Frédéric Holweck

About

I am an Associate Professor at University of Technology Belfort-Montbéliard in France and a member of the Quantum Interactions and Control (ICQ) team of the Interdisciplinaire Carnot de Bourgogne (ICB) Laboratory. My research is on applied (algebraic) geometry with a specific interest in quantum information theory. I am a former student of Joseph Landsberg and colaborate today with several coauthors from around the world. Check out my publications to get an idea of my research topics.

At UTBM, I teach undergraduate and graduate students enrolled in engineering degrees in Computer Science and Mechanical Engineering. Resources for my classes can be found here (in french). I also teach in an international Master in Physics, Photonics and Nanotechnology at University Bourgogne Franche-Comté as well as in the French-Togolese Master degree in Computer Science at Lomé University in Togo.

In 2022-2023, I was a visiting associate professor at the Maths department of Auburn University.

Here is my vitae and a link to my Google Scholar profile.

frederic.holweck[at]utbm[dot]fr

Research

My current research is on applications of algebraic geometry to quantum information theory. This geometric approach splits in two directions: geometric description of entanglement and operator-based proofs of contextuality. In 2019 I defended my habilitation thesis intitled On the projective geometry of entanglement and contextuality. Here are my coauthors.

Publications/papers

1. Classically-embedded split Cayley hexagons rule three-qubit contextuality with three-element contexts (with Metod Saniga , Colm Kelleher, Axel Muller , Alain Giorgetti and Henri de Bourtray). arxiv.2312.07738
2. Two new non-equivalent three-qubit CHSH games (with Hamza Jaffali). arxiv.2312.00578
3. Implementing 2-qubit pseudo-telepathy games on noisy intermediate scale quantum computers with ( Colm Kelleher and Mohammad Rommy). arxiv.2310.07441
4. Maximally entangled real states and SLOCC invariants: the 3-qutrit case (with Hamza Jaffali and Luke Oeding). arxiv.2307.00970
5. New and improved bounds on the contextuality degree of multi-qubit configurations (with Metod Saniga , Axel Muller , Alain Giorgetti and Henri de Bourtray). arxiv.org.2305.10225
6. A hyperdeterminant on Fermionic Fock Space (with Luke Oeding). arxiv.2301.10660. To appear in Annales de l'Institut Henri Poincaré D
7. Graph States and the Variety of Principal Minors (with Vincenzo Galgano).Annali di Matematica Pura ed Applicata (1923-) 203 (1), 273-295. (2023).
8. Digital Optimal Robust Control (with Meri Harutyunyan, Dominique Sugny and Stéphane Guérin). Phys. Rev. Lett. 131, 200801
9. Quantum Control by Few-Cycles Pulses: The Two-Level Problem (with François Peyraut and Stéphane Guérin). Entropy 25 (2), 212
10. Contextuality degree of quandrics in multi-qubit symplectic polar space (with Henri de Bourtray, Pierre-Alain Masson, Alain Giorgetti and Metod Saniga). ournal of Physics A: Mathematical and Theoretical 55 (47), 475301 (2022).
11. Jordan Decompositions of Tensors (with Luke Oeding ). arxiv.2206.13662
12. Multi-qubit doilies: Enumeration for all ranks and classification for ranks four and five (with Axel Muller , Metod Saniga, Alain Giorgetti and Henri de Bourtray). Journal of Computational Science 64, 101853 (2022)
13. Three-qubit-embedded split Cayley hexagon is contextuality sensitive (with Henri de Bourtray, Metod Saniga). Scientific Reports 12 (1), 8915
14. Hyperdeterminants from the E8 Discriminant (with Luke Oeding ). Journal of Algebra (2022)
15. Entanglement and non-locality of four-qubit connected hypergraph states (with Grâce Amouzou, Jeoffrey Boffelli, Hamza Jaffali and Kossi Atchonouglo ). International Journal of Quantum Information 20 (03), 2250001 (2022)
16. A new hyperelastic strain energy function and integrity basis of invariants for modelling transversely isotropic materials(with Renye Cai, Feng Zhi-Qiang , François Peyraut). International Journal of Solids and Structures Volume 229, 15 October 2021, 111133.
17. Integrity basis of polyconvex invariants for modeling hyperelastic orthotropic materials — Application to the mechanical response of passive ventricular myocardium(with Renye Cai, Feng Zhi-Qiang , François Peyraut). International Journal of Non-Linear Mechanics Volume 133, July 2021, 103713.
18. Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank (with Metod Saniga, Henri de Bourtray and Alain Giorgetti). Mathematics 2021, 9(18), 2272; https://doi.org/10.3390/math9182272
19. Testing quantum contextuality of binary symplectic polar spaces on a Noisy Intermediate Scale Quantum Computer Quantum Inf Process 20, 247 (2021). https://doi.org/10.1007/s11128-021-03188-9
20. X-States from a finite geometric perspective (with Colm Kelleher, Peter Levay and Metod Saniga ). arxiv.2008.03063
21. Taxonomy of Three-Qubit Mermin Pentagrams (with Metod Saniga and Hamza Jaffali). Symmetry 12 (4), 534
22. Mermin Polynomials for Non-locality and Entanglement Detection in Grover's algorithm and Quantum Fourier Transform (with Henri de Bourtray, Hamza Jaffali, Pierre-Alain Masson and Alain Giorgetti). arXiv.2001.05192. Quantum Information Processing (2021) 20 (3), 1-29
23. Quantum Entanglement involved in Grover's and Shor's algorithms: the four-qubit case (with Hamza Jaffali). Quantum Information Processing 18 (5)
24. A finite geometric toy model of space-time as an error correcting code (with Péter Lévay). Phys. Rev. D. 99
25. Geometric constructions over ℂ and 𝔽2 for Quantum Information . in Quantum Physics and Geometry (Lecture Notes of the Unione Matematica Italiana) Springer 2019
26. Veldkamp Spaces of Low-Dimensional Ternary Segre Varieties (with Metod Saniga, Jérôme Boulmier and Maxime Pinard). Results in Mathematics 74 (1)
27. A fermionic code related to the exceptional group E 8 (with Peter Levay). Journal of Physics A: Mathematical and Theoretical 2018.
28. Magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy (with Metod Saniga, Peter Levay). Phys. Rev. D 96, 026018 – Published 24 July 2017.
29. A simple polyconvex strain energy density with new invariants for modeling four-fiber family biomaterials(with Renye Cai, Feng Zhi-Qiang , François Peyraut). International Journal of Solids and Structures Vol 115-116 2017.
30. Contextuality with Small Number of Observables (with Metod Saniga). International Journal of Quantum Information 15 (04) 2017.
31. Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world) (with Jean-Gabriel Luque and Jean-Yves Thibon). Journal of Mathematical Physics 58 (2) 2017.
32. Grover's Algorithm and the Secant Varieties (with Hamza Jaffali and Ismaël Nounouh). Quantum Information Processing 15 (11) 2016.
Three-qutrit entanglement and simple singularities (avec Hamza Jaffali). Journal of Physics A: Mathematical and Theoretical 49 ((46) 2016.
33. Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups (with Metod Saniga and Petr Pracna) . International Journal of Geometric Methods in Modern Physics 14(05) 2017.
34. Classification of multipartite systems featuring only |W⟩ and |GHZ⟩ genuine entangled states (with Peter Levay). Journal of Physics A: Mathematical and Theoretical 49 (8), 085201 (2016).
35. From Cayley-Dickson Algebras to Combinatorial Grassmannians (with Metod Saniga and Petr Pracna). arXiv.1405.6888. Mathematics (2015)
36. A new hyperelastic model for anisotropic hyperelastic materials with one fiber family (with Renye Cai, Feng Zhi-Qiang , François Peyraut). Accepted in International Journal of Solids and Structures (2015)
37. Quantum contextual finite geometries from dessin d'enfants (with Michel Planat, Alain Giorgetti and Metod Saniga). Int. J. Geom. Methods Mod. Phys. 12, 1550067 (2015). arXiv.13104267.
38. Veldkamp-Space Aspects of a Sequence of Nested Binary Segre Varieties (with Metod Saniga, Hans Havlicek, Michel Planat and Petr Pracna). Annales de l'Institut Henri Poincaré Série D (AIHPD) vol 2 No 3 (2015).
39. Embedding qubits into fermionic Fock space, peculiarities of the four-qubit cas (with Peter Levay). Phys.Rev. D91 (2015) 12, 125029 arXiv:1502.04537
40. A constructive apporach of invariants of behaviour laws with respect to an infinite symmetry group - Application to an anisotropic hyperelastic material with one fiber family (with Anh-Tuan Ta, Nadia Labed, Alain Thionnet, François Peyraut). International Journal of Solids and Structures 51.21 (2014): 3579-3588.
41. Singularity of type $D_4$ arising from four qubit systems (with Jean-Gabriel Luque and Michel Planat). Journal of Physics A: Mathematical and Theoretical 47 (2014) 135301 doi:10.1088/1751-8113/47/13/135301
42. A Notable Relation Between N-Qubit and 2^{N-1}-Qubit Pauli Groups via Binary LGr(N,2N) (with Metod Saniga and Peter Levay). SIGMA 10 (2014), 041
43. Entanglement of four qubit systems: a geometric atlas with polynomial compas I (the finite world) (with Jean-Gabriel Luque and Jean-Yves Thibon). Journal of Mathematical Physics 55 (2014) (1): 012202 .
44. A new invariant-based method for building biomechanical behaviour laws - Application to an anisotropic hyperelastic material with two fiber familes (with Anh-Tuan Ta, Nadia Labed, Alain Thionnet, François Peyraut). International Journal of Solids and Structures (2013).
45. Distinguished three-qubit "magicity" via automorphisms of the split Cayley hexagon (with Michel Planat and Metod Saniga). Quantum Information Processing (2013) DOI:10.1007/s11128-013-0547-3.
46. Geometric descriptions of entangled states by auxiliary varieties (with Jean-Gabriel Luque and Jean-Yves Thibon). Journal of Mathematical Physics 53 (2012): 102203.
47. Singularities of duals of Grassmannians. Journal of Algebra Volume 337, Issue 1, July 2011.
48. Lieu singulier des variétés duales : approche géométrique et applications aux variétés homogènes. Thèse de doctorat soutenue le 10 septembre 2004. Université Paul Sabatier. Toulouse.

Coauthors

Since 2011 I have been colaborated with Mathematicians, Computer Scientists and Physicists. Here is the list of my coauthors by chronological order of cooperations and with the number of join publications:

• Jean-Gabriel Luque (4)
• Jean-Yves Thibon (3)
• Michel Planat (4)
• Metod Saniga (10)
• François Peyraut (4)
• Anh-Tuan Ta (2)
• Nadia Labed (2)
• Alain Thionnet (2)
• Renye Cai (2)
• Alain Giorgetti (2)
• Peter Levay (5)
• Hans Havlicek (1)
• Petr Pracna (3)
• Hamza Jaffali (4)
• Luke Oeding (1)
• Henri de Bourtray (1)
• Pierre-Alain Masson (1)

Teaching

Depuis 2006 j'enseigne les mathématiques dans les formations d'ingénieur de l'UTBM. J'interviens dans les enseignements du premier cycle et des cycles ingénieur mécanique et ingénieur informatique. Je participe aussi au master international Physics Photonics and Nanotechnology d'UBFC et au master de l'UTBM en informatique délocalisé à l'Université de Lomé.

Géométries pour l'ingénieur

Paul de Faget de Casteljau, inventeur de l'algorithme du même nom, qui précéda Pierre Bézier dans la découverte des courbes à Pôles, nous a écrit une préface. Enfin on pourra consulter l'avant-propos ou encore la table des matières pour se faire une idée du contenu de l'ouvrage.

UV à projet

L'UTBM offre la possibilité aux étudiants du TC et des cycles ingénieurs de suivre des UV à projets (AC, TX, TO, TW, MR). C'est un excellent moyen pour les étudiants de travailler sur un sujet original, de développer de l'autonomie dans le travail, de se former en profitant des opportunités offertes par les nouvelles technologies (MOOC, conférences en lignes). Depuis 3 ans je propose des sujets en lien avec mes thèmes de recherche. Les rapports des projets que j'ai encadrés se trouvent sur la page UV à projet. N'hésitez pas à me contacter si vous êtes intéressés par ce type de travail.

Enseignements Printemps 2020

Je suis responsable de ce cours. Il s'agit d'une introduction à l'analyse numérique mais avec une orientation pour les métiers de l'image puisqu'on y aborde les courbes et surfaces de Bezier ainsi que les courbes splines. On y découvre en particulier le très joli algorithme de de Casteljau qui contient dans son écriture toutes les propritétés des courbes et surfaces de Bézier. On peut télécharger le cours ici et les travaux dirigés là. Ce semestre le cours est enseigné à distance depuis le 17 mars via la plateforme Discord et des resources supplémentaires d'accompagnement sont disponibles sur Moodle.

Students

I supervise PhD theses, master projects but also undergaduate reseach projects (AC20 and TX projects) on topics related to mathematics, quantum information and computer science.

PhD

1. Colm Kelleher. Colm is currently my PhD student. Colm is working on quantum games based on configurations from finite geometry. He has been implemented some orignal games on the IBM Quantum Experience.
2. Grâce Amouzou. Grâce started her PhD in March 2020. She has been working on the quantification of nonlocality of quantum pure states by geometrical tools. In Spring 2020 she collaborated with my master student Jeoffrey Boffeli to study hypergraph states. Grâce is in a dual PhD program between University of Lomé and UBFC. Her advisor at Lomé University is Kossi Atchonouglo.
3. Henri de Bourtray. I cosupervised Henri's thesis with Alain Giorgetti and Pierre-Alain Masson. Henri worked on proofs and verifications of quantum programs. He studied quantum properties that can be checked on quantum computers during quantum programs execution. In the second part of his thesis, Henri discussed questions related to contextualiy of configuration of observables. Henri defended his thesis in December 2022 and is now a researcher at Colibri .
4. Hamza Jaffali. Hamza defended his PhD in October 2020 on quantifying entanglement in quantum algorithms by geometric tools. He has published several works on Grover's and Shor's algorithms and proposed to use Machine Learning techniques to classify entanglement. Hamza's PhD was funded by the regional grant PHYFA (Photonic Platform for HYperentanglement in Frequencies and its Application). Hamza works as a researcher at Colibri
5. Renye Cai. Renye was a PhD student in nonlinear mechanics at UTBM from 2014 to 2017. She defended her thesis in March 2017 where she introduced new models of behavior law for anisotropic materials. I was cosupervising Renye's work with François Peyraut and Zhi-Qiang Feng. Renye is now working in China.
6. Ahn Tuan Ta. Ahn Tuan worked as a PhD student at UTBM between 2011 and 2014. He built - using the invariant theory techniques - some new bases of invariants for studying anisotropic materials. I did cosupervise his work with François Peyraut, Nadia Labed and Alain Thionnet.

Masters projects

1. (Spring 2020) M2 project of Colm Kelleher. Colm is a student of the International Master Math4Phys at UBFC. Colm is working on a finite geometric understanding of X-states density matrices
2. (Spring 2020) M2 internship of Jeoffrey Boffeli for the UBFC International Master Pysics Photonics and Nanotechnology. Jeoffrey is studying nonlocality of hypergraph states on the IBM Quantum Experience.
3. (Spring 2018) M1 project of Yeva Poghosyan for the International Master Physics Photonics and Nanotechnology, University Bourgogne Franche-Comté. Yeva worked on the use of Finite Elements Methods for solving Schrödinger equation.
4. (Spring 2018) M1 projet of Jérôme Boulmier and Maxime Pinard for the engineering Master degree in computer science at UTBM. This work was co-supervised with Metod Saniga. The paper "Veldkamp Spaces of Low-Dimensional Ternary Segree" in Results in Mathematics has been written at the end of the projet and is based on Jérôme and Maxime's programs.
5. (Fall 2017) M2 project of Hamza Jaffali and Ismaël Nounouh for the engineering Master degree in computer science of UTBM. Hamza and Ismaël wrote a report on quantum games and potential applications to Smart grids.
6. (Spring 2016) M1 project of Hamza Jaffali (UTBM). Hamza computed the singular types of hyperplane sections of the variety of separable states in the three-qutrit case. His work was used to write the paper "Three-qutrit entanglement and simple singularities" published in Journal of Physics A

Undergraduate Research

Music

I play the hurdy-gurdy, a medieval French instrument, that I have been performing with since I'm 14. I taught for more than 10 years at the conservatory of Belfort and I have been playing with many bands over the past 30 years. Music have always been a way to meet great artists, performers, and most importantly wonderfull human beings on stage or next to it with the audience. Currently I'm a member of the following bands.

The Gaulway Ramblers

I'm currently a member of the Gaulway Ramblers an american-irish-quebec-french band that was formed in Auburn, Alabama. In May 2022, we recorded our first album and have been played in a couple of music festival in the south of US, inluding the Celtic-Bayou Festival of Lafayette, Lousiana, as well as the celtic fest of the Rez in Jacksonville, Mississippi. Here is a short video of our gig at the Loft in Columbus, Alabama.

Chiceface

I also have been playing with Chicheface over the past 8 years. Chicheface is a folk band based on Belfort. Here is a video made by my sister (with only one camera !) for our first FIMU festival in 2015. Chicheface has been playing in the region Bourgogne Franche-Comté but also in Palestine with the conservatory Edward Said.

AC20-TX

Sur cette page vous trouverez quelques rapports et documents concernant les UV AC20 (Tronc Commun) ou TX (Branche) que j'ai encadré ces dernières années.

Printems 2021

Automne 2019

Automne 2016

Printemps 2016

Printemps 2014

Automne 2013

Miscellaneous

A few websites, links and other resources:

Mathematics Genealogy Project. Le site des généalogies mathématiques. Si vous vous intéressez à la géométrie, on est sûrement cousins.

Wolfram Mathworld et WolframAlpha . Des ressources et des calculs via Mathematica.

Les Elements. Le best-seller d'Euclide en ligne.

Images des Mathématiques. Un site où des chercheurs présentent pour le grand public la recherche en mathématiques vivante et active. Un jeu de couleur "Piste verte, piste bleue,..." permet de faire son chemin parmi les articles écrit pour une très grande audiance jusqu'à ceux qui nécessitent quelques connaissances en mathématiques.

Tout est quantique. Des animations très sympas pour découvrir de façon ludique quelques étrangetés du monde quantique.

Courrier International. Un excellent journal pour multiplier les points de vue.

Ojos Fritos. Pour finir un petit blog pour mettre un peu de culture dans un monde de brutes.

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';