## Full Professor in Computer Science

HDR Computer Science

PhD Quantum Theoretical Physics

MSc Theoretical Physics of Complex Systems

MSc Theoretical Economics

I am full professor at Aix- Marseille University and a researcher in the CaNa team of the LIS. I got my 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 discrete mathematics and 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

Physical Review B 106 (10), 104309

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

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

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.

Physical Review A 105 (6), 062420

Geodesic quantum walks with Victor Deng

We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalise the duality principle introduced in~\cite{arrighi2019curved}, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

A relativistic discrete spacetime formulation of 3+ 1 QED with Nathanael Eon, Giuseppe Magnifico and Pablo Arrighi

We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalise the duality principle introduced in~\cite{arrighi2019curved}, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

Scientific reports 12 (1), 1-9

A discrete relativistic spacetime formalism for 1+ 1-QED with continuum limits with Kevissen Sellapillay and Pablo Arrighi

We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut–Susskind staggered version of 1+1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.

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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, elec- tromagnetism, 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