Related papers: Numerical search for a fundamental theory
This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Quantum Monte Carlo simulations offer an unbiased means to study the static and dynamic properties of quantum critical systems, while quantum field theory provides direct analytical results. We study three dimensional, critical quantum…
Using the discrete-scale invariance theory, we show that the coupling constants of fundamental forces, the atomic masses and energies, and the elementary particle masses, obey to the fractal properties.
The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as…
We show, through Monte Carlo simulations, that the Alcock-Paczynski test, as applied to quasar clustering, is a powerful tool to probe the cosmological density and equation of state parameters, Omega_{m0}, Omega_{x0} and w. By taking into…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…
Precision measurements of the fundamental constants are tour de force of basic metrology, where the useful information is usually beyond the last digit of the measured value. They challenge theoretical models and measurement technologies…
This review article is devoted to application of precision molecular spectroscopy to studies of the possible spatial and temporal variations of the fundamental constants. Both astrophysical observations and laboratory experiments are…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called…
A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every…
It is argued that the CODATA recommended values of the fundamental physical constants could not be used as the reference data in searching the hypothetical space-time variations of the fundamental physical constants. It is shown that the…
We consider the current results in search for and description of temporal variations of fundamental physical constants (FPCs) obtained under laboratory and astrophysical conditions. On the basis of fixed values of base constants, those FPCs…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the…