## Professor in Computer Science

HDR Computer Science

PhD Quantum Theoretical Physics

MSc Theoretical Physics of Complex Systems

MSc Theoretical Economics

I am professor at Aix-Marseille University and researcher in the CaNa team of the LIS. I got my habilitation (HDR) in Computer Science at AMU and earlier on I did my Ph.D in Theoretical Quantum Physics at the Université Pierre et Marie Curie (Sorbonne Université).

My research activities take place in theoretical computer science and deals with quantum cellular automata, simulations, models and algorithms.

I am currently coordinator of the ANR-JCJC DisQC and local coordinator of the PEPR EPiQ and QuantEdu-France.

I am member of the Scientific Council (CSI) of the INS2I.

I also animate the quantum activities at the LIS (give a look here) and since 2017 I organise the LIS seminars for the 'Pole Calcul'.

Get in touch!

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## Recent selected publications

European Physical Journal D 77:80 (2023)

Twisted quantum walks, generalised Dirac equation and Fermion doubling with Nicolas Jolly

Quantum discrete-time walkers have since their introduction demonstrated applications in algo- rithmics and to model and simulate a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalised Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well-known Fermion doubling problem.

Physical Review B 106 (10), 104309 (2022)

Ergodicity breaking is observed in the blockade regime of Rydberg atom arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations which propagate entanglement. Evidence of nonlocal entanglement is found, showing that these nonthermal chaotic states may be useful to quantum computation.

Physical Review A 106 (3), 032408 (2022)

Quantum simulations of hydrodynamics via the Madelung transformation with Julien Zylberman, Marc Brachet, Nuno F Loureiro, and Fabrice Debbasch

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces.

Uncertainty in Artificial Intelligence, 1697-1706 (2022)

Quantum perceptron revisited: Computational-statistical tradeoffs with Hachem Kadri and Mathieu Roget

We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile.

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## Research projects

2022–2026 ANR JCJC DisQC, Distributed Quantum Computing ANR National grant/PI and Scientific Coordinator

The ~250k€ (HT) grant will fund a three years PhD. The overall project intends to bring together scientific experts from the disciplines of quantum computing, distributed algorithm and complexity, to work together towards the common goal of 1) exploring and exploiting further synergies between these fields, 2) identifying fundamental strategies and methods to design fault-tolerant quantum algorithms, and 3) developing new ideas for implementing quantum algorithms on distributed architecture.

2022–2025 AMIDEX grant, Algorithms, Quantum Error Correcting codes and implementations in distributed quantum computing/ PI and Scientific Coordinator

The ~100k€ (HT) grant will fund a two years postdoc.

2022–2028 PEPR on Quantum Technologies EPiQ /ANR National grant/PI and Local leader

Member of the consortium of the large scale national initiative on quantum technology. I am the local leader of the consortium. The ~300k€ (HT) grant will fund a two years postdoc on formal methods and a three years PhD on quantum distributed algorithms.

2019–2022/2023–2026 Quantum Information Structure of Spacetime JTF Large grant, 2M € - PI

I contributed to compose this 14 site international consortium made of top researchers, worldwide. I was PI for the LIS partner in the first phase (2019–2022) and I am affiliated in the second phase (2023–2026).

The following is a membership:

2019-2023 Quantum Machine Learning ANR JCJC at LIS, 214k €

Closed :

2021 Fault Invariant Distributed Quantum Algorithm /QuAlgo

Volet exploratoire INS2I 20k € - PI

2019-2021 Discrete Time Quantum Simulator Pépinière d’excellence AMIDEX, 25k € - PI

2018-2021 Quantum Walk and geometry PICS CNRS France-Espagne, 12k € - PI

2018 Lattice Quantum Simulation Theory / LaQuSim, PI, Infiniti CNRS

2017 Quantum networks and Growing /QuNet, PI, JCJC INS2I

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## Teaching

### @all my students : rendez-vous sur AMETICE pour vos cours

During my PhD, I had the opportunity to teach at the Sorbonne’s physics department 64h per year (statistical physics, electromagnetism, classical mechanics). Since my recruitment at the Department of Informatics and Interactions at Aix-Marseille University, I have taught at all levels (∼220h/y). Below is a summary list:

Courses/Master and PhD level

2021–today Quantum Machine Learning ED184, AMU, taught in english

2021–today Quantum Cryptography M2 FSI, AMU

2020–today Computer Security Watch M2 FSI, AMU

2016–today Models of Natural Computing M2 IMD, AMU

2018–2019 Security, Internet, Networks M1 FSI, AMU

2016– 2020 Complexity Theory M1 Informatique, AMU

2018–today Quantum Computation M1 Informatique, AMU

Courses/Undergraduate level

2022–today Algorithms 1, L2, AMU

2022–today Introduction to quantum computing, L2 -MPCI, AMU

2018–today Probability for computer scientists L2, AMU

2016–2021 Introduction to informatics L1, AMU

Research schools

-2022 Lecture on "Quantum Boltzmann Machines" at the von Karman Institut (NATO research institute, Belgium) during a research schools on quantum computing in fluid dynamics.

-2022 Series of lectures "Quantum natural computing: from simulation to algorithms", at Univ. Buenos Aires, for the ECI22