Exact Numerical Processing

Paper submitted to Euromicro Symposium on Digital Systems Design (DSD), Belek-Antalya, Turkey, 2003.A model of an exact arithmetic processing is presented. We describe a representation format that gives us a greater expressive capability and covers a wider numerical set. The rational numbers are represented by means of fractional notation and explicit codification of its periodic part. We also give a brief description of exact arithmetic operations on the proposed format. This model constitutes a good alternative for the symbolic arithmetic, in special when numerical exact values are required. As an example, we show an application of the exact numerical processing to calculate the perpendicular vector to another one for aerospace purposes.This work is being backed by grant DPI2002-04434-C04-01 from the Ministerio de Ciencia y Tecnología of the Spanish Government

Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain

Quantum dynamics of magnetic order in a chiral multiferroic chain is studied. We consider two different scenarios: Ultrashort terahertz (THz) excitations or a sudden electric field quench. Performing analytical and numerical exact diagonalization calculations we trace the pulse induced spin dynamics and extract quantities that are relevant to quantum information processing. In particular, we analyze the dynamics of the system chirality, the von Neumann entropy, the pairwise and the many body entanglement. If the characteristic frequencies of the generated states are non-commensurate then a partial loss of pair concurrence occurs. Increasing the system size this effect becomes even more pronounced. Many particle entanglement and chirality are robust and persist in the incommensurate phase. To analyze the dynamical quantum transitions for the quenched and pulsed dynamics we combined the Weierstrass factorization technique for entire functions and Lanczos exact diagonalization method. For a small system we obtained analytical results including the rate function of Loschmidt echo. Exact numerical calculations for a system up to 40 spins confirm phase transition. Quench- induced dynamical transitions have been extensively studied recently. Here we show that related dynamical transitions can be achieved and controlled by appropriate electric field pulses.Comment: 13 pages, 10 figures, submitted in PR

Fast Digital Convolutions using Bit-Shifts

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the Discrete Fourier Transform, with the canonical harmonics replaced by a set of cyclic integers computed using only bit-shifts and additions modulo a prime number. The prime number may be selected to occupy contemporary word sizes or to be very large for cryptographic or data hiding applications. The transform is an extension of the Rader Transforms via Carmichael's Theorem. These properties allow for exact convolutions that are impervious to numerical overflow and to utilise Fast Fourier Transform algorithms.Comment: 4 pages, 2 figures, submitted to IEEE Signal Processing Letter

Perturbation Theory for Quantum Computation with Large Number of Qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.Comment: 8 pages RevTex including 2 figure

Performance of Optimum Combining in a Poisson Field of Interferers and Rayleigh Fading Channels

This paper studies the performance of antenna array processing in distributed multiple access networks without power control. The interference is represented as a Poisson point process. Desired and interfering signals are subject to both path-loss fading (with an exponent greater than 2) and to independent Rayleigh fading. Using these assumptions, we derive the exact closed form expression for the cumulative distribution function of the output signal-to-interference-plus-noise ratio when optimum combining is applied. This results in a pertinent measure of the network performance in terms of the outage probability, which in turn provides insights into the network capacity gain that could be achieved with antenna array processing. We present and discuss examples of applications, as well as some numerical results.Comment: Submitted to IEEE Trans. on Wireless Communication (Jan. 2009