Nicolas Macris
Adjunct Professor
+41 21 693 81 14
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+41 21 693 81 14
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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.
Awards
Publications
Selected publications
| A. Bodin, N. Macris Proceedings of Machine Learning Research (2021) 34th Conference on Learning Theory COLT; Boulder |
Rank-one matrix estimation: analytic time evolution of gradient descent dynamics |
| J. Barbier, F. Krzakala, N. Macris, L. Miolane, L. Zdeborová Proceedings of the National Academy of Science (PNAS) vol 116 (12) pp. 5451-5460 (2019) |
Optimal errors and phase transitions in high-dimensional generalized linear models |
| J. Barbier, N. Macris Journal of Physics A: Mathematical and General (2019); Special issue in honour of G. Parisi’s 70th birthday, Disordered serendipity: a glassy path to discovery |
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models |
| A. Giurgiu, N. Macris and R. Urbanke IEEE Transactions on Information Theory vol 62, no 10, pp. 5281-5295 (2016) |
Spatial Coupling as a Proof Technique and Three Applications |
| S. Kumar, A. J. Young, N. Macris, H. D. Pfister IEEE Transactions on Information Theory vol 60, no 12, pp. 7389-7415 (2014) |
Threshold saturation for spatially-coupled LDPC and LDGM codes on BMS channels |
| N. Macris IEEETransactions on Information Theory, vol 53 pp. 664-683 (2007) |
Griffiths-Kelly-Sherman correlation inequalities:A useful tool in the theory of error correcting codes |
| T. C. Dorlas, N. Macris and J. V. Pulé Communications in Mathematical Physics, vol 204 pp. 367-396 (1999) |
Characterization of the spectrum of the Landau Hamiltonian with delta impurities |
| N. Macris, P. A. Martin and J. V. Pulé Journal of Physics A: Mathematical General, vol 32 pp. 1985-1996 (1999) |
On edge states in semi-infinite quantum Hall systems |
Research
Brief description
My recent research has focused on error correction and graphical models, as well as inference and learning theory. The problems involved have deep relations, both in terms of concepts and methods, with the statistical mechanics of disordered systems and in particular spin and structural glasses on sparse or dense graphs. The emphasis is on rigorous results and methods, and these subjects are investigated using a mix of methods from mathematical and statistical physics, probability, functional analysis and discrete mathematics.I am also interested in various aspects of quantum information theory.
In the past I have also worked in the field of mathematical physics on quantum Coulomb systems, quantum statistical mechanical models related to condensed matter physics, random magnetic Schroedinger operators, and mathematical aspects of the quantum Hall effect.
This research is supported by grants of the Swiss National Foundation for Science.
Selected publications organized by themes are found below.
Inference and learning theory
Rank-one matrix estimation: analytic time evolution of gradient descent dynamics; to appear in Proceedings of Machine Learning Research 2021, 34th Conference on Learning Theory COLT; A. Bodin, N. MacrisTensor estimation with structured priors; IEEE Journal on Selected Areas in Information Theory, vol 1, Issue 3, pp. 705 - 722 (2020); C. Luneau, N. Macris
Optimal errors and phase transitions in high-dimensional generalized linear models; Proceedings of the National Academy of Science (PNAS) vol 116 (12) pp. 5451-5460 (2019); J. Barbier, F. Krzakala, N. Macris, L. Miolane, L. Zdeborová
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models; Journal of Physics A: Mathematical and General (2019); Special issue in honour of G. Parisi’s 70th birthday, Disordered serendipity: a glassy path to discovery; J. Barbier, N.Macris
The layered structure of tensor estimation and its mutual information, 55th Annual Allerton Conference on Communication, Control, and Computing Allerton (2017); J. Barbier, N. Macris, L. Miolane
Graphical models and error correction
Displacement convexity in spatially coupled scalar recursions, IEEE Transactions on InformationTheory, vol 65, no 1, pp. 604-621 (2019) pp. 1-33; R. El-Khatib, N. Macris, T. Richardson, R. UrbankeSpatial coupling as a proof technique and three applications, IEEE Transactions on Information Theory vol 62, no 10, pp. 5281-5295 (2016); A. Giurgiu, N. Macris and R. Urbanke
Threshold saturation for spatially-coupled LDPC and LDGM codes on BMS channels, IEEE Transactions on Information Theory vol 60, no 12, pp. 7389-7415 (2014); arXiv:1309.7543; S. Kumar, A. J. Young, N. Macris, H. D. Pfister
Bounds for random constraint satisfaction problems via spatial coupling, in Proceedings 27th ACM SIAM Symposium on Discrete Algorithms (SODA) 2016, pp 469-479; D. Achlioptas, H. Hassani, N. Macris and R. Urbanke [long version is here]
Griffiths-Kelly-Sherman correlation inequalities: A useful tool in the theory of error correcting codes, IEEE Transactions on Information Theory, vol 53 pp. 664-683 (2007); N. Macris
Quantum information
Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer; Entropy 2021, 23(7), 797; Elias Riedel Garding, Nicolas Schwaller, Su Yeon Chang, Samuel Bosch, Willy Robert Laborde, Javier Naya Hernandez, Chun Lam Chan, Frédéric Gessler, Xinyu Si, Marc-André Dupertuis, Nicolas Macris (IBM Q second prize best paper award 2019)Efficient Quantum Algorithms for GHZ and W States, and Implementation on the IBM Quantum Computer ; Advanced Quantum Technologies 2 (5-6) (2019); Diogo Cruz, Romain Fournier, Fabien Gremion, Alix Jean- nerot, Kenichi Komagata, Tara Tosic, Jarla Thiesbrummel, Chun Lam Chan, Nicolas Macris, Marc-André Dupertuis, Clément Javerzac-Galy (IBM Q second prize best paper award 2018)Magnetic Schroedinger operators and quantum Hall e
Spectral flow and level spacing of edge states for quantum Hallhamiltonians, Journal of Physics A: Mathematical and General, vol 36 pp. 1565-1581 (2003); N. MacrisOn the equality of edge and bulk conductance in the integer Hall effect: a microscopic analysis, N. Macris (2002)
unpublished preprint
On edge states in semi-infinite quantum Hall systems, Journal of Physics A: Mathematical and General,vol 32 pp. 1985-1996 (1999); N. Macris, P. A. Martin and J. V. Pulé
Characterization of the spectrum of the Landau hamiltonian with delta impurities, Communications in Mathematical Physics, vol 204 pp. 367-396 (1999); T. C. Dorlas, N. Macris and J. V. Pulé
The nature of the spectrum for a Landau hamiltonian with delta impurities, Journal of Statistical Physics, vol 87 pp. 847-875 (1997); T. C. Dorlas, N. Macris and J. V. Pulé
Quantum statistical mechanics
On kink states of ferromagnetic chains, Physica A, vol 279 pp. 386-397 (2000) special issue in honor of Joel Lebowitz; Ky-Thuan Bach and N. MacrisPhase separation and the segregation principle in the infinite-U spinless Falicov-Kimball model, Physical Review B, vol 60 pp. 1617-1626 (1999); J. K. Freericks, C. Gruber and N. Macris
On the flux phase conjecture at half filling: an improved proof, Journal of Statistical Physics, vol 85 pp. 745-761 (1996); N. Macris and B. Nachtergaele
Ground states and low temperature phases of itinerant electrons interacting with classical fields: a review of rigorous results, Journal of Mathematical Physics, vol 38 pp. 2084-2103 (1997) special issue on condensed matter physics; J. L. Lebowitz and N. Macris
The Falicov-Kimball model: a review of exact results and extensions, Helvetica Physica Acta, vol 69 pp. 850-907 (1996) special issue in honor of K. Hepp and W. Hunziker; C. Gruber and N. Macris
Teaching & PhD
Teaching
Communication Systems
Computer Science
Electrical and Electronics Engineering
PhD Students
George Anand Jerry, Remizova Anastasia, Vantalon Perrine Karine Christiane,Past EPFL PhD Students
Bodin Antoine Philippe Michel , Chan Chun Lam , Dia Mohamad Baker , El-Khatib Rafah , Giurgiu Andrei , Hassani Seyed Hamed , Korada Satish Babu , Kudekar Shrinivas , Luneau Clément Dominique , Pourkamali Farzad , Vuffray Marc ,Lecture notes
N-body methods in condensed matter, Lecture notes of the troisième cycle de la physique en Suisse Romande, 160 pp, first version (2002), second revised version (2009), D. Baeriswyl and N. Macris, https://physique.cuso.ch/cours/archives/notes-de-cours-2008Statistical Physics for Communications, Signal Processing, and Computer Science, 364 pp, Lecture notes in progress, doctoral class (2017 edition) N. Macris and R. Urbanke
Courses
Introduction to 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.
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.
Learning theory
- Basics : statistical learning framework, Probably Approximately Correct (PAC) learning, learning with a finite number of classes, Vapnik-Chervonenkis (VC).
- Bias-variance tradeoff and modern double descent phenomena.
- Stochastic gradient descent, modern aspects: mean field approach, neural tangent kernel.
- Diffusion methods.
- Tensor decompositions and fac
Introduction to quantum science and technology
Introduction
- Overview of the frontiers of quantum science, technology and applications.
- Introduction to qubits, quantum states, measurements, evolution. Axiomatic formulation.
- Illustration with two level systems, Bloch sphere, Spin, spin Hamiltonians
Aspects of quantum science and sustainability
We explore the intersection of quantum technologies and sustainability. Topics: 1)discussions of fundamental aspects of thermodynamics of computation; 2)analysis and benchmarks of energy consumption in current and near term real quantum devices; 3)projects on use cases through personal student work.