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Person# Nicolas Macris

Biography

Nicolas Macris received the PhD degree in theoretical physics from EPFL and then pursued his scientific activity at the mathematics department of Rutgers University (NJ, USA). He then joined the Faculty of Basic Science of EPFL, working in the field of quantum statistical mechanics and mathematical aspects of the quantum Hall effect. Since 2005 he is with the Communication Theories Laboratory and Information Processing group of the School of Communication and Computer Science and currently works at the interface of statistical mechanics, information theory and error correcting codes, inference and learning theory. He held long-term visiting appointments and collaborations with the University College and the Institute of Advanced studies in Dublin, the Ecole Normale Supérieure de Lyon, the Centre de Physique Theorique Luminy Marseille, Paris XI Orsay, the ETH Zürich and more recently Los Alamos National Lab. CV and publication list.

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Courses taught by this person (7)

COM-309: Quantum information processing

Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prior knowledge of quantum physics is required.

COM-516: Markov chains and algorithmic applications

The study of random walks finds many applications in computer science and communications. The goal of the course is to get familiar with the theory of random walks, and to get an overview of some applications of this theory to problems of interest in communications, computer and network science.

COM-611: Quantum Information Theory and Computation

Today one is able to manipulate matter at the nanoscale were quantum behavior becomes important and possibly information processing will have to take into account laws of quantum physics. We introduce concepts developed in the last 25 years to take advantage of quantum resources.

Related research domains (89)

In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed usi

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies th

In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for c

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Jean François Emmanuel Barbier, Chun Lam Chan, Nicolas Macris

Recently, a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and generalized estimation, sparse superposition codes, and low-rank matrix / tensor estimation. For all these systems, the adaptive interpolation method directly proves that the replica-symmetric prediction is exact, in a simple and unified manner. When the underlying factor graph of the inference problem is sparse the replica prediction is considerably more complicated, and rigorous results are often lacking or obtained by rather complicated methods. In this work we show how to extend the adaptive path interpolation method to sparse systems. We concentrate on a censored block model, where hidden variables are measured through a binary erasure channel, for which we fully prove the replica prediction.

Jean François Emmanuel Barbier, Nicolas Macris

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existing literature concerned with the low-rank (i.e., constant-rank) regime. We first consider a class of rotationally invariant matrix denoising problems whose mutual information and minimum mean-square error are computable using techniques from random matrix theory. Next, we analyze the more challenging models of dictionary learning. To do so we introduce a combination of the replica method from statistical mechanics together with random matrix theory, coined spectral replica method. This allows us to derive variational formulas for the mutual information between hidden representations and the noisy data of the dictionary learning problem, as well as for the overlaps quantifying the optimal reconstruction error. The proposed method reduces the number of degrees of freedom from circle minus(N-2) matrix entries to circle minus(N) eigenvalues (or singular values), and yields Coulomb gas representations of the mutual information which are reminiscent of matrix models in physics. The main ingredients are a combination of large deviation results for random matrices together with a replica symmetric decoupling ansatz at the level of the probability distributions of eigenvalues (or singular values) of certain overlap matrices and the use of Harish-Chandra-Itzykson-Zuber spherical integrals.

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We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.

2021