Related papers: Integrals of functions containing parameters
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
Gauge-invariance is a mathematical concept that has profound implications in Physics---as it provides the justification of the fundamental interactions. It was recently adapted to the Cellular Automaton (CA) framework, in a restricted case.…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
These lecture notes from the 2019 Les Houches Summer School on 'Quantum Information Machines' are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems…
A sketch of a recent approach to quantum gravity is presented which involves several unconventional aspects. The basic ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach for…
Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com putations update internal states and…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…