7.1.1 FiatLux

• Keywords:
  Cellular automaton, Multi-agent, Distributed systems
• 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.
• News of the Year:
  The latest version of the software incorporates improvements that were implemented by Océane Chazé, a second-year student at Télécom Nancy. She improved the User Interface by simplifying the interactions with the grid of cells. She also improved the software by introducing new features which allow users to encode initial conditions and transitions rules in a more elaborate way. This allows users to import some well-known models from external websites, e.g. Langton's self-reproducing rule or "classical" patterns in the Game of Life.
• URL:
  https://­project.­inria.­fr/­fiatlux/
• Contact:
  Nazim Fates
• Participants:
  Nazim Fates, Olivier Boure
• Partners:
  ENS Lyon, Université de Lorraine

7.1.2 ComplexityParser

• Name:
  ComplexityParser
• Keywords:
  Static analysis, Complexity, Static typing
• Functional Description:
  ComplexityParser is a static complexity analyzer for Java programs using a tier-based typing discipline. If a program is typable, this guarantees its runtime to be polynomial on the condition that it halts. The type inference is automatic, its complexity is linear in the size of the input program in practice.
• URL:
  https://­gitlab.­inria.­fr/­complexityparser/­complexityparser
• Contact:
  Romain Péchoux

7.1.3 Qimaera

• Name:
  Qimaera
• Keyword:
  Quantum programming
• Functional Description:
  Variational Quantum Algorithms are hybrid classical-quantum algorithms where classical and quantum computation work in tandem to solve computational problems. These algorithms create interesting challenges for the design of suitable programming languages. We introduce Qimaera, which is a set of libraries for the Idris 2 programming language that enable the programmer to implement (variational) quantum algorithms where the full power of the elegant Idris language works in synchrony with quantum programming primitives that we introduce. The two key ingredients of Idris that make this possible are (1) dependent types which allow us to implement unitary (i.e. reversible and controllable) quantum operations, and (2) linearity which allows us to enforce fine-grained control over the execution of quantum operations that ensures compliance with the laws of quantum mechanics. We demonstrate that Qimaera is suitable for variational quantum programming by providing implementations of the two most prominent variational quantum algorithms – QAOA and VQE. To the best of our knowledge, this is the first implementation of these algorithms that has been achieved in a type-safe framework.
• URL:
  https://­github.­com/­zamdzhiev/­Qimaera
• Publication:
  hal-03519238
• Contact:
  Vladimir Zamdzhiev
• Participants:
  Liliane-Joy Dandy, Emmanuel Jeandel, Vladimir Zamdzhiev

8.1.1 Fixed-point property for represented spaces

A space with a structure has the fixed-point property if every structure-preserving function from the space to itself has a fixed-point. We investigate which spaces have the fixed-point property for computable multivalued functions. We prove in particular that among the countably-based topological spaces, they are exactly the omega-continuous domains, an important class coming from semantics of programming languages. We apply our results to identify the complexity of indexing a basis of a topological space. Our article has been accepted in the Annals of Pure and Applied Logic17.

8.1.2 Algorithmic properties of sets

We investigated the relationship between the computability of sets and their topological properties. More precisely, we are studying which sets have “computable type”, which is the property that any algorithm that semidecides the set can be converted into an algorithm that fully decides the set. We have obtained a topological characterization of this property for a large class of sets, namely the finite simplicial complexes. Our results give an easy way of determining whether a given set has computable type. In particular we have settled the question for famous sets from topology: the dunce hat, and Bing's house. An article is currently submitted.

We have also obtained a partial characterization of this property using homology theory. Essentially, this property is related to the fact that every point belongs to a cycle, a notion provided by homology, extending the notion of cycle in a graph. We obtained a complete characterization of the finite simplicial complexes having computable type, the result was presented in ICALP 20.

8.2.1 Probabilistic cellular automata for problem solving

We designed new solutions to the cellular automata parity problem 41. The model is an interacting particles system, that is, a particular kind of stochastic cellular automton where cells are updated by pairs, randomly chosen at each time step. We analysed the convergence properties of two rules and show that they possess the required properties to classify the parity of the initial configurations. We present a formal analysis of the classification time, as well as numerical simulations, to establish that the classification time scales quadratically with the number of cells.

Our work on a bio-inspired mechanism for data clustering has finally been published 28. Our method uses amoebae which evolve according to cellular automata rules: they contain the data to be processed and emit reaction-diffusion waves at random times. The waves transmit the information across the lattice and cause other amoebae to react, by being attracted or repulsed. The local reactions produce small homogeneous groups which progressively merge and realize the clustering at a larger scale.

We continued our work with Régine Marchand (IECL, Université de Lorraine) and Irène Marcovici (IECL, Université de Lorraine) on the problem of detecting failures in a distributed network  53. The question that drives our research is to find out how we can detect that the failure rate has exceeded a given threshold without any central authority when some components progressively break down.

The special issue on complex systems following the SOLSTICE'19 conference was published. Entitled "Discrete Models of Complex Systems: recent trends and analytical challenges”, it contains 13 papers devoted to exploring differents topics related to the theme of complex sytems and non-classical models of computation (cellular automata, boolean networks, etc.) 15.

8.2.2 Diagrams for symbolic dynamics

One of the main open question in the field of symbolic dynamics is to decide whether the conjugacy problem is computable. This is a problem on shifts of finite type, that can be reformulated in terms of matrices. Two matrices $M$ and $N$ with nonnegative integer coefficients are said to be strong-shift-equivalent in one step if $M=RS$ and $N=SR$ for nonnecessarily square matrices $R$ and $S$ with nonnegative integer coefficients. Strong shift equivalence is the reflexive and transitive closure of this relation.

In  55 we show how to use results from category theory, in particular the concept of PROPs as used for instance in the ZX-calculus, to provide a purely categorical version of this question. Rather than just a technical exercise, we show in the same paper that we can recover many invariants of strong shift equivalence rather surprisingly by considering preexisting categories with bialgebras that are well known in mathematics. Whether the approach could lead to the computability of strong shift equivalence remains to be seen.

This paper was presented this year in the conference (without proceedings) ACT.

8.2.3 Analysis of graphs in the field of economics

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  51. 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. After designing a policy which finds a trade-off for the funding, we tested our methods on an empirical dataset from an electronic invoicing operator consisting of more than 60,000 companies. The first results show that this method is economically significant and feasible and these methods are now investigated in more details in the MURENE project, with the PhD of Joannès Guichon.

8.2.4 Rice-like theorems on automata networks

In collaboration with Pierre Guillon, Guillaume Theyssier and Kévin Perrot (respectively I2M, I2M, LIS, all Aix-Marseille University), we obtained very general complexity lower bounds on automata networks, a type of dynamical system that resembles generalized cellular automata. Any problem expressible in Monadic Second-Order logic on a reasonable condition that satisfies a mild technical condition is either trivial, or NP-hard, or coNP-hard. In particular it is not possible to design a polynomial-time solvable question on automata networks (even on purpose). Recently we showed that, should the mild technical condition be negated, either the MSO problem is also computationally hard, or standard complexity assumptions do not hold.

8.3.1 Characterizations of the class of Basic Feasible Functionals

In 16, we have provided a characterization of the class of Basic Feasible Functionals (BFF), the second-order counterpart of the class FP of first-order functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a programming language with a type system guaranteeing this complexity bound. The characterization of BFF based on an imperative language with oracle calls using a tier-based type system whose inference is decidable. BFF is exactly the class of second-order functionals in the simply-typed lambda-closure of functions computable by typed and terminating programs.

The result of 16 has been improved in 24, where it is shown that:

• the simply-typed lambda-closure can be internalized in the programming language so that no external lambda-closure (i.e., on the computed functions) is required to ensure completeness,
• the termination requirement on programs can be specified to some tractable instance (a restriction of size-change termination decidable in polynomial time),
• the inference remains decidable.

To sum up, 24 provides a first implicit, tractable, and complete and, hence, has solved a problem opened for 20 years. This paper has obtained the EATCS best paper award at ETAPS 2022.

8.3.2 Quantum expectation transformers

In 21, we introduce a new kind of expectation transformer for a mixed classical-quantum programming language. This semantic approach relies on a new notion of a cost structure, which we introduce, and which can be seen as a specialization of the Kegelspitzen of Keimel and Plotkin. This weakest precondition analysis is both sound and adequate with respect to the operational semantics of the language. Using the induced expectation transformer, a formal analysis methods for the expected cost analysis and expected value analysis of classical-quantum programs can be performed. The usefulness of this technique is illustrated by computing the expected cost of several well-known quantum algorithms and protocols, such as coin tossing, repeat until success, entangled state preparation, and quantum walks.

8.4.1 Preimages under the bubblesort operator.

This is a joint project with Luca Ferrari (University Florence, Italy) and his PhD student Lapo Cioni (who visited Loria for a month in the Fall 2021).

The bubblesort operator $𝖡$ is a operator acting on permutations (seen as arrays of numbers) like the bubblesort algorithm, but stopping after having scanned the array only once. For example, $𝖡\left(451362\right)=413526$. It is one of several operators on permutations which “partially sort” permutations (in a sense that can be made precise), like the most famous stacksort operator $𝖲$ or the queuesort operator $𝖰$.

In the article 14, we study preimages of permutations under the bubblesort operator $𝖡$, in a fashion similar to what has been done for $𝖲$ and $𝖰$ in the past. We achieve a description of these preimages much more complete than what is known for the more complicated sorting operators $𝖲$ and $𝖰$. We describe explicitly the set of preimages under $𝖡$ of any permutation $\pi$ from the left-to-right maxima of $\pi$, showing that there are $2k-1$ such preimages if $k$ is the number of these left-to-right maxima. We further consider, for each $n$, the tree $T_n$ recording all permutations of size $n$ in its nodes, in which an edge from child to parent corresponds to an application of $𝖡$ (the root being the identity (or sorted) permutation $12\cdots n$), and we present several properties of these trees.

8.4.2 Random cographs

This paragraph concerns three papers published in 2022, which already appeared as preprints in RA of previous years. They are joint papers with Frédérique Bassino (LIPN, Université Paris Nord), Michael Drmota (TU Wien, Austria), Valentin Féray (IECL, Université de Lorraine), Lucas Gerin (CMAP, École Polytechnique), Mickaël Maazoun (Oxford's Department of Statistics, UK) and Adeline Pierrot (LISN, Université Paris-Sud).

Cographs form one of the simplest hereditary graph classes. They can be defined as the graphs not containing the path with 4 vertices as an induced subgraph. A characterization of cographs which is essential for us is the following: cographs are the graphs which can be encoded by trees in a specific family, called cotrees.

In 12 and 11, we are interested in the asymptotic properties of uniform random cographs when the number of vertices tends to infinity. To achieve these results, we use a methodology inspired from our previous work on permutation, the latest paper of this series being 13.

In the first paper 12, we prove convergence towards a Brownian limiting object in the space of graphons, which we call the Brownian cographon. We then show that the degree of a uniform random vertex in a uniform cograph with $n$ vertices is of order $n$, and converges after normalization to the Lebesgue measure on $[0,1]$. We finally analyze the vertex connectivity (i.e. the minimal number of vertices whose removal disconnects the graph) of random connected cographs, and show that this statistics converges in distribution without renormalization. Our proofs use the encoding of cographs via cotrees, combined with the symbolic method and singularity analysis.

In the second paper 11, we focus on independent sets (or equivalently, cliques) in uniform random cographs. First, we prove that, with high probability as $n$ gets large, the largest independent set in a uniform random cograph with $n$ vertices has size $o\left(n\right)$, answering a question of Kang, McDiarmid, Reed and Scott. The proof relies on the convergence to the Brownian cographon, and on the self-similarity properties of this object. Second, and unexpectedly given the above results, we show that for $\beta >0$ sufficiently small, the expected number of independent sets of size $\beta n$ in a uniform random cograph with $n$ vertices grows exponentially fast with $n$. This time the proof relies on singularity analysis of the associated bivariate generating functions.

In 11, we also prove permutation analogues of all the results mentioned above.

8.4.3 Scaling limits of graph classes through split decomposition

This is a joint project 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). With this group of authors, we have an established collaboration, started approximately ten years ago and which continues until today (see also the previous paragraph). The common theme of the research we do together is to establish limit shape results for constrained combinatorial structures, using methods from analytic combinatorics (which is original in the landscape of the research on this topic). More precisely, we study families of permutations or graphs defined by the avoidance of substructures, and we answer (formally) the (informally phrased) question: “if we choose uniformly at random an object of large size in the considered family, what does it look like?”.

In the paper 35, we consider the three following families of graphs: distance-hereditary graphs, 2-connected distance-hereditary graphs and 3-leaf power graphs (the latter two being subclasses of the first one). We prove that the scaling limit of uniform random graphs in each of these families, with respect to the Gromov–Prokhorov topology, is the famous Brownian Continuum Random Tree of Aldous. Although such results are quite expected for families of graphs that are “almost trees” (like the ones we consider), our approach to establish this result is original, relying on the split decomposition of graphs (from the graph algorithms and graph theory literature) and on analytic combinatorics.

8.4.4 Convergence law for 231-avoiding permutations

In earlier work with Michael Albert and Valentin Féray, we compared the expressibility of two logics on permutations, called TOOB (theory of one bijection, seeing permutations as a bijection) and TOTO (theory of two orders, seeing permutations as a pair of total orders). In the recent paper 32, we focus on TOTO, and study a different problem. Namely, we investigate the existence of 0/1 or convergence laws when the domain is restricted to families of permutations avoiding patterns, similarly to a classical approach in the study of graphs.

Specifically, we prove that the class of 231-avoiding permutations satisfies a convergence law (but not a 0/1 law). In other words, for any first-order sentence $\psi$ in the language TOTO of two total orders, the probability $p_n\left(\psi \right)$ that a uniform random 231-avoiding permutation of size $n$ satisfies $\psi$ admits a limit as $n$ is large. Moreover, we establish two further results about the behaviour and value of $p_n\left(\psi \right)$: (i) it is either bounded away from 0, or decays exponentially fast; (ii) the set of possible limits is dense in $[0,1]$. Our tools come mainly from analytic combinatorics and singularity analysis. We hint at possible generalisations to other families of pattern-avoiding permutaitons.

8.4.5 Enumeration of pattern-avoiding inversion sequence

The results presented here have been obtained by Benjamin Testart during his Master internship and the first few weeks of his PhD thesis. 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  56, 49. These two initial articles 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 Mansour and Yildirim.

The paper 43, solves the final case by making use of a decomposition of inversion sequences avoiding the pattern 010. This decomposition needs to take into account the maximal value, and the number of distinct values occurring in the inversion sequence. The method is then expanded to solve the enumeration of inversion sequences avoiding the pairs of patterns $\{010,000\}$,$\{010,110\}$, $\{010,120\}$, and $\{010,201\}$ (solving therefore also $\{010,210\}$ whose enumeration is already known to coincide with that of $\{010,201\}$). For each family of pattern-avoiding inversion sequences considered, its enumeration requires the enumeration of some family of constrained words avoiding the same patterns, a question which Benjamin also solves along the way.

8.5.1 Development of the ZX-Calculus

This year, we have contributed in several ways to the foundations and the applications of the ZX-calculus, a diagrammatic language for quantum computing.

One of the main contribution concerns the development of a framework for adding two ZX-diagrams. In the ZX-calculus, each diagram represent a matrix. The formalism makes it easy to compose them sequentially or in parallel (which corresponds mathematically to multiplication and tensor product), but there is no easy way to obtain, from two diagrams representing matrices $M_1$ and $M_2$, a diagram that represent their addition, the matrix $M_1+M_2$.

Addition might not appear at first as an important property when manipulating diagrams that represents quantum evolution, but it appears naturally when trying to automatically differentiate diagrams: Indeed, the differentiation of a product $MN$ involves the sum $\partial MN+M\partial N$. Differentation of ZX-diagrams is central in many application in quantum machine learning, or quantum optimisation. For instance, it is an interesting potential development of a work in collaboration with EDF and the start-up Pasqal that has been published this year 23, a case study of an quantum optimisation in the field of smart-charging of electric vehicles.

This framework was developed by E. Jeandel, S. Perdrix and M. Veshchezerova and was presented this year in FSCD 2022 30.

8.5.2 Optimising resources for quantum coherent control

Coherent control of quantum computation can be used to improve some quantum protocols and algorithms.

This year, we have extended the PBS-calculus 48, a graphical language for coherent control which is inspired by quantum optics. This language can be used to describe coherently controlled quantum computation. Our main contribution is the development of procedure for optimising the resources required by a PBS-diagram for solving a particular task: we introduce an efficient procedure to minimise the number of oracle queries of a given diagram. We also consider the problem of minimising both the number of oracle queries and the size of the diagram. We show that this optimisation problem is NP-hard in general, but introduce an efficient heuristic that produces optimal diagrams when at most one query to each oracle is required.

This result has been presented at MFCS'22 29.

8.5.3 LOv-calculus, a language for optical quantum computing

We have started this year a fruitful collaboration with the start-up Quandela, which is working on the development of an optical-based quantum computer. The objective was the development of a graphical but formal language for describing quantum computing based on quantum optical devices. In collaboration with the Inria Quacs team, we have introduced the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We equiped the language with an equational theory that we proved to be sound and complete: two LOv-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOv-calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LOv-circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits.

This paper has been presented at MFCS'22  22. Notice that based on this result, we have more recently introduced the fist complete equational theory for quantum circuits, solving a 30-year open problem for the most comonly used model in quantum computing. This last result is currently available as a pre-print  39.

8.6.1 Encoding High-level Quantum Programs as SZX-diagrams

The Scalable ZX-calculus is a compact graphical language used to reason about linear maps between quantum states. These diagrams have multiple applications, but they frequently have to be constructed in a case-by-case basis. In this work we present a method to encode quantum programs implemented in a fragment of the linear dependently typed Proto-Quipper-D language as families of SZX-diagrams. We define a subset of translatable Proto-Quipper-D programs and show that our procedure is able to encode non-trivial algorithms as diagrams that grow linearly on the size of the program.

This paper has been presented at QPL'2022 27.

8.6.2 Variational quantum programming in idris

Variational Quantum Algorithms 58, 57, 50 are hybrid classical-quantum algorithms where classical and quantum computation work in tandem to solve computational problems. These algorithms create interesting challenges for the design of suitable programming languages, because they have to be able to accommodate both classical and quantum programming primitives simultaneously.

As part of this research project, we develop a set of libraries for the Idris 2 programming language that enable the programmer to implement (variational) quantum algorithms where the full power of the elegant Idris language works in synchrony with quantum programming primitives that we introduce. The two key ingredients of Idris that make this possible are (1) dependent types which allow us to implement unitary (i.e. reversible and controllable) quantum operations; and (2) linearity which allows us to enforce fine-grained control over the execution of quantum operations that ensures compliance with the laws of quantum mechanics. We demonstrate that our libraries, named Qimaera, are suitable for variational quantum programming by providing implementations of the two most prominent variational quantum algorithms – QAOA 50 and VQE 58. To the best of our knowledge, this is the first implementation of these algorithms that has been achieved in a type-safe framework.

The results of this work are described in a preprint 40, that has been accepted in 2023 in the conference ESOP. The software is open-source, available under the MIT license here. These results were obtained during the (bachelor) internship of Liliane-Joy Dandy in our team and she was awarded the "Research Internship Prize" at École Polytechnique for her work.

8.6.3 Semantics for variational quantum programming

The results in the previous research project show how we may approach variational quantum programming within an existing programming language. As part of this research project, we adopt a more theoretical and formal viewpoint and we consider a type system for variational quantum programming and we show how to design a suitable mathematical semantics for it.

In particular, we consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming. The classical subsystem of the language is the Probabilistic FixPoint Calculus (PFPC), which is a lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice. The quantum subsystem is a first-order linear type system that can manipulate quantum information. The two subsystems are related by mixed classical/quantum terms that specify how classical probabilistic effects are induced by quantum measurements, and conversely, how classical (probabilistic) programs can influence the quantum dynamics. We also describe a sound and computationally adequate denotational semantics for the language. Classical probabilistic effects are interpreted using a recently-described commutative probabilistic monad on DCPO. Quantum effects and resources are interpreted in a category of von Neumann algebras that we show is enriched over (continuous) domains. This strong sense of enrichment allows us to develop novel semantic methods that we use to interpret the relationship between the quantum and classical probabilistic effects. By doing so we provide the first denotational analysis that relates models of classical probabilistic programming to models of quantum programming.

The results of this project are published in POPL'22 25.

8.7.1 Compilation of Clifford isometries

This work is in collaboration with Simon Martiel (Atos). An important subset of quantum circuits is the group of Clifford circuits. It is efficiently simulable classically but only needs the addition of a single non-Clifford gate, usually the single-qubit T gate, to become universal. It is very common to target the universal gate set Clifford+T for a fault-tolerant implementation of quantum circuits. Being able to compile and optimize Clifford circuits, particularly the two-qubit count or depth constitute a crucial task in the development of the quantum computing stack. In 38 we propose a framework for the compilation of Clifford isometries. This framework encompass previous normal forms and permit to derive efficient synthesis algorithms. We demonstrate the use of this framework by benchmarking several synthesis algorithms derived from it and showing improvements of the 2-qubit count and depth for circuits taken from quantum chemistry experiments.

8.7.2 Hadamard count minimization in Clifford+T circuits

This work is in collaboration with Simon Martiel (Atos). 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. In both cases minimizing the number of Hadamard gate in the circuit beforehand can also help reducing the number of T gates overall. Lead by Vivien Vandalele for his PhD we are currently in the process of writing a paper tackling this problem.

8.8.1 Dehn twists on 2D color codes

Quantum error correcting code 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 qubit 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 between the logical qubits of the handle. Lead by Alexandre Guernut for his PhD we are studying the generalization of Dehn-twists to other 2D codes, namely color codes.

8.8.2 Quantum rotor codes

This work 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 have 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 of 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.

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

10.1.2 STIC/MATH/CLIMAT AmSud projects

10.2.1 Visits of international scientists

10.2.2 Visits to international teams

10.3.1 Horizon Europe

10.3.2 H2020 projects

10.4.1 ANR

10.4.2 Other initiatives

11.1.1 Scientific events: organisation

• Simon Perdrix participated to the organisation of EQIP Challenge workshop in Strasbourg Nov. 2022.

11.1.2 Journal

11.1.3 Invited talks

• Romain Péchoux has given an invited talk at the LoReL's seminar, 28 of November 2022, CONICET, Buenos Aires, (see webpage).
• Nazim Fatès has given an invited talk at the Summer Solstice Workshop on Complex systems, May 2022.
• Mathilde Bouvel has given invited talks at the London Colloquia in Combinatorics, Queen Mary University, London, (see webpage), and at the Permutation Patterns conference, Valparaiso University, Indiana, USA, (see webpage).

11.1.4 Leadership within the scientific community

Nazim Fatès is the head of the IFIP working group 1.5 on Cellular Automata and Discrete Complex Systems.

11.1.5 Scientific expertise

Romain Péchoux has been expert and referee for the HORIZON MSCA call.

Nazim Fatès was a member of a working group, lead by the INRS Institute1, which conducted a foresight exercises devoted to the theme “L’intelligence artificielle au service de la santé et sécurité au travail, enjeux et perspectives à l’horizon 2035”. The working group, composed of about twenty persons from the academic and industrial areas, presented their work on November 18, 2002, at the Maison de la RATP in Paris, with 90 in-person participants et more than 400 participants online. A 226-page report was produced and a short synthesis document was diffused.

11.1.6 Research administration

• Romain Péchoux is principal investigator of the Inria associate team TC(Pro)${}^3$.
• Christophe Vuillot is the principal investigator of the Inria associated team QASAR, and workpackage leader PEPR NISQ2LSQ.
• Simon Perdrix is coordinator of PEPR EPIQ, WP leader for EQIP Inria Challenge.

11.2.1 Supervision

• PhD: Robert Booth, “Formalismes pour la vérification de technologies quantiques”, Start: November 2018, Advisors: Damian Markham and Simon Perdrix. Robert defended in February 2022.
• PhD: Margarita Veshchezerova, “Quantum Computing for Combinatorial Optimisation”, Start: October 2019, Advisors: Emmanuel Jeandel and Simon Perdrix, joint supervision with Marc Porcheron at EDF (CIFRE). Margarita defended in December 2022.
• PhD in progress: Djamel Eddine Amir, “Computability of subsets of topological spaces”, Start: October 2020, Advisors: Emmanuel Jeandel and Mathieu Hoyrup.
• PhD in progress: Agustin Borgna “Vers une formalisation d’une chaˆıne de compilation pour un ordinateur quantique”, Start: October 2019, Advisors: Simon Perdrix and Benoit Valiron (LMF).
• PhD in progress: Nathan Claudet, “Structures fondamentales et applications des états graphes et du calcul par mesures”, Start: October 2022 (Master internship from March to September 2022), Advisors: Simon Perdrix and Mathilde Bouvel.
• PhD in progress: Alexandre Clément, “Graphical Languages for Quantum Control”, Start: September 2019, Advisors: Emmanuel Jeandel and Simon Perdrix.
• PhD in progress, Kinnari Vijay Dave, “Quantum programming with (co)inductive types”, Start: November 2022, Advistors: Romain Péchoux and Vladimir Zamdzhiev.
• PhD in progress: Alexandre Guernut, “Efficient Fault-Tolerant Quantum Computation with Quantum LDPC Codes”, Start: October 2021, Advisors: Emmanuel Jeandel and Christophe Vuillot.
• PhD in progress: Joannès Guichon, “B2B exchange networks and liquidity-saving mechanism by mutualisation of debt”, Start: October 2022, Advisors: Nazim Fatès and Sylvain Contassot-Vivier.
• PhD in progress: Mario Machado Da Silva, “Computational complexity of reversible computations and applications to quantum programming”, Start: October 2021, Advisors: Emmanuel Hainry and Romain Péchoux.
• PhD in progress: Benjamin Testart, “Énumération et formes limites des tables d'inversions évitant des motifs”, Start: October 2022 (Master internship from March to September 2022), Advisors: Mathilde Bouvel and Emmanuel Jeandel.
• PhD in progress: Vivien Vandaele, “Optimisation du calcul quantique tolérant aux fautes par le ZX-Calculus”, Start: September 2021, Advisors: Simon Perdrix and Christophe Vuillot, joint supervision with Simon Martiel at ATOS (CIFRE).

11.2.2 Juries

• Emmanuel Jeandel participated in the PhD defense of Justine Basselin (Université de Lorraine)
• Emmanuel Jeandel reviewed the PhD manuscript of Kostia Chardonnet (Université Paris-Saclay), Quentin Guilmant (Ecole Polytechnique) and Solène Esnay (Université Toulouse III)
• Mathilde Bouvel reviewed the PhD manuscripts of Benoît Corsini (McGill, Montréal, Canada), and of Michal Opler (Charles University, Prague, Czech Republic).
• Simon Perdrix participated in the PhD defense of Amélia Durbec (Aix Marseille Université), of Richard East (Université Grenoble Alpes), and of Adrien Suau (Université Montpellier).

11.3.1 Articles and contents

• Nazim Fatès, « L’intelligence artificielle, un défi pour l’être humain », RCF Nancy, émission « Destination inconnue », interview with Nicolas Dufour, November 2022.
• Nazim Fatès, « Lumière sur l'intelligence artificielle », Podcast Science en Lumière, interview with Véronique Bronner, May 2022.

11.3.2 Education

• Nazim Fatès, « Visite guidée de quelques automates cellulaires liés à la modélisation de phénomènes urbains », online talk for the students of the Classes préparatoires of the lycée Henri-Poincaré, Nancy.

11.3.3 Interventions

• Nazim Fatès, « Le temps passe-t-il pour l’intelligence artificielle ? », Wide-audience conference in the program Sciences et société, Nancy, March 31, 2022.
• Guilhem Gamard and Emmanuel Jeandel, « le puzzle de l'informaticien », stand at the « nuit des chercheur.e.s » science festival, Nancy, September 30, 2022.

International journals

• 11 articleF.Frédérique Bassino, M.Mathilde Bouvel, M.Michael Drmota, V.Valentin Feray, L.Lucas Gerin, M.Mickaël Maazoun and A.Adeline Pierrot. Linear-sized independent sets in random cographs and increasing subsequences in separable permutations.Combinatorial Theory232022, https://escholarship.org/uc/item/23340676
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• 12 articleF.Frédérique Bassino, M.Mathilde Bouvel, V.Valentin Féray, L.Lucas Gerin, M.Mickaël Maazoun and A.Adeline Pierrot. Random cographs: Brownian graphon limit and asymptotic degree distribution.Random Structures and Algorithms602March 2022, 166-200
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• 13 articleF.Frédérique Bassino, M.Mathilde Bouvel, V.Valentin Féray, L.Lucas Gerin, M.Mickaël Maazoun and A.Adeline Pierrot. Scaling limits of permutation classes with a finite specification: a dichotomy.Advances in Mathematics405August 2022, 108513
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• 14 articleM.Mathilde Bouvel, L.Lapo Cioni and L.Luca Ferrari. Preimages under the bubblesort operator.The Electronic Journal of Combinatorics294November 2022, https://www.combinatorics.org/ojs/index.php/eljc/article/view/v29i4p32
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• 15 articleA.Andreas Deutsch, N. A.Nazim A. Fatès and D.Danuta Makowiec. Discrete models of complex systems: Recent trends and analytical challenges.Physica D: Nonlinear Phenomena436August 2022, 133328
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• 16 articleE.Emmanuel Hainry, B.Bruce Kapron, J.-Y.Jean-Yves Marion and R.Romain Péchoux. A tier-based typed programming language characterizing Feasible Functionals.Logical Methods in Computer Science181February 2022, 31
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• 17 articleM.Mathieu Hoyrup. The fixed-point property for represented spaces.Annals of Pure and Applied Logic1735May 2022
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• 18 articleA.Anthony Leverrier, S.Simon Apers and C.Christophe Vuillot. Quantum XYZ Product Codes.QuantumJuly 2022
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• 19 articleC.Christophe Vuillot and N. P.Nikolas P. Breuckmann. Quantum Pin Codes.IEEE Transactions on Information TheoryApril 2022
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International peer-reviewed conferences

• 20 inproceedingsD. E.Djamel Eddine Amir and M.Mathieu Hoyrup. Computability of finite simplicial complexes.ICALPParis, FranceJuly 2022
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• 21 inproceedingsM.Martin Avanzini, G.Georg Moser, R.Romain Péchoux, S.Simon Perdrix and V.Vladimir Zamdzhiev. Quantum Expectation Transformers for Cost Analysis.Symposium on Logic In Computer Science LICS ’22Haifa, IsraelAugust 2022
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• 22 inproceedingsA.Alexandre Clément, N.Nicolas Heurtel, S.Shane Mansfield, S.Simon Perdrix and B.Benoît Valiron. LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits.Leibniz International Proceedings in Informatics (LIPIcs)47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)241Vienna, AustriaAugust 2022, 35:1--35:16
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• 23 inproceedingsC.Constantin Dalyac, L.Loic Henriet, E.Emmanuel Jeandel, W.Wolfgang Lechner, S.Simon Perdrix, M.Marc Porcheron and M.Margarita Veshchezerova. Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles.ROADEF 2022 - 23ème congrès annuel de la Société Française de Recherche Opérationnelle et d'Aide à la DécisionVilleurbanne - Lyon, FranceFebruary 2022
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• 24 inproceedingsE.Emmanuel Hainry, B. M.Bruce M Kapron, J.-Y.Jean-Yves Marion and R.Romain Péchoux. Complete and tractable machine-independent characterizations of second-order polytime.FoSSaCS 2022 - 25th International Conference on Foundations of Software Science and Computation Structures13242Lecture Notes in Computer ScienceMunich, GermanySpringer International PublishingMarch 2022, 368-388
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• 25 inproceedingsX.Xiaodong Jia, A.Andre Kornell, B.Bert Lindenhovius, M.Michael Mislove and V.Vladimir Zamdzhiev. Semantics for Variational Quantum Programming.POPL 2022 - 49th ACM SIGPLAN Symposium on Principles of Programming LanguagesPhiladelphia, United StatesJanuary 2022
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• 26 inproceedingsA. E.Ala Eddine Laouir and A.Abdessamad Imine. On Privacy of Multidimensional Data Against Aggregate Knowledge Attacks.Lecture Notes in Computer SciencePSD 2022 : PRIVACY IN STATISTICAL DATABASES 202213463International Conference on Privacy in Statistical Databases, PSD 2022Paris, FranceSpringer ChamSeptember 2022, 13
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Conferences without proceedings

• 27 inproceedingsA.Agustín Borgna and R.Rafael Romero. Encoding High-level Quantum Programs as SZX-diagrams.QPL2022Oxford, United KingdomJune 2022
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Scientific book chapters

• 28 inbookA.Amaury Saint-Jore, N. A.Nazim A. Fatès and E.Emmanuel Jeandel. Amoebae for clustering: a bio-inspired cellular automata method for data classification.42Automata and ComplexitySpringer, ChamApril 2022, 417-432
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Edition (books, proceedings, special issue of a journal)

• 29 proceedingsA.Alexandre ClémentS.Simon PerdrixResource Optimisation of Coherently Controlled Quantum Computations with the PBS-Calculus.MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE. INTERNATIONAL SYMPOSIUM. 47TH 2022. (MFCS 2022) (2 PARTS)241August 2022
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• 30 proceedingsE.Emmanuel JeandelS.Simon PerdrixM.Margarita VeshchezerovaAddition and Differentiation of ZX-Diagrams.2022
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Doctoral dissertations and habilitation theses

• 31 thesisM.Mathieu Hoyrup. Topological Aspects of Representations in Computable Analysis.Université de LorraineJanuary 2023
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Reports & preprints

• 32 miscM.Michael Albert, M.Mathilde Bouvel, V.Valentin Féray and M.Marc Noy. Convergence law for 231-avoiding permutations.December 2022
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• 33 miscD. E.Djamel Eddine Amir and M.Mathieu Hoyrup. Comparing computability in two topologies.June 2022
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• 34 miscD. E.Djamel Eddine Amir and M.Mathieu Hoyrup. Strong computable type.October 2022
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• 35 miscF.Frédérique Bassino, M.Mathilde Bouvel, V.Valentin Féray, L.Lucas Gerin and A.Adeline Pierrot. Scaling limit of graph classes through split decomposition.October 2022
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• 36 miscR.Robert Booth and T.Titouan Carette. Complete ZX-calculi for the stabiliser fragment in odd prime dimensions.April 2022
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• 37 miscR.Robert Booth, U.Ulysse Chabaud and P.-E.Pierre-Emmanuel Emeriau. Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements.January 2022
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• 38 miscT. G.Timothée Goubault de Brugière, S.Simon Martiel and C.Christophe Vuillot. A graph-state based synthesis framework for Clifford isometries.December 2022
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• 39 miscA.Alexandre Clément, N.Nicolas Heurtel, S.Shane Mansfield, S.Simon Perdrix and B.Benoit Valiron. A Complete Equational Theory for Quantum Circuits.January 2023
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• 40 miscL.-J.Liliane-Joy Dandy, E.Emmanuel Jeandel and V.Vladimir Zamdzhiev. Qimaera: Type-safe (Variational) Quantum Programming in Idris.January 2022
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• 41 reportN. A.Nazim A. Fatès. An asynchronous cellular system that solves the parity problem.Inria Nancy Grand-Est2022
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• 42 miscE.Emmanuel Hainry, R.Romain Péchoux and M.Mário Silva. A programming language characterizing quantum polynomial time.December 2022
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• 43 miscB.Benjamin Testart. Inversion sequences avoiding the pattern 010.December 2022
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• 44 miscC.Christophe Vuillot. Planar Floquet Codes.February 2022
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Other scientific publications

• 45 inproceedingsE.Emmanuel Hainry, R.Romain Péchoux and M.Mário Silva. An imperative programming language characterizing FBQP.QPL 2022 - Quantum Physics and LogicOxford, United KingdomJune 2022
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