RESEARCH CENTRE

Inria Saclay Centre
at Université Paris-Saclay

2023
ACTIVITY REPORT

IN PARTNERSHIP WITH:

Université Paris-Saclay

Project-Team

QUACS

Quantum Computation Structures

IN COLLABORATION WITH: Laboratoire de Méthodes Formelles

DOMAIN

Algorithmics, Programming, Software and
Architecture

THEME

Proofs and Verification

Contents

Project-Team QUACS

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

3.1 Quantum simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Semantics and Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Graphical languages and optimization for quantum computation . . . . . . . . . . . . . . .

4 Application domains

4.1 Quantum simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Semantics and Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Graphical languages and optimization for quantum computation . . . . . . . . . . . . . . .

5 New software, platforms, open data

5.1 New platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing .

6 New results

6.1 Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments of
Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Compositionality of Planar Perfect Matchings . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Complete Graphical Language for Hermiticity-Preserving Superoperators . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
6.4 A Complete Equational Theory for Quantum Circuit
6.5 Quantum Circuit Completeness: Extensions and Simplifications . . . . . . . . . . . . . . . .
6.6 On new PageRank computation methods using quantum computing . . . . . . . . . . . . .
6.7 Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time
quantum walks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 Central Submonads and Notions of Computation: Soundness, Completeness and Internal
Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9 Type-safe Quantum Programming in Idris . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 A quantum simulation algorithm for 3+1 QED . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 Addressable Quantum Gates
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Graph Subshifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.13 Measurement events relative to temporal quantum reference frames . . . . . . . . . . . . .
6.14 Graphical Language for Tensor and Coproduct . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Bilateral contracts and grants with industry

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8 Partnerships and cooperations

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8.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
8.2 European initiatives
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

9 Dissemination

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9.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
9.1.1 Full Organisation of an International Conference . . . . . . . . . . . . . . . . . . . . . 14
9.1.2 Other scientific events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9.1.3 Journal
9.1.4 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.1.5 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.1.6 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

9.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
9.2.2 Teaching administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.2.3 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.2.4 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.3.1 Internal or external Inria responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.3.2 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

10 Scientific production

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10.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10.2 Publications of the year

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Project-Team QUACS

Creation of the Project-Team: 2021 December 01

Keywords

Computer sciences and digital sciences

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

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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]

Post-Doctoral Fellows

• Titouan Carette [UNIV PARIS SACLAY, until Aug 2023]

• Alexandre Clement [INRIA, Post-Doctoral Fellow, from May 2023]

• James Hefford [INRIA, Post-Doctoral Fellow, from Oct 2023]

• Timothée Hoffreumon [UNIV PARIS SACLAY, from Nov 2023]

• Augustin Vanrietvelde [INRIA, Post-Doctoral Fellow, until Oct 2023]

PhD Students

• Dogukan Bakircioglu [INRIA, from Dec 2023]

• Kostia Chardonnet [UNIV PARIS SACLAY, until Jan 2023]

• Marin Costes [ENS PARIS-SACLAY]

• Nicolas Heurtel [LMF, from Dec 2023]

• Louis Lemonnier [ENS PARIS-SACLAY]

• Octave Mestoudjian [ED STIC, from Sep 2023]

• Jérôme Ricciardi [CEA]

Technical Staff

• Tristan Cam [INRIA, Engineer, from Dec 2023]

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Interns and Apprentices

• Samuel Aychet-Claisse [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 PARIS-SACLAY, from Mar 2023 until Aug 2023]

• Tianyi Li [INRIA, Intern, from May 2023 until Jul 2023]

• Fatima-Zahra 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 [IRT-SystemX, 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 Chapuis-Chkaiban [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 lambda-calculus, 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.

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3 Research program

3.1 Quantum simulation

One usually distinguishes three main fields of applications of Quantum Computing: quantum cryp-
tography (short-term), quantum simulation (mid-term), quantum algorithmic (long-term). Quantum
simulation then divides into two subfields: continuous-time quantum simulation, which is very physicky
and consists of ad hoc emulation of one Hamiltonian by another, and discrete-time quantum simulation,
which is much closer to quantum algorithmic: this is where we stand. In particular, we focus on the
provision of a quantum-circuit 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 max-
imum 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 quantum-circuit 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 pro-
grams and other computational models (e.g., the small-step semantics of quantum lambda calculi,
token-machine semantics of quantum diagrammatic calculi).

• Mathematical and denotational semantics: a mathematical interpretation of a quantum program-
ming 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-, ZH-calculi, but also languages for linear optics, such as the LOv-calculus. 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.

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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 com-
puters» 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 specific-purpose molecules, materials, nanotechnologies, with
applications in chemistry, biochemistry, electronics, mechanics. At QuaCS we focus on the bottom layer:
the quantum-simulation 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 ZX-calculus 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 ZX-diagram, 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.

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[6]
We introduce Perceval , an open-source software platform for simulating and interfacing with discrete-
variable photonic quantum computers, and describe its main features and components. Its Python front-
end allows photonic circuits to be composed from basic photonic building blocks like photon sources,
beam splitters, phase-shifters and detectors. A variety of computational back-ends are available and
optimised for different use-cases. These use state-of-the-art 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 discrete-
variable photonic experiment, for theoreticians wishing to design algorithms and applications for discrete-
variable photonic quantum computing platforms, and for application designers wishing to evaluate
algorithms on available state-of-the-art photonic quantum computers.

6 New results

6.1 Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Frag-

ments of Quantum Computation

Participants:

Renaud Vilmart.

[16]
We consider the Toffoli-Hadamard fragment of quantum computing (one of the simplest universal
fragment), in the setting of "Sum- Over-paths", 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.

[10]
We show that graphical language ZW-calculus 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 Hermiticity-Preserving Superoperators

Participants:

Renaud Vilmart, Titouan Carette, Timothée Hoffreumon.

[8]
We introduce the first complete universal graphical language for Hermiticity-preserving superoperat-
ors. Antiunitarity, and negativity in the density matrix formalism, although non physical, is a useful tool
for physicists, and is now useable in a ZX-like graphical language.

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6.4 A Complete Equational Theory for Quantum Circuit

Participants:

Alexandre Clement, Nicolas Heurtel, Shane Mansfield, Simon Perdrix.

[14, 13]
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 multi-controlled 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.

[12]
The first completeness result for arbitrary quantum circuits, involved a few non-intuitive 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 Chapuis-Chkaiban, Zeno Toffano, Benoît Valiron.

[4]
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 Quantum-Based 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 Adjustable-depth quantum circuit for position-dependent coin operators of

discrete-time quantum walks

Participants: Ugo Nzongani, Pablo Arnault.

[20]
Discrete-time quantum walks with position-dependent coin operators have numerous applications.
For a position dependence that is sufficiently smooth, it has been provided in an approximate quantum-
circuit implementation of the coin operator that is efficient. If we want the quantum-circuit implementa-
tion 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 non-smooth position dependence), but the depth of the circuit not to scale exponentially,
then we can use the linear-depth 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 adjustable-depth

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quantum circuit for the exact implementation of the position-dependent coin operator. This adjustable-
depth circuit consists in (i) applying in parallel, with a linear-depth circuit, only certain packs of coin
operators (rather than all of them as in the original linear-depth 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.

[9]
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 well-known 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 Type-safe Quantum Programming in Idris

Participants:

Vladimir Zamdzhiev.

[15]
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. 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
classical-quantum 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 fine-grained 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.

[5]
We achieved the first quantum cellular automaton model for real-life 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

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reminiscent of fault-tolerance in Computer Science. This opens the way for natively discrete formulations
of quantum field theories, otherwise renowned for their ill-definedness.

6.11 Addressable Quantum Gates

Participants:

Pablo Arrighi, Marin Costes, Benoît Valiron.

[3]
We extended the circuit model of quantum computation so that the wiring between gates is soft-
coded 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 beam-splitter 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 non-trivially upon the names.

6.12 Graph Subshifts

Participants:

Pablo Arrighi.

[7]
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.

Publication
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 "Many-World Calculus" (MWC), a graphical language designed to
expand quantum circuits to fully capture quantum supperposition, into the "Tensor-Plus Calculus" (TPC).
The TPC is a graphical language that bridge the gap between languages like quantum circuits or the
ZX-calculus, 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

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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, Ben-
oit 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, Aix-Marseille University

• Quantum Group and Clarendon Laboratory, University of Oxford

• Perimeter Institute

• University of Paris-Saclay, 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: 2023-2026

Additionnal info:

Project QUACS

11

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 Aix-Marseille,
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, Ben-
oit 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: 2021-2024

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.

12

Inria Annual Report 2023

In doing so, HPCQS will become an incubator for quantum-HPC hybrid computing that is unique in the
world.

The seamless integration of quantum hardware with classical computing resources will enable re-
search 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 cloud-based
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 world-leading HPC infrastructure.

8.3 National initiatives
EPiQ (PEPR Quantique)

Participants:

Pablo Arnault, Pablo Arrighi, Esteban Castro, Marc de Visme, Ben-
oit 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: 2022-2027

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 high-level
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 intensifica-
tion 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
fault-tolerant 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, Ben-
oit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title: Engineering for Quantum Information Processors

Project QUACS

13

Partner Institution:

• INRIA, France

Date: 2021-2024

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 micro-processor. 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 long-term 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, Ben-
oit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title: Taming Quantum Causality

Partner Institutions:

• UPSaclay - LMF Université Paris-Saclay - Laboratoire Méthodes Formelles

• Inria Centre de Recherche Inria de Lyon - AT-LYS

• NEEL Institut Néel

• LARSIM Commissariat à l’énergie atomique et aux énergies alternatives

Date: 2023-2027

Additionnal info:

Quantum technologies provide advantages by exploiting non-classical resources, such as superposi-
tion 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 non-classical 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

14

Inria Annual Report 2023

clarify which causally indefinite process are physical and what precise role is played by genuinely non-
classical 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 ZX-Calculus to harness the
capabilities of causal indefiniteness at the compilation level. Using ZX-Calculus 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, Ben-
oit Valiron, Renaud Vilmart, Vladimir Zamdzhiev.

Title: Hybrid HPC-Quantum 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: 2022-2027

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 HPC-QC Initiative.

HQI is an integrated initiative. It combines a hybrid computing platform that couples several quantum
processors with GENCI’s Joliot-Curie supercomputer hosted at TGCC (CEA), and an academic and
industrial research program with user enablement.

This HPC-QC 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

Project QUACS

15

Participants:

Vladimir Zamdzhiev, Benoît Valiron, Shane Mansfield, Augustin Vanri-
etvelde, 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 quantum-inspired 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 co-chairs. 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 non-proceedings 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 TCS-C

• 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

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Inria Annual Report 2023

9.1.4 Invited talks

• Benoît Valiron for EDF-CEA-Inria 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 Founda-

tions 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 PEPR-EPIQ.

• Pablo Arrighi is the PI of the Paris-Saclay 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 M1-MPRI and M1-QDCS.

Participants:

Benoît Valiron.

• Various teaching at CentraleSupelec, for a total of 198h (equivalent TD).

• Introductory course on Quantum computation and Programming in M1-QDCS.

• Introductory course on Quantum computation and Programming in Arteq.

Participants:

Renaud Vilmart.

• Computer science project in L2-InfoMaths.

• Initiation to functional programming in L2-InfoMaths.

• Advanced quantum computation and error correction in M2-QDCS.

• Elements of computer science for quantum technologies in Arteq.

Project QUACS

17

Participants: Marc De Visme.

• Elements of computer science for quantum technologies in Arteq.

Participants:

Vladimir Zamdzhiev.

• Introduction to Categories in M1-MPRI.

• Initiation to Research in M1-MPRI.

• Logique in L3-ENS Paris Saclay

9.2.2 Teaching administration

Participants:

Pablo Arrighi, Esteban Castro.

• Pablo Arrighi is co-responsible for the M1 MPRI of the Faculty of Science of U, and co-responsible
for the M1 & M2 QDCS of the Faculty of Science of U. Paris-Saclay. Both until September 2023

• Esteban Castro is co-responsible for the M1 & M2 QDCS of the Faculty of Science of U. Paris-Saclay,

starting from September 2023

9.2.3 Supervision

• Benoît Valiron has co-supervised 4 PhD students in 2023: Kostia Chardonnet (defense in january

2023), Nicolas Heurtel, Louis Lemonier, and Jérome Ricciardi.

• Pablo Arrighi has co-supervised 6 PhD students in 2023: Kostia Chardonnet (defense in janu-
ary 2023), Dogukan Bakircioglu, Octave Mestoudjian, Marin Costes, Nicolas Heurtel, and Louis
Lemonnier.

• Vladimir Zamdzhiev has co-supervised 2 PhD stuendes in 2023: Kinnari Dave, and Louis Lem-

monier.

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 Angles-Castillo, 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.

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Inria Annual Report 2023

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] A. Clément, N. Heurtel, S. Mansfield, S. Perdrix and B. Valiron. ‘A Complete Equational Theory for
Quantum Circuits’. In: 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
States: IEEE, July 2023, pp. 1–13. DOI: 10.1109/LICS56636.2023.10175801. URL: https://hal
.science/hal-03926757.

[2] N. Eon, G. D. Molfetta, G. Magnifico and P. Arrighi. ‘A relativistic discrete spacetime formulation
of 3+1 QED’. In: Quantum 7 (8th Nov. 2023), p. 1179. DOI: 10.22331/q-2023-11-08-1179. URL:
https://hal.science/hal-03944082.

10.2 Publications of the year

International journals

[3] P. Arrighi, C. Cedzich, M. Costes, U. Rémond and B. Valiron. ‘Addressable quantum gates’. In: ACM
Transactions on Quantum Computing 4.3 (24th Apr. 2023), pp. 1–41. DOI: 10.1145/3581760. URL:
https://hal.science/hal-03936367.

[4] T. Chapuis-Chkaiban, Z. Toffano and B. Valiron. ‘On new PageRank computation methods using
quantum computing’. In: Quantum Information Processing 22.3 (Mar. 2023), p. 138. DOI: 10.1007
/s11128-023-03856-y. URL: https://centralesupelec.hal.science/hal-04056045.

[5] N. Eon, G. D. Molfetta, G. Magnifico and P. Arrighi. ‘A relativistic discrete spacetime formulation
of 3+1 QED’. In: Quantum 7 (8th Nov. 2023), p. 1179. DOI: 10.22331/q-2023-11-08-1179. URL:
https://hal.science/hal-03944082.

[6] N. Heurtel, A. Fyrillas, G. D. Gliniasty, R. Le Bihan, S. Malherbe, M. Pailhas, E. Bertasi, B. Bourdoncle,
P.-E. Emeriau, R. Mezher, L. Music, N. Belabas, B. Valiron, P. Senellart, S. Mansfield and J. Senellart.
‘Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing’. In: Quantum 7
(21st Feb. 2023), p. 931. DOI: 10.22331/q-2023-02-21-931. URL: https://hal.science/hal-
03874624.

International peer-reviewed conferences

[7] P. Arrighi, A. Durbec and P. Guillon. ‘Graph Subshifts’. In: Unity of Logic and Computation. 19th
Conference on Computability in Europe, CiE 2023. Vol. 13967. Lecture Notes in Computer Science.
Batumi, Georgia: Springer Nature Switzerland, 19th July 2023, pp. 261–274. DOI: 10.1007/978-3-
031-36978-0_21. URL: https://hal.science/hal-04310695.

1Past or future : what’s the difference ? A toy model provably featuring a time arrow without past hypothesis.
2Science coffee : Is the quantum computer the ultimate computer ?

Project QUACS

19

[8] T. Carette, T. Hoffreumon, É. Larroque and R. Vilmart. ‘Complete Graphical Language for Hermiticity-
Preserving Superoperators’. In: 38th Annual ACM/IEEE Symposium on Logic in Computer Science
(LICS) 2023. Boston, United States, 9th Feb. 2023, pp. 1–22. DOI: 10.1109/LICS56636.2023.1017
5712. URL: https://hal.science/hal-04001823.

[9] T. Carette, L. Lemonnier and V. Zamdzhiev. ‘Central Submonads and Notions of Computation:
Soundness, Completeness and Internal Languages’. In: 2023 38th Annual ACM/IEEE Symposium
on Logic in Computer Science (LICS). Boston (MA), United States, 2023. DOI: 10.1109/LICS56636
.2023.10175687. URL: https://hal.science/hal-03662565.

[10] T. Carette, E. Moutot, T. Perez and R. Vilmart. ‘Compositionality of planar perfect matchings: A
universal and complete fragment of ZW-calculus’. In: 50th International Colloquium on Automata,
Languages, and Programming (ICALP 2023). Vol. 261. Paderborn, Germany, 17th Feb. 2023, 120:1–
120:17. DOI: 10.4230/LIPIcs.ICALP.2023.120. URL: https://hal.science/hal-04002282.

[11] K. Chardonnet, A. Saurin and B. Valiron. ‘A Curry-Howard Correspondence for Linear, Reversible
Computation’. In: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). CSL 2023 -
31st EACSL Annual Conference on Computer Science Logic. Varsovie (Warsaw), Poland: Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2023. DOI: 10.4230/LIPIcs.CSL.2023.13. URL:
https://hal.science/hal-04308283.

[12] A. Clément, N. Delorme, S. Perdrix and R. Vilmart. ‘Quantum Circuit Completeness: Extensions
and Simplifications’. In: International Conference on Computer Science Logic CSL 2024. Naples,
Italy, Feb. 2024. URL: https://hal.science/hal-04016498.

[13] A. Clément, N. Heurtel, S. Mansfield, S. Perdrix and B. Valiron. ‘A Complete Equational Theory for
Quantum Circuits’. In: 18th Conference on the Theory of Quantum Computation, Communication
and Cryptography (TQC 2023). Aveiro, Portugal, 24th July 2023. URL: https://hal.science/hal-
04318291.

[14] A. Clément, N. Heurtel, S. Mansfield, S. Perdrix and B. Valiron. ‘A Complete Equational Theory for
Quantum Circuits’. In: 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
States: IEEE, July 2023, pp. 1–13. DOI: 10.1109/LICS56636.2023.10175801. URL: https://hal
.science/hal-03926757.

[15] L.-J. Dandy, E. Jeandel and V. Zamdzhiev. ‘Type-safe Quantum Programming in Idris’. In: Lecture
Notes in Computer Science. ESOP 2023 - European Symposium on Programming. Vol. LNCS-13990.
Programming Languages and Systems. Paris, France: Springer, 17th Apr. 2023, pp. 507–534. DOI:
10.1007/978-3-031-30044-8_19. URL: https://inria.hal.science/hal-03519238.

[16] R. Vilmart. ‘Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments
of Quantum Computation’. In: CSL 2023 - 31st EACSL Annual Conference on Computer Science
Logic. Vol. 252. Warsaw, Poland, 11th Jan. 2023, 36:1–36:17. DOI: 10.4230/LIPIcs.CSL.2023.36.
URL: https://hal.science/hal-03654438.

Scientific book chapters

[17] C. Chareton, S. Bardin, D. Lee, B. Valiron, R. Vilmart and Z. Xu. ‘Formal Methods for Quantum
Algorithms’. In: Handbook of Formal Analysis and Verification in Cryptography. 1. CRC Press,
1st Aug. 2023, pp. 319–422. DOI: 10.1201/9781003090052-7. URL: https://hal.science/hal-
04311441.

Reports & preprints

[18] P. Arrighi, D. M. Giuseppe, I. Márquez-Martín and A. Pérez. Dirac equation as a quantum walk
over the honeycomb and triangular lattices. June 2018. DOI: 10.1103/PhysRevA.97.062111. URL:
https://amu.hal.science/hal-03594743.

[19] A. Clément, N. Delorme and S. Perdrix. Minimal Equational Theories for Quantum Circuits. 13th Nov.

2023. URL: https://hal.science/hal-04399210.

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Inria Annual Report 2023

[20] U. Nzongani and P. Arnault. Adjustable-depth quantum circuit for position-dependent coin operators

of discrete-time quantum walks. 16th Jan. 2024. URL: https://hal.science/hal-04396459.

[21] U. Nzongani, J. Zylberman, C.-E. Doncecchi, A. Pérez, F. Debbasch and P. Arnault. Quantum
circuits for discrete-time quantum walks with position-dependent coin operator. 13th Jan. 2023. URL:
https://hal.science/hal-03938358.
<scratchpad>
- Main topic: Research Centre QUACS (Quantum Computation Structures)
- Key points:
  - QUACS is a research centre at Inria Saclay Centre at Université Paris-Saclay.
  - The centre focuses on quantum information processing, algorithmics, programming, software, and architecture.
  - Research areas include quantum simulation, semantics and programming, graphical languages and optimization for quantum computation.
- Structure: The document is organized into sections, including activity report, project-team, research program, application domains, new software and platforms, new results, bilateral contracts and grants with industry, partnerships and cooperations, dissemination, scientific production, and more.
- Potential artifacts to ignore: web-related elements such as links, HTML tags, and unnecessary formatting.
</scratchpad>

<final_summary>
The Research Centre QUACS, located at Inria Saclay Centre at Université Paris-Saclay, focuses on quantum information processing and its applications. The centre's research areas include quantum simulation, semantics and programming, and graphical languages and optimization for quantum computation. QUACS aims to develop new quantum simulation algorithms, improve the understanding of quantum computing, and explore the potential of quantum information processing in various fields. The centre collaborates with industry partners and academic institutions to advance the field of quantum computing and its applications.
The Research Centre QUACS, located at Inria Saclay Centre at Université Paris-Saclay, focuses on quantum information processing and its applications. The centre's research areas include quantum simulation, semantics and programming, and graphical languages and optimization for quantum computation. QUACS aims to develop new quantum simulation algorithms, improve the understanding of quantum computing, and explore the potential of quantum information processing in various fields. The centre collaborates with industry partners and academic institutions to advance the field of quantum computing and its applications.