Joint EigenValue Decomposition for Quantum Information Theory and Processing

The interest in quantum information processing has given rise to the development of programming languages and tools that facilitate the design and simulation of quantum circuits. However, since the quantum theory is fundamentally based on linear algebra, these high-level languages partially hide the underlying structure of quantum systems. We show that in certain cases of practical interest, keeping a handle on the matrix representation of the quantum systems is a fruitful approach because it allows the use of powerful tools of linear algebra to better understand their behavior and to better implement simulation programs. We especially focus on the Joint EigenValue Decomposition (JEVD). After giving a theoretical description of this method, which aims at finding a common basis of eigenvectors of a set of matrices, we show how it can easily be implemented on a Matrix-oriented programming language, such as Matlab (or, equivalently, Octave). Then, through two examples taken from the quantum information domain (quantum search based on a quantum walk and quantum coding), we show that JEVD is a powerful tool both for elaborating new theoretical developments and for simulation

“LORENZ ATTRACTOR” FROM DIFFERENTIAL EQUATIONS WITH PIECEWISE-LINEAR TERMS

International audienceIn this paper we present a simple piecewise-linear circuit which exhibits a chaotic attractor similar to that observed from the Lorenz equation. Whereas the nonlinearities in the Lorenz equation consists of two product terms between two state variables, the nonlinearities in our circuit consists of two piecewise-linear terms

Inverse of Fermat Number Transform Using the Sliding Technique

International audienceThis paper is about a new efficient method for the implementation of convolvers and correlators using the Fermat Number Transform (FNT) and the inverse (IFNT). The latter present advantages compared to Inverse Fast Fourier Transform (IFFT). An efficient state space method for implementing the Inverse FNT (IFNT) over rectangular windows is proposed for the cases where there is a large overlap between the consecutive input signals. This is called Inverse Generalized Sliding Fermat Number Transform (IGSFNT) and is useful for reducing the computational complexity of finite ring convolvers and correlators. This algorithm uses the technique of Generalized Sliding associated to matricial calculation in the Galois Field. The computational complexity of this method is compared with that of standard IFNT

Optimal generalized design of transform-based block digital filters

International audienceTransform-based block implementation of digital filters is useful for high throughput filtering due to inherent parallelism and complexity reduction provided by using the fast transforms. In basic form, for example the overlap-save implementation, the block digital filter (BDF) is represented by a vector. In this paper, the basic form of block filtering and the optimal design of BDF are described. Therefore, we propose a generalization of the block digital filtering where the BDF is represented by a matrix. This generalized form and its corresponding optimal BDF design are developed. The generalized BDF allows reducing the global distortion of the block filtering

Block Robust Algorithm for Network Echo Cancellation

http://www.praiseworthyprize.com/IRECAP.htmInternational audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. Recently a fast converging algorithm called Robust Proportionate Normalized Least Mean Squares (RPNLMS++) against double-talk has been proposed. This paper presents a realization of an improved version of the previous RPNLMS++ adaptive filter using block structure in which the filter coefficients are adjusted one per each output block. Then, an efficient implementation of the block filtering process is proposed using Number Theoretic Transforms (NTT) which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor (DSP). Analyses of convergence properties, during single and double-talk, and complexity show that the new block adaptive filter permits fast implementations while maintaining performance equivalent to that of the widely used RPNLMS++ adaptive filter

New approach for the treatement of FBRLS algorithm with long impulse response

International audienc

Fast Algorithm for Optimal Design of Bloc Digital Filters Based on Circulant Matrices

International audienceBlock digital filtering has been suggested to reduce the computational complexity and to increase the parallelism of computation in digital filtering systems. In this letter, a fast algorithm for optimal design of block digital filters (BDFs) is developed. This algorithm, based on circulant, Toeplitz and shift cyclic matrices, not only reduces the computational complexity of the design process but also decreases the memory requirements

Overlap-Save and Overlap-Add Filters: Optimal Design and Comparison

International audienceOverlap-save (OLS) and overlap-add (OLA) are two techniques widely used in digital filtering. In traditional OLS and OLA implementations, the system is compelled to be time-invariant and conventional filter synthesis techniques are used for designing the block filter. In this paper, based on the OLS and the OLA structures, we develop a fast algorithm for designing the optimal OLS and OLA block filters using a quadratic criterion. Comparing OLA to OLS optimal design, we demonstrate that, as in classical design approaches, they show no difference when the filters are time-invariant. However, when aliasing is not zero, although the global aliasing is the same, its components with respect to frequency are different. This conclusion is supported by simulation results, and a comparison between the optimal approach and some other standard approaches is also provided

Design of a variable rate algorithm for CS-ACELP coder

International audienceThis paper is about the reduction of the computational complexity of the CS-ACELP codec, described in ITU recommendation G.729, and used for the transmission of voice over IP. A voice activity detection module is proposed to replace the G.729 Annex B algorithm. The new procedure was developed to allow its implementation with number theoretic transforms. The use of Fermat number transforms can reduce the cost of variable rate algorithm implementation on digital signal processor (DSP)

Fast pitch modelling for CS-ACELP coder using Fermat Number Transforms

International audienceThis paper presents a double improvements to reduce the speech coding complexity of the pitch prediction in a code-excited linear prediction (CELP) coder. First, the pitch analysis structure is modified. A new fast pitch modelling by linear-filtering (PMF) procedure will determine the adaptive and stochastic codebook contributions of the excitation signal. Afterwards, an efficient implementation of the PMF-CELP coding is proposed by using number theoretic transforms which can significantly reduce the algorithm computation complexity