7.1.1 FiatLux

• Keywords:
  Cellular automaton, Multi-agent, Distributed systems, Numerical simulations
• Scientific Description:
  FiatLux is a discrete dynamical systems simulator that allows the user to experiment with various models and to perturb them. It includes 1D and 2D cellular automata, moving agents, interacting particle systems, etc. Its main feature is to allow users to change the type of updating, for example from a deterministic parallel updating to an asynchronous random updating. FiatLux has a Graphical User Interface and can also be launched in a batch mode for the experiments that require statistics.
• Functional Description:
  FiatLux is a cellular automata simulator in Java specially designed for the study of the robustness of the models. Its main distinctive features are to allow users to perturb the updating of the system (synchrony rate) and the topology of the grid.
• URL:
  https://­project.­inria.­fr/­fiatlux/
• Contact:
  Nazim Fates
• Participant:
  Nazim Fates
• Partners:
  ENS Lyon, Université de Lorraine

8.1.1 Quantum Circuits

The quantum circuit model is the most standard model of quantum computing. Quantum circuits are ubiquitous in quantum computing, serving as both a low-level language and, surprisingly, a higher-level language used to describe certain quantum algorithms. We have introduced the first complete equational theory for quantum circuits, for reasoning on quantum circuits; we have also introduced new techniques for quantum circuit optimisation.

Completeness for Quantum Circuits. With the current advances in quantum technologies and quantum software, it is essential to develop formalisms for transforming and reasoning about quantum circuits. This is crucial for optimizing their size or depth, adapting code to architectural constraints, making it fault-tolerant, or verifying the equivalence of two circuits.

To achieve these goals, quantum circuits can be equipped with equational theories that enable the transformation of circuits using rules that are preferably simple and intuitive. These rules allow the replacement of a circuit fragment with an equivalent circuit. An equational theory is considered complete when, for any pair of circuits representing the same quantum evolution, there is a way to transform one into the other using only the rules of the equational theory.

We have recently introduced the first complete equational theory for quantum circuits 72, a problem which was open for more than 30 years. Indeed the only fragments equipped with a complete equational theory before, were non-universal and efficiently classically simulatable 80, 65, 66, 77. This year we have extended this completeness results to more expressive models of quantum circuits including ancillary qubits and quantum measurements . This result has been presented at CSL'24 42. Finally, we have introduced a minimal equational theory for vanilla quantum circuits (i.e. the standard model of quantum circuits without ancillary qubits) that we have proved to be minimal, i.e. each rule is necessary for the completeness 41 that has been presented at LICS 2024. One of the main and original contributions of this paper is demonstrating that the use of a rule acting on an unbounded number of qubits is necessary for completeness.

Hadamard count minimization in Clifford+T circuits. We have introduced an algorithm which essentially optimally minimizes the number of Hadamard in a Clifford+T circuit. When compiling quantum circuit with the gate set Clifford+T, one usually tries to minimize the number of T gates. This is because T gates are usually more costly to implement fault-tolerantly. This minimization problem when there are no Hadamard gates in the circuit is well understood. To handle the general case one can optimize around Hadamard gates or use some gadgetisation techniques (that consists in replacing a Hadamard with a few other operations requiring in particular an extra qubit). In both cases minimizing the number of Hadamard gate in the circuit beforehand can also help reducing the number of T gates overall.

This work has been done in collaboration with Simon Martiel (Atos), and has been publish in the ACM journal Transactions on Quantum Computing 81.

8.1.2 Quantum error correcting codes and fault-tolerance

Quantum error correcting codes are crucial in the quest of a fault-tolerant large-scale quantum computer. We have contributed to the development of fault-tolerant logical gates on toric codes, we have also introduced a new family of multimode bosonic codes, the quantum tiger codes, which opens up a new avenue in the field of bosonic codes to find efficient multimode bosonic codes with the promise of reducing hardware cost of quantum error correction.

Fault-tolerant Clifford gates on toric codes. Quantum error correcting codes with good encoding rates promise to reduce the cost of fault-tolerant quantum computation by reducing the number of physical qubits needed for a target level of protection and number of logical qubits needed. The savings come at the price of more complex procedures for the implementation of gates on logical qubits within the code. Alexandre Guernut for his PhD proposed a set of constant depth, fault-tolerant gates generating the Clifford group acting on copies of the toric code and evaluated the performance of these gates. The set combines several techniques, such as transversal and fold-transversal gates as well as instantaneous Dehn twists and shows very good performance. The preprint is awaiting review, 54.

Tiger codes. Quantum systems in real laboratories do not always consist in a set of qubits but often systems with a richer structure for their Hilbert space. For instance they are often infinite dimensional, as are quantum oscillators or quantum rotors. Exploiting the structure and knowledge of the full physical system when designing quantum error correcting codes is a promising way of reducing the overhead of error correction. The work 63 is a collaboration with Yijia Xu (University of Maryland), Yixu Wang (Tsinghua University) and Victor Albert (University of Maryland). Following-up on previous work which introduced quantum rotor codes 34, this work introduced tiger codes, showing how rotor codes could be embedded into bosonic modes to give multimode bosonic codes. Many pre-existing isolated examples of bosonic codes are subsumed by this new framework which also opens a big avenue for finding new codes. Because of their similarities with existing codes already implemented today, there is a clear path to have them implemented in practice in the future. Understanding the error correcting properties of these tiger codes can be done by directly studying the properties of the underlying rotor code which makes the search for new codes simplified.

Quantum error correcting codes are crucial in the quest of a fault-tolerant large-scale quantum computer. We have contributed to the development of surface codes, we have also introduced a new family of quantum codes, the quantum rotor codes, finally and may be more surprisingly, we have shown that minimalist error correcting codes can be used in near-term experiments for demonstrating a separation between classical and quantum computers.

Fault-tolerant Clifford gates on toric codes. Quantum error correcting codes with good encoding rates promise to reduce the cost of fault-tolerant quantum computation by reducing the number of physical qubits needed for a target level of protection and number of logical qubits needed. The savings come at the price of more complex procedures for the implementation of gates on logical qubits within the code. One technique for homological codes from 2D manifold is to apply a Dehn twist to a handle of the surface which implements a CNOT gate between the logical qubits of the handle. Alexandre Guernut for his PhD studied the generalization of Dehn-twists to other 2D codes, namely color codes. We discovered that in practice for small system size the color code Dehn twists were spreading too much the noise. Therefore we switched gears by unfolding the color code to two copies of the toric code and set out to design and evaluate the performance of a generating set of the Clifford group on toric codes that would have a constant-depth implementation. The numerical results are now promising and a paper is in preparation.

Quantum rotor codes. The work 34 is a collaboration in progress with Barbara Terhal (Delft University) and Allessandro Ciani (Forschungszentrum Jülich). Quantum systems in real laboratories do not always consist in a set of qubits but often systems with a richer structure for their Hilbert space. For instance they are often infinite dimensional, as are quantum oscillators or quantum rotors. Exploiting the structure and knowledge of the full physical system when designing quantum error correcting codes is a promising way of reducing the overhead of error correction. Quantum error correction with quantum oscillators has been well studied either for encoding qubits within quantum oscillators (the field of bosonic codes) or encoding oscillators in several oscillators for which several no-gos have been proven. Quantum rotors can be thought as intermediate systems between qubits (finite) and quantum oscillators (infinite and continuous). We are studying quantum error correcting codes for quantum rotors both encoding finite or infinite logical information. The codes we defined encoding finite systems have some similarity with so-called protected superconducting qubits such as the 0-$\pi$ qubit. Moreover our construction generalizes to more protected qubits potentially realizable in superconducting circuits. This was submitted and accepted for publication in Communication in Mathematical Physics.

Robust Sparse IQP Sampling in Constant depth. In collaboration with the Inria teams Quantic and Cosmiq we studied the problem of making the sparse instantaneous quantum polynomial-time (IQP) sampling problem robust to noise and constant depth, therefore making it more accessible to near-term experiments. Sparse IQP sampling problems are problems that are demonstrably hard to sample from with a classical computer but straightforward for a quantum computer and hence candidates for demonstration of quantum advantage. The problem is that convincing advantage needs to be able to scale up the quantum circuit which cannot be done in the presence of noise. This work shows how to use the minimal amount of quantum error correction necessary to be able to scale while correcting errors. This work has been accepted for a plenary talk at the QIP2024 conference 46.

8.1.3 Graph states and Measurement-based quantum computing

There are various models of quantum computation. Whereas unitary evolutions are at the heart of the standard model of quantum computing, measurement-based quantum computing (MBQC) is an alternative model introduced more than 20 years ago, which consists in performing quantum measurements over a large entangled initial resource called a graph state. This year, we solved an open problem concerning the graphical characterization of entanglement in graph states, contributed to advancements in measurement-based quantum computing (MBQC), and made progress on a recent graph-state-based protocol called $k$-parability, which serves as a primitive for distributed quantum computing.

Graphical characterisation of entanglement graph states. Two graph states have the same entanglement if they can be transformed in each other by means of local unitary transformations. Whereas it is well known that local complementation, preserve entanglement, the converse is however not true: in 2007 74 an example of two graphs that represent the same entanglement but cannot be transformed into each other by means of local complementations has been pointing out, leaving as an open question a graphical characterisation of entanglement for graph states . We have introduced this year a generalisation of local complementation that captures the entanglement of graph states 40. This result has been accepted at STAC 2025 and will also be presented at QIP 2025, the main conference in quantum computing. This graphical characterisation of entanglement is strongly based on a particular graph structure called minimal local set cover for which we have introduced an efficient algorithm this year, presented at WG'24 as a purely graph theory result 39. Notice that our algorithm for minimal local set cover has been used recently by Adam Burchardt, Jarn de Jong, Lina Vandré for introducing an algorithm for deciding the entanglement equivalence of graph states 69.

Small pairable states and Vertex minor universality. A $k$-pairable $n$-qubit state is a resource state that allows Local Operations and Classical Communication (LOCC) protocols to generate pairs of maximally entangled 2-qubit states among any $k$-disjoint pairs of the $n$ qubits. The best known resource states, introduced by Bravyi et al. 68, had a number of qubits growing exponentially with the parameter $k$. We have shown the existence of `small' pairable quantum states with a number $n$ of qubits polynomial in $k$. We have also established bounds on the pairability, relating this quantity to other graph parameters, in particular the local minimal degree. We have also extended the notion of pairability to vertex minor universality, a natural graph property. A preliminary work on this subject has been done in collaboration with Mehdi Mhalla (LIG, Grenoble) 71. We then extended the results with Stéphan Thomassé (LIP, ENS Lyon), Valentin Savin and Maxime Cautrès (CEA Grenoble), leading to a publication at ICALP 2024 70.

Algebraic formulation of Pauli flow. A measurement-based quantum computation must satisfy so-called flow properties in order to be implementable in a robustly deterministic way. It is known how to find flow structures in polynomial time when they exist; nevertheless, their lengthy and complex definitions often hinder working with them. We simplified these definitions by providing a new linear algebraic formulation of Pauli flow, the most general type of flow, in terms of properties of two matrices arising from the adjacency matrix of the underlying graph. Using this formulation, we obtained $𝒪\left(n^3\right)$ algorithms for finding Pauli flow, improving on previously-known algorithms; we also proved that these new algorithms are optimal barring progress in the computational complexity of matrix multiplication. This work was done in collaboration with Piotr Mitosek (University of Birmingham) 60.

8.2.1 Resource analysis of quantum programs

In 35, we have studied quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given quantum gate, etc. After studying the completeness of these problems in the arithmetical hierarchy over the Clifford+T fragment of quantum mechanics, we have expressed these problems using a variation of a quantum pre-expectation transformer, a weakest pre-condition based technique that allows to symbolically compute these quantitative properties. Under a smooth restriction—a restriction to polynomials of bounded degree over a real closed field—we show that the quantitative problem, which consists in finding an upper-bound to the pre-expectation, can be decided in time double-exponential in the size of a program, thus providing, despite its great complexity, one of the first decidable results on the analysis and verification of quantum programs. Finally, we sketch how the latter can be transformed into an efficient synthesis method.

8.2.2 Computable type

In 29 we have solved an open problem about a computability property of compact spaces called computable type. We have shown that this property is not closed under finite products. In order to build a counter-example, we have proved a characterization of this property in terms of homotopy of functions from a space to a sphere.

Our work on reducing the comparison between two computability notions to a comparison between two topologies, mentioned in the previous report, has been published in 28.

8.2.3 Presentations of topological spaces

In 59 we have studied a notion of presentation of countably-based topological spaces. We have surprisingly shown that every such space has a computable presentation.

8.2.4 Declassification policy for complexity analysis

In 45, we improved the expressivity of noninterference techniques for complexity by introducing a controlled declassification instruction. Noninterference-based type systems statically guarantee, via soundness, the property that welltyped programs compute functions of a given complexity class, e.g., the class FP of functions computable in polynomial time. These characterizations are also extensionally complete – they capture all functions – but are not intensionally complete as some polytime algorithms are rejected. This impact on expressive power is an unavoidable cost of achieving a tractable characterization. To circumvent this issue, an avenue arising from security applications is to find a relaxation of noninterference based on a declassification mechanism that allows critical data to be released in a safe and controlled manner. Following this path, we presented a new and intuitive declassification policy preserving FP-soundness and capturing strictly more programs than existing noninterference-based systems. We show the versatility of the approach: it also provides a new characterization of the class BFF of second-order polynomial time computable functions in a second-order imperative language, with first-order procedure calls. Type inference is tractable: it can be done in polynomial time.

8.3.1 Probabilistic cellular automata for problem solving

We presented two stochastic cellular automata that classify the parity of initial conditions 43. The model is an interacting particles system where cells are updated by pairs, randomly chosen at each time step. A first rule was proposed, with a symmetry between 0’s and 1’s. This rule classifies the parity of the initial configurations thanks to a non-biased random walk of the frontiers between 0’s and 1’s. We presented an analysis of the classification time, as well as numerical simulations, to establish that the classification time scales quadratically with the number of cells. In a second time, breaking the state symmetry, we proposed an improvement of this rule with the simultaneous use of two classifying systems. This work was presented at AUTOMATA 2024, the 30th International Workshop on Cellular Automata and Discrete Complex Systems 43.

8.3.2 Classification of asynchronous cellular automata

Reversibility is a well-studied property for deterministic cellular automata but it is only partially explored when randomness appears in the update. We presented a detailed study of 21 finite-size elementary cellular automata with a fully asynchronous updating and periodic boundary conditions 32. We estimated their degree of reversibility by counting the number of recurrent configurations as a function of the size of the automaton (number of cells). We showed that these rules exhibit various qualitative behaviours: some rules show a “strong reversibility” with a number of recurrent configurations that grows exponentially, while other rules have a “weak reversibility” with a linear growth. We also analysed the structure of the communication graph and report various scaling relations for the number of recurrent communication classes. We identified the cases where the divisibility of the size by 2 or 3 introduces some discontinuities in the behaviour. This study completes the characterization of the 256 elementary cellular automata with regard to their recurrence properties. These results were published in Theoretical Computer Science 32.

8.3.3 Enumerative or bijective combinatorics

Enumeration of pattern-avoiding inversion sequences. The results presented here have been obtained by Benjamin Testart during his PhD thesis (which started in 2022, and is running until 2025). They are concerned with inversion sequences, which are integer sequences $({\sigma }_1,\cdots ,{\sigma }_n)$ such that $0\le {\sigma }_i<i$ for all $1\le i\le n$. The study of pattern-avoiding inversion sequences began in two independent articles 78, 73, which solved the enumeration of inversion sequences avoiding a single pattern for every pattern of length 3 except the patterns 010 and 100. The case 100 was recently solved by Kotsireas, Mansour and Yildirim 76.

In a 2022 preprint (not meant for publication, and subsumed by 61), Benjamin solves the final case by making use of a decomposition of inversion sequences avoiding the pattern 010 according to original parameters. The method is then expanded to solve the enumeration of inversion sequences avoiding several pairs of patterns containing 010, most of the time solving also the enumeration of some family of constrained words as an auxiliary problem.

In his paper 61 (that is currently submitted to a journal), Benjamin in addition managed to obtain all missing enumerations for inversion sequences avoiding a pair of patterns of size 3 (17 such families in total). To achieve this, Benjamin has used in original ways the (established) method of generating trees in a few cases, and has otherwise used several decompositions of inversion sequences that he introduced.

Benjamin has a second paper currently submitted (to the DMTCS special issue that follows the conference Permutation Patterns 2024). In this paper 62, he focuses on proving algebraicity of generating functions using generating trees. More precisely, Benjamin studies two families of inversion sequences, provides a generating tree construction (which is original), and derives from it their algebraic generating function. (Although one case was know by another approach, the second one was only conjectured so far.) As expected in works of this type, the kernel method comes into play, but remarkably involves some original aspects that may well be useful elsewhere.

Enumeration of pattern-avoiding alternating sign matrices. Permutations can be described as square binary matrices containing exactly one 1 in each row and each column (using their classical permutation matrix representation). A common generalization of permutations consists in allowing entries 0, 1 and $-1$ in square matrices, imposing that in each row (resp. column), the non-zero entries alternate in sign and sum to 1. These objects are called alternating sign matrices (ASMs), and their study has been a challenging topic in enumerative combinatorics for the past four decades. However, so far, it seems that there have been very few studies of pattern-avoidance in ASMs, while this is a classical and rich topic in the combinatorics of permutations.

Therefore, in a collaborative project involving ASM experts and permutation patterns experts , we have explored the topic of pattern-avoiding ASMs. There are two different and natural ways to do so, which resulted in two different preprints this year.

The first one 52, coauthored by M. Bouvel with R. Smith and J. Striker, investigates the notion that we name key-avoidance in ASMs. Indeed, there is a classical procedure in the ASMs literature, that associates to each ASM a permutation, called its key. In this work, we enumerate ASMs whose key avoids a given set of permutation patterns in several instances. We show that ASMs whose key avoids 231 are permutations, thus the many known enumerations for a set of permutation patterns including 231 extends to ASMs. We furthermore enumerate by the Catalan numbers ASMs whose key avoids both 312 and 321. We also show ASMs whose key avoids 312 are in bijection with the gapless monotone triangles defined by Ayyer, Cori and Gouyou-Beauchamps in 2011. Thus key-avoidance generalizes the notion of 312-avoidance studied there, answering a question left open in their work. Finally, we enumerate ASMs with a given key avoiding 312 and 321 using a connection to Schubert polynomials, thereby deriving an interesting Catalan identity.

The second one 48, coauthored by M. Bouvel with E. Egge, R. Smith, J. Striker and J. Troyka, focuses on another way of defining avoidance of patterns in ASMs, by looking at submatrices, and which we refer to as classical avoidance. This has already appeared once in the literature, in a paper by Johansson and Linusson in 2007 75. We completely classify the asymptotic behavior of the number of ASMs classically avoiding a single permutation pattern. In particular, we give a uniform proof of an exponential upper bound for the number of ASMs classically avoiding one of twelve particular patterns, and a super-exponential lower bound for all other single-pattern avoidance classes. We also show that for any fixed integer $k$, there is an exponential upper bound for the number of ASMs that classically avoid any single permutation pattern and contain precisely $k$ negative ones. Finally, we prove that there must be at most 3 negative ones in an ASM which classically avoids both 2143 and 3412, and we exactly enumerate the number of them with precisely 3 negative ones.

The middle order on permutations Two extremely well-known partial orders exist on permutations of any given size: the Bruhat order, and the weak order. In this joint work 50 of M. Bouvel with L. Ferrari and B. Tenner, we introduce a third natural such partial order. Specifically, we define a partial order $P_n$ on permutations of any given size $n$, which is the image of a natural partial order on inversion sequences. We call this the “middle order”. We demonstrate that the poset $P_n$ refines the weak order on permutations and admits the Bruhat order as a refinement, justifying the terminology. These middle orders are distributive lattices and we establish some of their combinatorial properties, including characterization and enumeration of intervals and boolean intervals (in general, or of any given rank), and a combinatorial interpretation of their Euler characteristic. We further study the (not so well-behaved) restriction of this poset to involutions, obtaining a simple formula for the Möbius function of principal order ideals there.

8.3.4 Probabilistic or geometric combinatorics

Scaling limits of families of intersection graphs. This is the latest result of a collaboration of M. Bouvel with Frédérique Bassino (LIPN, Université Paris Nord), Valentin Féray (IECL, Université de Lorraine), Lucas Gerin (CMAP, École Polytechnique) and Adeline Pierrot (LISN, Université Paris-Sud) which started over ten years ago. The purpose of this collaboration is to establish limit shape results for combinatorial structures (like permutations or graphs) constrained by the avoidance of substructures, often using methods from analytic combinatorics (which is original in the landscape of the research on this topic).

In 47, we obtain the scaling limits of random graphs drawn uniformly in three families of intersection graphs: permutation graphs, circle graphs, and unit interval graphs. The two first families typically generate dense graphs (with a quadratic number of edges), and in these cases we prove almost sure convergence to an explicit deterministic graphon. Uniform unit interval graphs are nondense and we prove convergence in the sense of Gromov–Prokhorov after normalization of the distances.

Our newer project, started during the past year, goes back to permutations. It aims at describing limit shapes (precisely, limiting permutons – which are the analogues of graphons in this context) of uniform permutations in classes defined by the avoidance of any two patterns of size 4.

Record-biased permutations. With C. Nicaud and C. Pivoteau, M. Bouvel has had an on-going project for several years, focused on the study of a non-uniform distribution on permutations biased by their number of records that we call record-biased permutations. This project has come to a conclusion with the article 51. There, we give several generative processes for record-biased permutations, explaining also how they can be used to devise efficient (linear) random samplers. For several classical permutation statistics, we obtain their expectation using the above generative processes, as well as their limit distributions in the regime that has a logarithmic number of records (as in the uniform case). Finally, increasing the bias to obtain a regime with an expected linear number of records, we establish the convergence of record-biased permutations to a deterministic permuton, which we fully characterize.

Decomposition of order types, with applications to counting problems. This topic, at the interface of combinatorics and discrete geometry, has emerged as the result of a collaboration between several teams in Nancy, and involves M. Bouvel, V. Feray (IECL, Université de Lorraine), X. Goaoc (Gamble) and F. Koechlin (post-doc with X. Goaoc and V. Feray until September 2023). It is presented in a long preprint 49, and has been accepted as a talk at the conference SOCG, one of the main conferences in discrete geomery 36. In this work, we introduce and study an original notion of decomposition of planar point sets (or rather of their chirotopes, also called order types) as trees decorated by smaller chirotopes. This decomposition is based on the concept of mutually avoiding sets, and adapts in some sense the modular decomposition of graphs (or its cousin the substitution decomposition of permutations) in the world of chirotopes. We prove that the associated tree always exists and is unique up to some appropriate constraints. We also show how to compute the number of triangulations of a chirotope efficiently, starting from its tree and the (weighted) numbers of triangulations of its parts.

8.3.5 Analysis of graphs in the field of economics

In economy, a major issue is the potential lack of liquidity for settling the debts generated by payment delays among companies. In collaboration with Massimo Amato and Lucio Gobbi (Bocconi University and University of Trento), we developed some economic and operational foundations of a new method of financing companies’ financial obligations. In this new banking business model, a network funder sets an optimal combination of netting and financing. Given a network of companies and their respective invoices, and under the condition of a full settlement of the invoices, we applied a multilateral netting algorithm to the network, conceived as an oriented multi-graph. Our problem, which is NP-complete, was to find a set of invoices which maximises the amount of debt reduced given a quantity of loanable funds.

We compared different methods to detect structures or communities that could be helpful for debt netting algorithms. The structure of such networks is not currently well known. We give hints on how to sort and identify the type of B2B invoice graphs. In particular, we addressed the possibility to identify relevant communities in such networks. This work was presented in 2023 in the conference Complex networks and it was published in 2024 44. In 2024, we focused on developing debt netting algorithms and assessing their performance under various parameter settings, guided by specific economic constraints and expectations.

8.3.6 Local generation of tilings

Mathieu Hoyrup and Tom Favereau , during a research initiation internship, studied the possibility of generating tilings in a local way. We have proposed two definitions capturing this intuition and developed techniques to classify tilings according to these definitions. We have started a systematic classification of small Wang tilesets. The results are written in 57 and 58, currently submitted.

10.1.1 Inria associate team not involved in an IIL or an international program

10.2.1 Visits to international teams

10.3.1 Horizon Europe

10.3.2 H2020 projects

10.4.1 ANR

10.4.2 Other initiatives

Maquest - Maison du Quantique Grand Est

• Title:
  Maquest
• Duration:
  Jan. 2025 - Dec. 2027
• Coordinator:
  Guido Pupillo (Unistra)
• Local Coordinator:
  Simon Perdrix
• Local Members:
  Simon Perdrix , Miriam Backens
• Partner Institution(s):
  Unistra, UTT Troyes, URCA Reims, Centre Inria de l'Université de Lorraine
• Summary:
  The mission of the Maison du Quantique du Grand Est - MaQuEst project is to consolidate and position and strategically position the Grand Est region as a leading centre in the national and European high-performance computing (HPC) and quantum computing landscape. (HPC) and quantum computing, with 3 physical sites and 3 antennae to cover the region. The Grand Est region is home to a booming quantum ecosystem, characterised by cutting-edge research and educational educational programmes, cross-border collaboration and established multidisciplinary quantum established multidisciplinary quantum computing initiatives. The MaQuEst project represents an opportunity to increase awareness and to develop use cases that can drive advances in the region's biotechnology, artificial intelligence and nanotechnology industries. and finance industries, and thus help to strengthen France's position as a world leader in hybrid in hybrid computing. MaQuEst aims to develop collaborations between the worlds of industry and business entrepreneurial world, i.e. potential users of quantum technologies, and the academic world in the the Grand Est region, also involving quantum technology suppliers and facilitators. quantum technologies. Ultimately, this ‘Maison du Quantique du Grand-Est’ will encourage the adoption of quantum and hybrid computing by creating synergies between the expertise of the two worlds, so as to generate concrete and useful use cases, as well as and productivity gains through the dissemination of quantum science innovations across the regional, national and cross-border economic fabric. regional, national and cross-border economic fabric.
• Total Amount:
  12 millions euros (appel national Maison du Quantique Genci-CEA) + 12 millions euros (Région Grand Est).

11.1.1 Scientific events: organisation

11.1.2 Scientific events: selection

11.1.3 Journal

11.1.4 Invited talks

• Miriam Backens : talk at workshop Foundations of Quantum Computational Advantage, Perimeter Institute, Canada, April 2024.
• Miriam Backens : course (3h) at the summer school New trends in computing, Strasbourg, September 2024.
• Miriam Backens : talk at Graphix workshop, Paris, November 2024.
• Mathilde Bouvel : course (4h) at the Ecole jeunes chercheurs du GDR-IFM, Nantes, June 2024.
• Mathilde Bouvel : Talk at the national days of the GT CombAlg of the GDR-IFM, Lyon, October 2024.
• Simon Perdrix : talk at Graphix workshop, Paris, November 2024.
• Simon Perdrix : talk at "Quantum Circuit Design Automation" workshop, Banff International Research Station, June 2024 (videos).
• Christophe Vuillot : Talk at 804.WE-Heraeus Seminar, in Bad Honnef, Germany, January 2024
• Christophe Vuillot : Talk at the workshop on Advaces in Quantum Coding Theory, at Simons Institute, Berkeley US, February 2024
• Christophe Vuillot : Talk at the workshop on Quantum Error Correction meets operator Algebra, at the University of Oslo, June 2024
• Christophe Vuillot : Course on bosonic codes at the ML4Q summer school at the Bethe center, Bonn, September 2024.

11.1.5 Leadership within the scientific community

• Mathilde Bouvel : member of the steering committee of the series of conferences Permutation Patterns
• Nazim Fatès : head of the IFIP WG 1.5 on Cellular Automata and Discrete Complex Systems
• Mathieu Hoyrup : member of the steering committee of the series of workshops Computability and Complexity in Analysis

11.1.6 Scientific expertise

• Emmanuel Hainry has been an external evaluator on a research project for the ANR.
• Emmanuel Jeandel : member of a CoS for a professor position in Paris-Cité, IRIF.
• Emmanuel Jeandel : member of a CoS for a associate professor position in Université de Lorraine, Loria
• Romain Péchoux : member of a CoS for an associate professor position in quantum computing at CentraleSupélec.
• Simon Perdrix : member of a CoS for a associate professor position in Aix Marseille Université, LIS.
• Simon Perdrix : member of doctoral commission at LORIA.

11.1.7 Research administration

• Romain Péchoux : vice-chair of Horizon Europe MSCA.
• Simon Perdrix : coordinator EPIQ project, part of the PEPR quantique
• Simon Perdrix : WP leader in Défi Inria EQIP.
• Simon Perdrix : co-head of GT IQ at GdR IFM.
• Simon Perdrix : local PIQ representative.

11.2.1 Supervision

• Miriam Backens has supervised the PhD of George Kaye (University of Birmingham, UK, defense 11 September 2024) with Dan Ghica.
• Miriam Backens is supervising the PhD of Tommy McElvanney (University of Birmingham, UK, awaiting defense) with Martín Escardo.
• Miriam Backens is supervising the PhD of Piotr Mitosek (4th year, University of Birmingham, UK) with Paul Blain Levy.
• Miriam Backens is supervising the internship of Jules Dupont (École des Mines Nancy).
• Miriam Backens and Simon Perdrix are supervising the PhD of Colin Blake (1st year).
• Miriam Backens and Simon Perdrix are supervising the PhD of Noé Delorme (2nd year).
• Miriam Backens and Simon Perdrix are supervising the PhD of Nathan Claudet (3rd year).
• Mathilde Bouvel has supervised the internship of Aditi Muthkhod (Bachelor level at CMI, Chennai, India)
• Mathilde Bouvel and Emmanuel Jeandel are supervising the PhD of Benjamin Testard (3rd year).
• Alejandro Díaz-Caro is supervising the PhD of Cristian Sottile (5th year, of a 5-year program in Argentina).
• Alejandro Díaz-Caro is supervising the PhD of Rafael Romero (5th year, of a 5-year program in Argentina) with Octavio Malherbe.
• Alejandro Díaz-Caro is supervising the PhD of Malena Ivnisky (4th year, of a 5-year program in Argentina) with Octavio Malherbe.
• Alejandro Díaz-Caro is supervising the internship of Luciano Barletta (M2, UNR, Argentina).
• Alejandro Díaz-Caro is supervising the internship of Francisco Herrero (M1, UBA, Argentina).
• Alejandro Díaz-Caro is supervising the internship of Tomás Miguez (M1, UBA, Argentina).
• Alejandro Díaz-Caro is supervising the internship of Nicolás Monzón (M2, UADE, Argentina).
• Alejandro Díaz-Caro is supervising the internship of Carlos Miguel Sotto (M2, UBA, Argentina).
• Nazim Fatès is supervising the PhD of Joannès Guichon (3rd year) with Sylvain Contassot-Vivier (LORIA).
• Nazim Fatès has supervised the Master 2 internship of Nicolas Barreau (univ. de Lorraine, sciences cognitives).
• Emmanuel Hainry and Romain Péchoux have supervised the internship of Florent Ferrari (L3, ENS Lyon).
• Emmanuel Hainry and Romain Péchoux are supervising the PhD of Mario Silva (4th year).
• Emmanuel Hainry and Romain Péchoux are supervising the PhD of Thomas Vinet (1st year) .
• Mathieu Hoyrup has supervised the internship of Alexis Terrassin (M2, LMFI).
• Mathieu Hoyrup has supervised the internship of Tom Favereau (École des Mines de Nancy).
• Mathieu Hoyrup and Guilhem Gamard are supervising the PhD of Alexis Terrassin (1st year).
• Emmanuel Jeandel and Christophe Vuillot are supervising the PhD of Alexandre Gernut (4th year).
• Romain Péchoux and Simon Perdrix are supervising the PhD of Kathleen Barsse (1st year).
• Romain Péchoux is supervising the PhD of Kinnari Dave (3rd year) with Vladimir Zamdzhiev (Inria Saclay).
• Romain Péchoux is supervising the PhD of Issa Jad (1st year) with Christophe Chareton (CEA Saclay).
• Simon Perdrix and Christophe Vuillot , then Emmanuel Jeandel , are supervising the PhD of Sébastien Draux (1st year).
• Simon Perdrix has supervised the internship of Colin Blake (M2 MPRI).
• Simon Perdrix and Christophe Vuillot are supervising the PhD of Vivien Vandaele (4th year).

11.2.2 Juries

• Miriam Backens : external examiner for the programme Master in Mathematics and Foundations of Computer Science, University of Oxford, UK; external examiner for the Masters thesis of Benjamin Caldwell (University of Chicago, US), January 2024; external examiner for the PhD thesis of Muhammad Hamza Waseem (University of Oxford, UK), December 2024
• Mathilde Bouvel : member of the jury for the PhD defense of Zéphyr Salvy, December 2024, Marne-la-Vallée.
• Nazim Fatès : member of the habilitation thesis committee of Barbara Wolnik, Univeristy of Gdansk, Poland, April 2024.
• Mathieu Hoyrup : member of the jury for the PhD defense of Léo Paviet-Salomon, December 2024, Caen.
• Emmanuel Jeandel : member of the jury for the PhD thesis of Ugo Giocanti (Université Grenoble-Alpes), Nicolas Bitar (Université Paris-Saclay), Bastien Laboureix (Université de Lorraine). reviewer for the HDR defense of Benoît Valiron (Université Paris-Saclay)
• Romain Péchoux : rapporteur for the PhD thesis of Andrea Colledan, Universita di Bologna.
• Simon Perdrix : external examiner for the PhD of Kyriakos Georgiade (UCL London) ; President of jury for the PhD defense of Uta Isabella Meyer (Sorbonne Université); member of the jury for the PhD defense of Raphaël Mothe (Université Grenoble Alpes).
• Christophe Vuillot : member of the jury for the PhD defense of Aurélie Denys, April 2024.

11.3.1 Productions (articles, videos, podcasts, serious games, ...)

Nazim Fatès published an article in the Alliage journal, entitled « Que faire de l'expression “intelligence artificielle” ? » 30.

11.3.2 Participation in Live events

• Miriam Backens : talk at online school Introduction to Quantum Research for Girls, June 2024.
• Mathilde Bouvel : closing conference at the Tournoi français des jeunes mathématiciennes et mathématiciens, Nancy, April 2024.
• Nazim Fatès :
  • Talk for the high-schhol teachers : Les machines peuvent-elles « apprendre » ? at the Journées NSI, LORIA, April 3, 2024.
  • Talk on artificial intelligence for the lycée Vatelot in Toul ; April 18, 2024.
  • Wide-audience talk on the theme « Intelligence artificielle : entre technoscience et alchimie » in the Université populaire et participative de Vandœuvre (UP²V) ; May 15, 2024.
  • Talk « Visages de l’infini en informatique », at the Marathon des sciences in the Astronomy festival of Fleurance, August 3, 2024.

International journals

• 27 articleM.Michael Albert, M.Mathilde Bouvel, V.Valentin Féray and M.Marc Noy. Convergence law for 231-avoiding permutations.Discrete Mathematics and Theoretical Computer Science261April 2024HALDOI
• 28 articleD. E.Djamel Eddine Amir and M.Mathieu Hoyrup. Comparing computability in two topologies.The Journal of Symbolic Logic8932024, 1-19HALDOIback to text
• 29 articleD. E.Djamel Eddine Amir and M.Mathieu Hoyrup. The surjection property and computable type.Topology and its Applications355October 2024, 109020HALDOIback to text
• 30 article N.Nazim Fatès. What to do with the term 'artificial intelligence'? Alliage : Culture - Science - Technique 84 November 2024 HAL back to text
• 31 articleL.Louis Paletta, A.Anthony Leverrier, A.Alain Sarlette, M.Mazyar Mirrahimi and C.Christophe Vuillot. Robust sparse IQP sampling in constant depth.Quantum8May 2024, 1337HALDOI
• 32 articleS.Souvik Roy, N.Nazim Fatès and S.Sukanta Das. Reversibility of Elementary Cellular Automata with fully asynchronous updating: an analysis of the rules with partial recurrence.Theoretical Computer Science2024. In press. HALDOIback to textback to text
• 33 articleD.Diego Ruiz, J.Jérémie Guillaud, A.Anthony Leverrier, M.Mazyar Mirrahimi and C.Christophe Vuillot. LDPC-cat codes for low-overhead quantum computing in 2D.Nature Communications161January 2025, 1040HALDOI
• 34 articleC.Christophe Vuillot, A.Alessandro Ciani and B.Barbara Terhal. Homological Quantum Rotor Codes: Logical Qubits from Torsion.Communications in Mathematical Physics4052February 2024, 53HALDOIback to textback to text

International peer-reviewed conferences

• 35 inproceedingsM.Martin Avanzini, G.Georg Moser, R.Romain Péchoux and S.Simon Perdrix. On the Hardness of Analyzing Quantum Programs Quantitatively.Lecture Notes in Computer ScienceESOP 2024 - 33rd European Symposium on ProgrammingLecture Notes in Computer ScienceProgramming Languages and Systems : 33rd European Symposium on Programming, ESOP 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Luxembourg City, Luxembourg, April 6–11, 2024, Proceedings, Part IILNCS-14577Luxembourg, Luxembourg2024, 28HALDOIback to text
• 36 inproceedingsM.Mathilde Bouvel, V.Valentin Féray, X.Xavier Goaoc and F.Florent Koechlin. A Canonical Tree Decomposition for Chirotopes.40th International Symposium on Computational Geometry (SoCG 2024)40th International Symposium on Computational Geometry (SoCG 2024)Leibniz International Proceedings in Informatics (LIPIcs)Athens, GreeceSchloss Dagstuhl – Leibniz-Zentrum für Informatik2024HALDOIback to textback to text
• 37 inproceedingsM.Maxime Cautrès, N.Nathan Claudet, M.Mehdi Mhalla, S.Simon Perdrix, V.Valentin Savin and S.Stéphan Thomassé. Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems.European Association for Theoretical Computer Science (EATCS)ICALP 2024 51st EATCS International Colloquium on Automata, Languages and ProgrammingTallinn, EstoniaSchloss Dagstuhl – Leibniz-Zentrum für Informatik2024HALDOI
• 38 inproceedingsK.Kostia Chardonnet, L.Louis Lemonnier and B.Benoît Valiron. Semantics for a Turing-Complete Reversible Programming Language with Inductive Types.9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs)FSCD 2024 - 9th International Conference on Formal Structures for Computation and Deduction29919Tallinn, EstoniaSchloss Dagstuhl – Leibniz-Zentrum für Informatik2024, 19:1-19:19HALDOI
• 39 inproceedingsN.Nathan Claudet and S.Simon Perdrix. Covering a Graph with Minimal Local Sets.WG 2024: 50th International Workshop on Graph-Theoretic Concepts in Computer ScienceGozd Martuljek, SloveniaFebruary 2024HALback to text
• 40 inproceedingsN.Nathan Claudet and S.Simon Perdrix. Local equivalence of stabilizer states: a graphical characterisation.STACS: 42nd International Symposium on Theoretical Aspects of Computer ScienceJena, Germany2025HALback to text
• 41 inproceedingsA.Alexandre Clément, N.Noé Delorme and S.Simon Perdrix. Minimal Equational Theories for Quantum Circuits.LICS '24: 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science27Tallinn, EstoniaACMJuly 2024, 1-14HALDOIback to textback to text
• 42 inproceedingsA.Alexandre Clément, N.Noé Delorme, S.Simon Perdrix and R.Renaud Vilmart. Quantum Circuit Completeness: Extensions and Simplifications.International Conference on Computer Science Logic CSL 2024Naples, ItalyFebruary 2024HALDOIback to textback to text
• 43 inproceedingsN. A.Nazim A. Fatès. Asynchronous cellular system that solves the parity problem.30th International Workshop on Cellular Automata and Discrete Complex SystemsLNCSLecture Notes in Computer Science14782Durham (GB), FranceSpringer Nature Switzerland2024, 133-145HALDOIback to textback to text
• 44 inproceedingsJ.Joannès Guichon, N. A.Nazim A. Fatès, S.Sylvain Contassot-Vivier and M.Massimo Amato. Properties of B2B invoice graphs and detection of structures.Complex Networks 20231143Studies in Computational IntelligenceMenton, FranceSpringer Nature SwitzerlandFebruary 2024, 444-455HALDOIback to text
• 45 inproceedingsE.Emmanuel Hainry, B. M.Bruce M Kapron, J.-Y.Jean-Yves Marion and R.Romain Péchoux. Declassification Policy for Program Complexity Analysis.LICS '24: 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceTallinn Estonia, FranceACMJuly 2024, 1-14HALDOIback to textback to text

Conferences without proceedings

• 46 inproceedingsL.Louis Paletta, A.Anthony Leverrier, A.Alain Sarlette, M.Mazyar Mirrahimi and C.Christophe Vuillot. Robust sparse IQP sampling in constant depth.QIP2024Taipei, TaiwanMay 2024, 1337HALDOIback to text

Reports & preprints

• 47 miscF.Frédérique Bassino, M.Mathilde Bouvel, V.Valentin Féray, L.Lucas Gerin and A.Adeline Pierrot. Dense and nondense limits for uniform random intersection graphs.February 2024HALback to text
• 48 miscM.Mathilde Bouvel, E. S.Eric S. Egge, R. N.Rebecca N. Smith, J.Jessica Striker and J. M.Justin M. Troyka. Enumeration of pattern-avoiding alternating sign matrices: An asymptotic dichotomy.November 2024HALback to text
• 49 miscM.Mathilde Bouvel, V.Valentin Féray, X.Xavier Goaoc and F.Florent Koechlin. A canonical tree decomposition for order types, and some applications.March 2024HALback to text
• 50 miscM.Mathilde Bouvel, L.Luca Ferrari and B. E.Bridget Eileen Tenner. Between weak and Bruhat: the middle order on permutations.May 2024HALback to text
• 51 miscM.Mathilde Bouvel, C.Cyril Nicaud and C.Carine Pivoteau. Record-biased permutations and their permuton limit.September 2024HALback to text
• 52 miscM.Mathilde Bouvel, R.Rebecca Smith and J.Jessica Striker. Key-avoidance for alternating sign matrices.August 2024HALback to text
• 53 miscA.Alejandro Díaz-Caro, E.Emmanuel Hainry, R.Romain Péchoux and M.Mário Silva. A feasible and unitary quantum programming language.March 2024HAL
• 54 miscA.Alexandre Guernut and C.Christophe Vuillot. Fault-Tolerant Constant-Depth Clifford Gates on Toric Codes.November 2024HALback to text
• 55 miscJ.Joannès Guichon, S.Sylvain Contassot-Vivier and N.Nazim Fatès. Integral B2B Debt Netting: Model and Static Algorithm.February 2025HAL
• 56 miscE.Emmanuel Hainry, R.Romain Péchoux and M. A.Mário Alberto Machado da Silva. Branch Sequentialization in Quantum Polytime.December 2024HAL
• 57 miscM.Mathieu Hoyrup and T.Tom Favereau. Local generation of tilings.November 2024HALback to text
• 58 miscM.Mathieu Hoyrup and T.Tom Favereau. Local generation of tilings: the even bicolor Wang tilesets.November 2024HALback to text
• 59 miscM.Mathieu Hoyrup, A.Alexander Melnikov and K. M.Keng Meng Ng. Computable topological presentations.December 2024HALback to text
• 60 miscP.Piotr Mitosek and M.Miriam Backens. An algebraic interpretation of Pauli flow, leading to faster flow-finding algorithms.October 2024HALback to text
• 61 miscB.Benjamin Testart. Completing the enumeration of inversion sequences avoiding one or two patterns of length 3.December 2024HALback to textback to text
• 62 miscB.Benjamin Testart. Generating trees growing on the left for pattern-avoiding inversion sequences.November 2024HALback to text
• 63 miscY.Yijia Xu, Y.Yixu Wang, C.Christophe Vuillot and V. V.Victor V. Albert. Letting the tiger out of its cage: bosonic coding without concatenation.November 2024HALback to text

Scientific popularization

• 64 inbookI.Imad Assayakh, J.Joannès Guichon, P.-A.Pierre-Antoine Rault and C.Celina Treuillier. IZLife.Think before loading2024HAL