2023Activity reportProjectTeamQUACS
RNSR: 202124178U Research center Inria Saclay Centre at Université ParisSaclay
 In partnership with:Université ParisSaclay
 Team name: Quantum Computation Structures
 In collaboration with:Laboratoire de Méthodes Formelles
 Domain:Algorithmics, Programming, Software and Architecture
 Theme:Proofs and Verification
Keywords
Computer Science and Digital Science
 A2.1.1. Semantics of programming languages
 A2.2.1. Static analysis
 A2.4. Formal method for verification, reliability, certification
 A2.4.1. Analysis
 A2.4.3. Proofs
 A6.5. Mathematical modeling for physical sciences
 A7.1.4. Quantum algorithms
 A7.2.3. Interactive Theorem Proving
 A8. Mathematics of computing
 A8.6. Information theory
Other Research Topics and Application Domains
 B5.11. Quantum systems
1 Team members, visitors, external collaborators
Research Scientists
 Pablo Arrighi [Team leader, UNIV PARIS SACLAY, Professor Detachement, from Sep 2023, HDR]
 Pablo Arnault [INRIA, Researcher]
 Marc De Visme [INRIA, Researcher]
 Renaud Vilmart [INRIA, ISFP]
 Vladimir Zamdzhiev [INRIA, ISFP]
Faculty Members
 Pablo Arrighi [Team leader, UNIV PARIS SACLAY, Professor, until Aug 2023, HDR]
 Esteban Castro [UNIV PARIS SACLAY, Chaire Junior Professor]
 Luidnel Maignan [UPEC, Associate Professor, Delegation INRIA]
 Benoît Valiron [CENTRALESUPELEC, Associate Professor]
PostDoctoral Fellows
 Titouan Carette [UNIV PARIS SACLAY, until Aug 2023]
 Alexandre Clement [INRIA, PostDoctoral Fellow, from May 2023]
 James Hefford [INRIA, PostDoctoral Fellow, from Oct 2023]
 Timothée Hoffreumon [UNIV PARIS SACLAY, from Nov 2023]
 Augustin Vanrietvelde [INRIA, PostDoctoral Fellow, until Oct 2023]
PhD Students
 Dogukan Bakircioglu [INRIA, from Dec 2023]
 Kostia Chardonnet [UNIV PARIS SACLAY, until Jan 2023]
 Marin Costes [ENS PARISSACLAY]
 Nicolas Heurtel [LMF, from Dec 2023]
 Louis Lemonnier [ENS PARISSACLAY]
 Octave Mestoudjian [ED STIC, from Sep 2023]
 Jérôme Ricciardi [CEA]
Technical Staff
 Tristan Cam [INRIA, Engineer, from Dec 2023]
Interns and Apprentices
 Samuel AychetClaisse [LMF, from Apr 2023 until Jul 2023]
 Dogukan Bakircioglu [UNIV PARIS SACLAY, from May 2023 until Aug 2023]
 Colin Blake [INRIA, Intern, from Mar 2023 until Jun 2023]
 Rui Cesista [INRIA, Intern, from May 2023 until Jul 2023]
 Evi Kasnetsi [UNIV PARIS SACLAY, from Mar 2023 until Aug 2023]
 Charlène Laffond [UNIV PARIS SACLAY, from Apr 2023 until Jul 2023]
 Julien Lamiroy [ENS PARISSACLAY, from Mar 2023 until Aug 2023]
 Tianyi Li [INRIA, Intern, from May 2023 until Jul 2023]
 FatimaZahra Merimi [INRIA, Intern, from May 2023 until Aug 2023]
 Octave Mestoudjian [LMF, from Feb 2023 until Aug 2023]
 Joaquim Minarelli Gaspar [INRIA, Intern, from Jun 2023 until Aug 2023]
 Mohamed Nazib [UNIV PARIS SACLAY, from Mar 2023 until Jul 2023]
 Ugo Nzongani [UNIV PARIS SACLAY, from Mar 2023 until Jun 2023]
 Sunheang Ty [IRTSystemX, from Mar 2023 until Sep 2023]
 Lucien Wacquez [INRIA, Intern, from Feb 2023 until Jul 2023]
Administrative Assistant
 Joyce Soares Brito [INRIA]
External Collaborators
 Théodore ChapuisChkaiban [Consensys]
 Shane Mansfield [Quandela]
 Simon Perdrix [INRIA]
 Zeno Toffano [CENTRALE]
2 Overall objectives
Quantum information processing is one of the rising forces of the information era. Encoding information within quantum systems and manipulating them promises to lead to great advantages, with three main application domains: quantum cryptography, quantum simulation, and quantum algorithmics. To understand its strengths and limits, we take a transversal stance and seek to capture which resources are granted to us by nature, at the fundamental level, for the sake of computing (e.g. quantum and spatial parallelism). We do so by abstracting away physics’ ability to compute, into formal models of quantum computation (e.g. quantum automata and graph rewriting models). We then verbalize its main structures as quantum programming languages (e.g. quantum lambdacalculus, process algebra). Actually, the process goes both ways, when developments in quantum programming languages lead to the discovery of new structures which may or may not be compilable into formal models of quantum computation, raising the sometimes fascinating question of the physicality of these resources.
3 Research program
3.1 Quantum simulation
One usually distinguishes three main fields of applications of Quantum Computing: quantum cryptography (shortterm), quantum simulation (midterm), quantum algorithmic (longterm). Quantum simulation then divides into two subfields: continuoustime quantum simulation, which is very physicky and consists of ad hoc emulation of one Hamiltonian by another, and discretetime quantum simulation, which is much closer to quantum algorithmic: this is where we stand. In particular, we focus on the provision of a quantumcircuit description of the dynamics of fundamental particles. In particular, as we design these quantum simulation schemes, our focus is on retaining the symmetries of the simulated model. This is both a matter of efficiency and correctness. For instance, our discretizations have a maximum speed of propagation of the information, which coincides with the speed of light in the simulated system, as a first step towards retaining Lorentz symmetry. Similarly, our discretizations exhibit the gauge symmetries that motivate the different fundamental particles. The long term goal of this program is to provide a satisfactory quantumcircuit descriptions of the whole standard model of particle physics.
3.2 Semantics and Programming
In the research program on Semantics, the QuaCS team is working on developing mathematical methods and tools that formulate the precise meaning and behavior of (quantum) systems, processes, type systems and programming languages, other formal languages and computational models. This includes, but is not limited, to the following:
 Operational semantics: a mathematically precise description of the dynamics of quantum programs and other computational models (e.g., the smallstep semantics of quantum lambda calculi, tokenmachine semantics of quantum diagrammatic calculi).
 Mathematical and denotational semantics: a mathematical interpretation of a quantum programming language, process theory, diagrammatic calculus, etc., which is always expected to be sound and often expected to be adequate or complete.
This line of research is focused on identifying fundamental connections between the static specification (e.g. syntax) of quantum languages, their dynamic behavior (e.g. operational semantics) and their mathematical interpretation (e.g. denotational semantics) with the intention of developing each of these components further.
3.3 Graphical languages and optimization for quantum computation
The QuaCS team is involved in the development and study of graphical calculi such as quanctum circuits, ZX, ZW, ZHcalculi, but also languages for linear optics, such as the LOvcalculus. These languages are supposed to represent particular features of quantum computing, and hence are designed with a particular semantics in mind. A question of interest in the field is that of completeness with respect to that semantics : the ability to graphically turn any two equivalent diagrams into one another, making it possible to entirely reason within the language. The team is interested in the structure quantum operators have, that can be exhibited by the graphical approach, and depending on the model of computation at hand. It then becomes possible to study the links between the graphical languages, and hence, between the different models of computation. Recently, some focus has been put in the use of graphical languages for the study of indefinite causal orders, a extension to the usual quantum computation model, where not only data is quantum, but also the control flow of the program, which is allowed by the theory but still not well understood.
4 Application domains
4.1 Quantum simulation
Feynman’s invention of Quantum Computing really came out of a frustration: that of seeing classical computers take such a long time to simulate quantum systems. His intuition was that «quantum computers» would do a better job at simulating quantum systems. There is not the slightest doubt indeed that quantum simulation will have major outcomes for society. Thinking about it, most of the objects that surround us (cars, computers, furniture…) are designed on computers, thanks to the fact that we can prototype and simulate them on classical computers. That is, up to a certain scale. Below that we are left in the dark as quantum effects come into play, yielding an exponential blow up of the cost or simulation. For now. But, the day we will have good quantum computers and good quantum simulation algorithms to run upon them, we will be able to simulate these particles, atoms, molecules and the way they interact. Consequently we will be able to design specificpurpose molecules, materials, nanotechnologies, with applications in chemistry, biochemistry, electronics, mechanics. At QuaCS we focus on the bottom layer: the quantumsimulation algorithms for fundamental particles. After all, to be able to efficiently simulate fundamental interactions is to be able to simulate virtually everything, from first principles. An added bonus of this strand of research is that usually when we express some physics as a quantum algorithm, it becomes way simpler, more explanatory.
4.2 Semantics and Programming
This line of research can reveal interesting connections between mathematical structures, computational models, type systems and other formal languages. Ideally, one endpoint of such a connection can be used to influence the design and development of the other endpoint, because these connections can allow us to improve our understanding of the different aspects of the (quantum) systems and computational models under consideration.
For instance, monads in category theory were the inspiration for introducing monads in programming languages. Another example includes categorical quantum mechanics which lead to the development of the ZXcalculus along with other useful tools, such as PyZX/QuiZX, which may be used for optimisation of quantum circuits and classical simulation of quantum processes.
4.3 Graphical languages and optimization for quantum computation
One of the main features of graphical languages is that they can be made abstract enough to remove unnecessary clutter and ease reasoning on quantum operators. This has several consequences : They are rather intuitive to work with, while at the same time being completely formal They can provide an intermediate representation of quantum programs, with enough abstraction to reason about and modify the program during compilation. The most illustrative example of such modification is circuit optimisation, where the goal is to reduce the number of "expensive" quantum gates in the circuit, which can be achieved by turning the circuit into a ZXdiagram, then using its equational theory to perform the reduction. Together with the simplification heuristic, it is possible to exploit this "uncluttering" effect to perform more efficient classical simulation of quantum programs. It can be exploited to perform automated verification of quantum programs.
5 New software, platforms, open data
5.1 New platforms
5.1.1 Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing
Participants: Benoît Valiron, Nicolas Heurtel, Shane Mansfield.
We introduce Perceval , an opensource software platform for simulating and interfacing with discretevariable photonic quantum computers, and describe its main features and components. Its Python frontend allows photonic circuits to be composed from basic photonic building blocks like photon sources, beam splitters, phaseshifters and detectors. A variety of computational backends are available and optimised for different usecases. These use stateoftheart simulation techniques covering both weak simulation, or sampling, and strong simulation. We give examples of Perceval in action by reproducing a variety of photonic experiments and simulating photonic implementations of a range of quantum algorithms, from Grover's and Shor's to examples of quantum machine learning. Perceval is intended to be a useful toolkit for experimentalists wishing to easily model, design, simulate, or optimise a discretevariable photonic experiment, for theoreticians wishing to design algorithms and applications for discretevariable photonic quantum computing platforms, and for application designers wishing to evaluate algorithms on available stateoftheart photonic quantum computers.
6 New results
6.1 Completeness of SumOverPaths for ToffoliHadamard and the Dyadic Fragments of Quantum Computation
Participants: Renaud Vilmart.
We consider the ToffoliHadamard fragment of quantum computing (one of the simplest universal fragment), in the setting of "Sum Overpaths", a symbolic approach to efficiently representing quantum processes, used for specification and verification, e.g. in CEA's Qbrick tool. We show that a simple set of equations makes the framework complete. We then extend this result to all dyadic fragments of quantum computing (used e.g. in the QFT in Sho'r algorithm). [cite] (associated special issue paper under reviewing).
6.2 Compositionality of Planar Perfect Matchings
Participants: Renaud Vilmart, Titouan Carette.
We show that graphical language ZWcalculus has tight links with counting perfect matchings in graphs. From the equational theory of ZW, we were able to reprove Kasteleyn's result which is that the counting problem becomes polynomial when the graph is planar. Our proof is purely graphical and very different from Kasteleyn's. It highlights an efficiently simulable fragment of ZW, something of interest for optimisation and classical simulation, paths that we are currently exploring.
6.3 Complete Graphical Language for HermiticityPreserving Superoperators
Participants: Renaud Vilmart, Titouan Carette, Timothée Hoffreumon.
We introduce the first complete universal graphical language for Hermiticitypreserving superoperators. Antiunitarity, and negativity in the density matrix formalism, although non physical, is a useful tool for physicists, and is now useable in a ZXlike graphical language.
6.4 A Complete Equational Theory for Quantum Circuit
Participants: Alexandre Clement, Nicolas Heurtel, Shane Mansfield, Simon Perdrix.
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations. The proof is based on the properties of multicontrolled gates – that are defined using elementary gates – together with an encoding of quantum circuits into linear optical circuits, which have been proved to have a complete axiomatisation.
6.5 Quantum Circuit Completeness: Extensions and Simplifications
Participants: Alexandre Clement, Renaud Vilmart.
The first completeness result for arbitrary quantum circuits, involved a few nonintuitive and hard to use equations. We simplify the equational thoery here, first for the most constrained case of unitary circuits, then simplify it further in settings that allow ancillary qubits.
6.6 On new PageRank computation methods using quantum computing
Participants: Théodore ChapuisChkaiban, Zeno Toffano, Benoît Valiron.
In this paper we propose several new quantum computation algorithms as an original contribution to the domain of PageRank algorithm theory, Spectral Graph Theory and Quantum Signal Processing. We first propose an application to PageRank of the HHL quantum algorithm for linear equation systems. We then introduce one of the first QuantumBased Algorithms to perform a directed Graph Fourier Transform with a low gate complexity. After proposing a generalized PageRank formulation, based on ideas stemming from Spectral Graph Theory, we show how our quantum directed graph Fourier Transform can be applied to compute our generalized version of the PageRank.
6.7 Adjustabledepth quantum circuit for positiondependent coin operators of discretetime quantum walks
Participants: Ugo Nzongani, Pablo Arnault.
Discretetime quantum walks with positiondependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in an approximate quantumcircuit implementation of the coin operator that is efficient. If we want the quantumcircuit implementation to be exact (e.g., either, in the case of a smooth position dependence, to have a perfect precision, or in order to treat a nonsmooth position dependence), but the depth of the circuit not to scale exponentially, then we can use the lineardepth circuit of the previous reference, which achieves a depth that is linear at the cost of introducing an exponential number of ancillas. In this paper, we provide an adjustabledepth quantum circuit for the exact implementation of the positiondependent coin operator. This adjustabledepth circuit consists in (i) applying in parallel, with a lineardepth circuit, only certain packs of coin operators (rather than all of them as in the original lineardepth circuit), each pack contributing linearly to the depth, and in (ii) applying sequentially these packs, which contributes exponentially to the depth.
6.8 Central Submonads and Notions of Computation: Soundness, Completeness and Internal Languages
Participants: Titouan Carette, Louis Lemonnier, Vladimir Zamdzhiev.
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute with all other effects, may be formulated for strong monads acting on symmetric monoidal categories. We identify three equivalent conditions which characterise the existence of the centre of a strong monad (some of which relate it to the premonoidal centre of Power and Robinson) and we show that every strong monad on many wellknown naturally occurring categories does admit a centre, thereby showing that this new notion is ubiquitous. More generally, we study central submonads, which are necessarily commutative, just like the centre of a strong monad. We provide a computational interpretation by formulating equational theories of lambda calculi equipped with central submonads, we describe categorical models for these theories and prove soundness, completeness and internal language results for our semantics.
6.9 Typesafe Quantum Programming in Idris
Participants: Vladimir Zamdzhiev.
Variational Quantum Algorithms are hybrid classicalquantum 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. In this paper we introduce Qimaera, which is a set of libraries for the Idris 2 programming language that enable the programmer to implement hybrid classicalquantum algorithms where the full power of the elegant Idris language works in synchrony with quantum programming primitives. The two key ingredients of Idris that make this possible are (1) dependent types which allow us to implement unitary quantum operations; and (2) linearity which allows us to enforce finegrained control over the execution of quantum operations so that we may detect and reject many physically inadmissible programs. We also show that Qimaera is suitable for variational quantum programming by providing implementations of two prominent variational quantum algorithms – QAOA and VQE. Remark: most of the work was done in 2021 when Vladimir was a member of the MOCQUA team.
6.10 A quantum simulation algorithm for 3+1 QED
Participants: Pablo Arrighi.
We achieved the first quantum cellular automaton model for reallife interacting particles, namely electrons and photons, a.k.a 3+1 quantum electrodynamics. We motivated our construction by proposing a discrete version of a fundamental symmetry of Physics, namely gauge symmetry, which turns out to be reminiscent of faulttolerance in Computer Science. This opens the way for natively discrete formulations of quantum field theories, otherwise renowned for their illdefinedness.
6.11 Addressable Quantum Gates
Participants: Pablo Arrighi, Marin Costes, Benoît Valiron.
We extended the circuit model of quantum computation so that the wiring between gates is softcoded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we expressed the quantum switch and the polarizing beamsplitter within the model. In this context, the names used as addresses should not matter beyond the wiring they describe; i.e., quantum evolutions should commute with “renamings.” We have shown that these quantum evolutions can still act nontrivially upon the names.
6.12 Graph Subshifts
Participants: Pablo Arrighi.
We proposed a definition of graph subshifts of finite type. These are sets of graphs that are defined by forbidding finitely many local patterns. This is interesting because it is a natural generalisation of both 1/ the notions of subshifts of finite type from classical symbolic dynamics and 2/ finitely presented groups from combinatorial group theory. In this paper, we focussed on the question whether such local conditions can rigidify the shape of the graph.
6.13 Measurement events relative to temporal quantum reference frames
Participants: Esteban Castro.
We compare two known consistent models for the emergence of time evolution as correlations between a system and a quantum clock. The two models give the same predictions when the clocks are ideal but differ radically in the nonideal case. We clarify the operational interpretation of each, explaining the discrepancy.
6.14 Graphical Language for Tensor and Coproduct
Participants: Kostia Chardonnet, Marc De Visme, Renaud Vilmart, Benoît Valiron.
We refined previous works on the "ManyWorld Calculus" (MWC), a graphical language designed to expand quantum circuits to fully capture quantum supperposition, into the "TensorPlus Calculus" (TPC). The TPC is a graphical language that bridge the gap between languages like quantum circuits or the ZXcalculus, where two wires in parallel corresponds to a pair of data, and languages for quantum linear optic, where two wires in parallel correspond to two alternative paths that photons can take. Contrary to the MWC, the TPC does not rely on an additional structure of "worlds": the language is minimalistic, the additional structure is fully implicit and can be deduced by the way the functions are plugged into one another. We provide a complete equational theory for this language, and a clear categorical presentation.
7 Bilateral contracts and grants with industry
Quandela
Participants: Benoît Valiron, Pablo Arrighi, Nicolas Heurtel.
In the context of a PhD funded by CIFRE, QuaCS and Quandela are building a collaboration on the study of quantum linear optics. The approach is both theoretical –with the development of a formal language for reasoning on optical circuits, and practical, targeted towards simulation.
8 Partnerships and cooperations
8.1 International initiatives
QISS (John Templeton grant)
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
The Quantum Information Structure of Spacetime

Partner Institutions:
 Institute for Quantum Optics and Quantum Information, Vienna
 Rotman Institute for Philosophy, Western University
 Center for Theoretical Physics, AixMarseille University
 Quantum Group and Clarendon Laboratory, University of Oxford
 Perimeter Institute
 University of ParisSaclay, Quantum Computation Structures group
 Quantum Information and Computation Initiative, HKU
 Okinawa Institute of Science and Technology
 University of California Santa Barbara, Physics dpt
 Center for Quantum Information and Communication, Brussels
 Quantum Information Laboratory, Rome La Sapienza University
 Penn State University, Institute for Gravitation and the Cosmos
 Center for Mathematical Sciences, UNAM
 Bard College, New York
 ETH Zürich
 The University of Melbourne
 Royal Holloway, University of London
 Universität Bonn

Date:
20232026
 Additionnal info:
QISS aims to found the physics of quantum spacetime on an information theoretical basis, bring within reach empirical access to quantum gravity phenomenology leveraging rapidly advancing quantum technologies, and promote interactions between physicists and philosophers. The broader scope of the consortium is to establish a long term research program that brings together the represented communities, towards the common goal of unravelling the Quantum Information Structure of Gravity.
QISS was initially conceived from interactions between the Quantum Gravity Group of the Center for Theoretical Physics and the Laboratory of Informatics and Systems at the University of AixMarseille, France. It was concretely conceived as an international collaborative project in fundamental research during an exploratory meeting held at the Slovak Academy of Sciences, Bratislava, in November 2018. QISS took off by a generous three year first phase grant by the John Templeton Foundation awarded to the Center for Space, Time and the Quantum that administers the project. A second phase grant was subsequently awarded to the QISS project by JTF.
8.2 European initiatives
HPCQS (EuroHPC project)
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
High Performance Computer – Quantum Simulator hybrid

Partner Institution:
 Jülich Supercomputing Centre (JSC), Germany
 ParTec, Germany
 Commissariat à l’énergie atomique et aux énergies alternatives (CEA), France
 Grand équipement national de calcul intensif (GENCI), France
 Barcelona Supercomputing Centre (BSC), Spain
 CINECA  Consorzio Interuniversitario, Italy
 Irish Centre for High End Computing (ICHEC), Ireland
 BULL SAS (ATOS), France
 FlySight, Italy
 ParityQC, France
 Sorbonne Université, France
 CentraleSupelec, France
 INRIA, France
 Consiglio Nazionale delle Ricerche (CNR), Italy
 The University of Innsbruck, Austria
 Fraunhofer IAF, Germany
 Eurice  European Research and Project Office GmbH, Germany

Date:
20212024
 Additionnal info:
The project HPCQS aims to integrate two quantum simulators, each controlling about 100+ quantum bits (qubits) in two already existing supercomputers:
 the supercomputer Joliot Curie of GENCI, the French national HPC organisation, located in France;
 the JUWELS supercomputer of the Jülich Supercomputing Centre (JSC), located in Germany.
In doing so, HPCQS will become an incubator for quantumHPC hybrid computing that is unique in the world.
The seamless integration of quantum hardware with classical computing resources will enable research entities and industries to exploit new quantum technologies and find solutions to complex challenges in physics, chemistry and numerical optimisation with practical applications, for example, to materials and drug design, logistics and transportation.
HPCQS will develop the programming platform for the quantum simulator and offer cloudbased access to users and researchers. The project will build an open and evolutionary infrastructure that aims at expanding in the future by including a diversity of quantum computing platforms at different technology readiness levels in an HPC system and by allowing the integration of other European partners. The HPCQS infrastructure is a first step towards a European quantum computing infrastructure in synergy with the ongoing European efforts to establish a worldleading HPC infrastructure.
8.3 National initiatives
EPiQ (PEPR Quantique)
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique

Partner Institutions:
 INRIA, France
 CNRS, France
 CEA, France

Date:
20222027
 Additionnal info:
The French quantum computing research community has always been at the forefront of international research. It thus provides the foundations for an ambitious strategy aiming at: (1) Understanding the advantages and limits of quantum computing via both quantum complexity research and the discovery and enhancement of algorithms (2) Defining the framework for quantum computation using highlevel languages, comparison of computational models as well as using their relations for program optimization (3) Develop simulation tools to anticipate the performances of algorithms on noisy quantum machines. Algorithmic aspects are key in the field of quantum computing which witnesses a tremendous intensification of research efforts worldwide. Indeed, in addition to determining the design and the construction of hardware quantum processors, algorithms also constitute the interface through which users will solve their practical use cases leading to potential economic gain. Based on the outstanding French position, our project aims at developing algorithmic techniques for both noisy quantum machines (NISQ) and faulttolerant ones so as to facilate their practical implementation. To this end, a first Work Package (WP) is dedicated to algorithmic techniques, a second one focuses on computational models and languages so as to facilitate the programming of quantum machines and to optimize the code execution steps. Lastly, the third WP aims at developing the simulation techniques of quantum computers.
EQIP (Inria challenge project)
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
Engineering for Quantum Information Processors

Partner Institution:
 INRIA, France

Date:
20212024
 Additionnal info:
While the technological development that has led us from the abacus to today’s supercomputers or even to the latest achievements of machine learning are quite spectacular, one should not forget that they all fit the very same model of computation, formalized by Turing in the 1930s, and therefore fall under the umbrella of classical computing. Quantum physics has played a major role in this story through the 1st quantum revolution which gave birth to the transistor, the laser and the microprocessor. Rather surprisingly, the impact of quantum physics on the theory of computation is very likely still in its infancy. There is little doubt that an unprecedented shift will occur in the decades to come and that an entirely new form of computing will be dominant in 50 years (and probably much sooner). This is the object of the 2nd quantum revolution which will harness the quantum properties of matter and light to process data much more efficiently than is possible by purely classical means. The scope of applications remains hard to delineate at this point but covers a large spectrum of human activities: simulation of quantum systems will be crucial to develop new medicine, help fighting climate change by developing better materials to store or transport energy, reducing CO2 emissions by developing efficient processes to capture CO2; quantum computing will also be instrumental to solve optimization problems intractable today. At the same time, quantum technologies will dramatically impact cryptography and requires to implement important changes right now.
If the first glimpse of this second quantum revolution can be traced back to visionaries like Feynman or Deutsch in the early 80s, the fields of quantum computation and quantum simulation really took off in the last decade or so. The longterm objective of this line of work is to build a large universal quantum computer and the main scientific challenges today are to identify potential approaches for scaling up the small quantum processors consisting of a few tens of qubits already available, to anticipate how to program these new machines, and to understand what new capabilities will become accessible once quantum computing becomes available.
TaQC (ANR)
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
Taming Quantum Causality

Partner Institutions:
 UPSaclay  LMF Université ParisSaclay  Laboratoire Méthodes Formelles
 Inria Centre de Recherche Inria de Lyon  ATLYS
 NEEL Institut Néel
 LARSIM Commissariat à l'énergie atomique et aux énergies alternatives

Date:
20232027
 Additionnal info:
Quantum technologies provide advantages by exploiting nonclassical resources, such as superposition or entanglement. Recently, it has been realized that one can obtain new advantages by exploiting causal structures that are inherently quantum. This quantum "causal indefiniteness" constitutes a novel resource and opens new perspectives in quantum information. Despite foundational progress and several experimental realizations, the concrete implications for quantum computing nevertheless remain poorly understood so far. In this project we will work to bridge this gap and to develop quantum causality as a new nonclassical resource on par with superposition and entanglement.
To achieve this, we will develop three directions. (1) Firstly, we will develop a Generalised Probabilistic Theories approach to understand causal indefiniteness within a larger class of models. This will help clarify which causally indefinite process are physical and what precise role is played by genuinely nonclassical resources such as superposition and entanglement. (2) Secondly, we will go beyond the standard example of the "quantum switch" to study more concrete models of causally indefinite computation. In doing so, we will systematically explore the possible applications of causal indefiniteness and unveil the potential of causally indefinite computations. (3) Finally, we will use ZXCalculus to harness the capabilities of causal indefiniteness at the compilation level. Using ZXCalculus as a springboard towards programming causally indefinite computations will help us optimize the use of this new resource.
Together, these goals work towards our ultimate objective of finding the right arguments in the right language to give causal indefiniteness a unique place among the leading conceptual and empirical paradigms of quantum information.
HQI (National Quantum Plan project )
Participants: Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Benoit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title:
Hybrid HPCQuantum platform and a research program

Partner Institutions:
 INRIA, France
 CNRS, France
 CEA, France
 GENCI, France
 France Universités, France
 ANR, France
 PIA4, France
 France Relance, France

Date:
20222027
 Additionnal info:
In January 4th 2022, one year after the National Quantum Plan was announced by the French President, Neil Abroug, the national strategy coordinator, launched HQI: France Hybrid HPCQC Initiative.
HQI is an integrated initiative. It combines a hybrid computing platform that couples several quantum processors with GENCI’s JoliotCurie supercomputer hosted at TGCC (CEA), and an academic and industrial research program with user enablement.
This HPCQC hybridization is an innovative and unique initiative that will benefit from the renowned expertise of the CEA/TGCC (Très Grand Centre de Calcul) teams in infrastructure operation, security and support to the scientific community.
The HQI initiative aims at serving the needs of French and European, academic and industrial research scientists, who want to evaluate free of charge, on a public infrastructure, the potential of quantum computing for their applications and develop international collaborations to foster open research.
9 Dissemination
9.1 Promoting scientific activities
9.1.1 Full Organisation of an International Conference
Participants: Vladimir Zamdzhiev, Benoît Valiron, Shane Mansfield, Augustin Vanrietvelde, Renaud Vilmart, Pablo Arrighi.
Quantum Physics and Logic (QPL) is an annual conference that brings together academic and industry researchers working on mathematical foundations of quantum computation, quantum physics, and related areas. It is one of the flagship conference for the topics of the QuaCS team. The main focus is on the use of algebraic and categorical structures, formal languages, type systems, semantic methods, as well as other mathematical and computer scientific techniques applicable to the study of physical systems, physical processes, and their composition. Work applying quantuminspired techniques and structures to other fields (such as linguistics, artificial intelligence, and causality) is also welcome.
The 2023 edition of QPL happened in July 2023. It was hosted in Paris by Inria and Quandela. Shane Mansfield, Benoît Valiron, and Vladimir Zamdzhiev were PC and OC cochairs. Additionally, Pablo Arrighi, Renaud Vilmart and Augustin Vanrietvelde were PC and OC members, and most members of the QuaCS teams were involved to some degree (reviewing paper, logistics, etc).
A record 152 submissions (excluding withdrawals and retractions) were considered for review by the PC. QPL 2023 had 54 accepted submissions in the nonproceedings track and 14 accepted submissions in the proceedings track. Most of the talks were presented during parallel sessions, but a selection of talks were presented during plenary sessions in the mornings. The program also had several poster sessions and one session dedicated to showcasing accepted programming tool submissions. There was also an industry session where industrial sponsors of QPL 2023 were given an opportunity to present their companies. The industry session consisted of two talks – one by Quandela (Diamond Sponsor) and one by Quantinuum (Gold Sponsor).
The QPL 2023 conference featured an award for Best Student Paper. Papers eligible for the award were those where all the authors are students at the time of submission. The PC decided to award the Best Student Paper award for QPL 2023 to Cole Comfort (Department of Computer Science, University of Oxford) for his paper "The Algebra for Stabilizer Codes".
9.1.2 Other scientific events
Member of the conference program committees
 Benoît Valiron for ESOP'24
 Vladimir Zamdzhiev for ACT'23
Reviewer
 Benoit Valiron for ESOP'24, WADT'23, PLDI'23
 Renaud Vilmart for ACT'23, FoSSaCS'23, LiCS'23, QPL'23
9.1.3 Journal
Member of the editorial boards
 Pablo Arrighi for TCSC
 Benoît Valiron for LMCS (since summer 2023)
Reviewer  reviewing activities
 Pablo Arrighi for Physical Review A, Foundations of Physics
 Renaud Vilmart for Quantum, TQE
 Vladimir Zamdzhiev for Quantum
9.1.4 Invited talks
 Benoît Valiron for EDFCEAInria summer school (), From Programming Language to Low Level interfaces.
9.1.5 Scientific expertise
 Benoît Valiron and Vladimir Zamdzhiev: members of the IFIP TC1/TC2 Working Group on Foundations of Quantum Computation ()
9.1.6 Research administration
 Renaud Vilmart took the supervision of Groupe de Travail Informatique Quantique (GT IQ), from GdR IM
 Benoît Valiron is the PI of WP2 of PEPREPIQ.
 Pablo Arrighi is the PI of the ParisSaclay node of the QISS consortium.
 Pablo Arrighi and Benoît Valiron are Executive committee members of the Quantum center of Saclay.
9.2 Teaching  Supervision  Juries
9.2.1 Teaching
Participants: Pablo Arnault.
 Foundations of Quantum Information in M1MPRI and M1QDCS.
Participants: Benoît Valiron.
 Various teaching at CentraleSupelec, for a total of 198h (equivalent TD).
 Introductory course on Quantum computation and Programming in M1QDCS.
 Introductory course on Quantum computation and Programming in Arteq.
Participants: Renaud Vilmart.
 Computer science project in L2InfoMaths.
 Initiation to functional programming in L2InfoMaths.
 Advanced quantum computation and error correction in M2QDCS.
 Elements of computer science for quantum technologies in Arteq.
Participants: Marc De Visme.
 Elements of computer science for quantum technologies in Arteq.
Participants: Vladimir Zamdzhiev.
 Introduction to Categories in M1MPRI.
 Initiation to Research in M1MPRI.
 Logique in L3ENS Paris Saclay
9.2.2 Teaching administration
Participants: Pablo Arrighi, Esteban Castro.
 Pablo Arrighi is coresponsible for the M1 MPRI of the Faculty of Science of U, and coresponsible for the M1 & M2 QDCS of the Faculty of Science of U. ParisSaclay. Both until September 2023
 Esteban Castro is coresponsible for the M1 & M2 QDCS of the Faculty of Science of U. ParisSaclay, starting from September 2023
9.2.3 Supervision
 Benoît Valiron has cosupervised 4 PhD students in 2023: Kostia Chardonnet (defense in january 2023), Nicolas Heurtel, Louis Lemonier, and Jérome Ricciardi.
 Pablo Arrighi has cosupervised 6 PhD students in 2023: Kostia Chardonnet (defense in january 2023), Dogukan Bakircioglu, Octave Mestoudjian, Marin Costes, Nicolas Heurtel, and Louis Lemonnier.
 Vladimir Zamdzhiev has cosupervised 2 PhD stuendes in 2023: Kinnari Dave, and Louis Lemmonier.
9.2.4 Juries
 Pablo Arrighi was external examiner for the PhD thesis of Aurélien Emmanuel and Matteo Luigi.
 Pablo Arrighi was member of the permanent position recuitement comitties of the Chaire d'excellence AMU, of an assistant profesor position at Télécom Paris IPP, and of a permanent CRCN reseearcher position at Inria Alpes and at Inria Lyon.
 Pablo Arnault was reviewer for the PhD thesis of Andreu AnglesCastillo, Universidad de Valencia.
9.3 Popularization
9.3.1 Internal or external Inria responsibilities
 Renaud Vilmart was member of Inria Saclay's Conseil Scientifique
 Marc de Visme was member of LMF's Conseil Scientifique.
 Pablo Arrighi was elected council member at the UPSaclay Graduate school of Computer Science.
9.3.2 Interventions
Participants: Pablo Arrighi.
 ¿Cuál es la diferencia entre el pasado y el futuro ? Un modelo de juguete con flecha del tiempo demostrable sin hipótesis de pasado.1, Depatments of Physics and Computer Science, Universidad de Buenos Aires, November 2023 and Universidad de la República, Montevideo, November 2003.
 Café de las Ciencias : Computadora cuántica, ¿la computadora definitiva ?2, Centro Cultural de la Ciencia (C3) of the Ministry of Sciences, Buenos Aires, November 2023.
10 Scientific production
10.1 Major publications
 1 inproceedingsA Complete Equational Theory for Quantum Circuits.38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)Boston, United StatesIEEEJuly 2023, 113HALDOI
 2 articleA relativistic discrete spacetime formulation of 3+1 QED.Quantum7November 2023, 1179HALDOI
10.2 Publications of the year
International journals
 3 articleAddressable quantum gates.ACM Transactions on Quantum Computing43April 2023, 141HALDOIback to text
 4 articleOn new PageRank computation methods using quantum computing.Quantum Information Processing223March 2023, 138HALDOIback to text
 5 articleA relativistic discrete spacetime formulation of 3+1 QED.Quantum7November 2023, 1179HALDOIback to text
 6 articlePerceval: A Software Platform for Discrete Variable Photonic Quantum Computing.Quantum7February 2023, 931HALDOIback to text
International peerreviewed conferences
 7 inproceedingsGraph Subshifts.Unity of Logic and Computation19th Conference on Computability in Europe, CiE 202313967Lecture Notes in Computer ScienceBatumi, GeorgiaSpringer Nature SwitzerlandJuly 2023, 261274HALDOIback to text
 8 inproceedingsComplete Graphical Language for HermiticityPreserving Superoperators.38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) 2023Boston, United StatesFebruary 2023, 122HALDOIback to text
 9 inproceedingsCentral Submonads and Notions of Computation: Soundness, Completeness and Internal Languages.2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)Boston (MA), United States2023HALDOIback to text
 10 inproceedingsCompositionality of planar perfect matchings: A universal and complete fragment of ZWcalculus.50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)261Paderborn, GermanyFebruary 2023, 120:1120:17HALDOIback to text
 11 inproceedingsA CurryHoward Correspondence for Linear, Reversible Computation.31st EACSL Annual Conference on Computer Science Logic (CSL 2023)CSL 2023  31st EACSL Annual Conference on Computer Science LogicVarsovie (Warsaw), PolandSchloss Dagstuhl  LeibnizZentrum für Informatik2023HALDOI
 12 inproceedingsQuantum Circuit Completeness: Extensions and Simplifications.International Conference on Computer Science Logic CSL 2024Naples, ItalyFebruary 2024HALback to text
 13 inproceedingsA Complete Equational Theory for Quantum Circuits.38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)Boston, United StatesIEEEJuly 2023, 113HALDOIback to text
 14 inproceedingsA Complete Equational Theory for Quantum Circuits.18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)Aveiro, PortugalJuly 2023HALback to text
 15 inproceedingsTypesafe Quantum Programming in Idris.Lecture Notes in Computer ScienceESOP 2023  European Symposium on ProgrammingLNCS13990Programming Languages and SystemsParis, FranceSpringerApril 2023, 507534HALDOIback to text
 16 inproceedingsCompleteness of SumOverPaths for ToffoliHadamard and the Dyadic Fragments of Quantum Computation.CSL 2023  31st EACSL Annual Conference on Computer Science Logic252Warsaw, PolandJanuary 2023, 36:136:17HALDOIback to text
Scientific book chapters
Reports & preprints
 18 miscDirac equation as a quantum walk over the honeycomb and triangular lattices.June 2018, 062111HALDOI
 19 miscMinimal Equational Theories for Quantum Circuits.November 2023HAL
 20 miscAdjustabledepth quantum circuit for positiondependent coin operators of discretetime quantum walks.January 2024HALback to text
 21 miscQuantum circuits for discretetime quantum walks with positiondependent coin operator.January 2023HAL