research outputs found
Minimal resources for linear optical one-way computing
We address the question of how many maximally entangled photon pairs are
needed in order to build up cluster states for quantum computing using the
toolbox of linear optics. As the needed gates in dual-rail encoding are
necessarily probabilistic with known optimal success probability, this question
amounts to finding the optimal strategy for building up cluster states, from
the perspective of classical control. We develop a notion of classical
strategies, and present rigorous statements on the ultimate maximal and minimal
use of resources of the globally optimal strategy. We find that this strategy -
being also the most robust with respect to decoherence - gives rise to an
advantage of already more than an order of magnitude in the number of maximally
entangled pairs when building chains with an expected length of L=40, compared
to other legitimate strategies. For two-dimensional cluster states, we present
a first scheme achieving the optimal quadratic asymptotic scaling. This
analysis shows that the choice of appropriate classical control leads to a very
significant reduction in resource consumption.Comment: 5 pages, 2 figures, title changed, presentation improved, bounds
improved, minor errors corrected, references update
Several types of types in programming languages
Types are an important part of any modern programming language, but we often
forget that the concept of type we understand nowadays is not the same it was
perceived in the sixties. Moreover, we conflate the concept of "type" in
programming languages with the concept of the same name in mathematical logic,
an identification that is only the result of the convergence of two different
paths, which started apart with different aims. The paper will present several
remarks (some historical, some of more conceptual character) on the subject, as
a basis for a further investigation. The thesis we will argue is that there are
three different characters at play in programming languages, all of them now
called types: the technical concept used in language design to guide
implementation; the general abstraction mechanism used as a modelling tool; the
classifying tool inherited from mathematical logic. We will suggest three
possible dates ad quem for their presence in the programming language
literature, suggesting that the emergence of the concept of type in computer
science is relatively independent from the logical tradition, until the
Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC
Software needs in special functions
AbstractCurrently available software for special functions exhibits gaps and defects in comparison to the needs of moderm high-performance scientific computing and also, surprisingly, in comparison to what could be constructed from current algorithms. In this paper we expose some of these deficiencies and identify the related need for user-oriented testing software
Chapter 1 Principles of Mathematical Modeling
Mathematical Modeling describes a process and an object by use of the mathematical language. A process or an object is presented in a "pure form" in Mathematical Modeling when external perturbations disturbing the study are absent. Computer simulation is a natural continuation of the Mathematical Modeling. Computer simulation can be considered as a computer experiment which corresponds to an experiment in the real world. Such a treatment is rather related to numerical simulations. Symbolic simulations yield more than just an experiment. Mathematical Modeling of stochastic processes is based on the probability theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools. Symbolic simulations are usually realized in the form of solution to equations in one unknown, to a system of linear algebraic equations, both ordinary and partial differential equations (ODE and PDE). Various mathematical approaches to stability are discussed in courses of ODE and PDE
Chapter 1 Principles of Mathematical Modeling
Mathematical Modeling describes a process and an object by use of the mathematical language. A process or an object is presented in a "pure form" in Mathematical Modeling when external perturbations disturbing the study are absent. Computer simulation is a natural continuation of the Mathematical Modeling. Computer simulation can be considered as a computer experiment which corresponds to an experiment in the real world. Such a treatment is rather related to numerical simulations. Symbolic simulations yield more than just an experiment. Mathematical Modeling of stochastic processes is based on the probability theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools. Symbolic simulations are usually realized in the form of solution to equations in one unknown, to a system of linear algebraic equations, both ordinary and partial differential equations (ODE and PDE). Various mathematical approaches to stability are discussed in courses of ODE and PDE
- …