I am Lecturer in the Informatics and Interactions department of Aix-Marseille University and a researcher in the CaNa team of the LIS laboratory. Earlier on I did my Ph.D in Theoretical Quantum Physics, in the Theoretical Astrophysics Laboratory (LERMA), at the Université Pierre et Marie Curie under the supervision of Fabrice Debbasch (UPMC) and  Marc E. Brachet (ENS), before I did my post-doc at  IFIC in Valencia. My research activities take place in discrete mathematics and theoretical computer science and deals with quantum cellular automata, simulations, models and applications to theoretical physics. Get in touch!

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Université Pierre et Marie Curie (Sorbonne)

I got my M.Sc. at the Université Pierre et Marie Curie in Paris. In the exciting environment of Jussieu, I started my PhD on Quantum Walks and Synthetic Gauge Fields Simulation under the supervision of Fabrice Debbasch (UPMC) and Marc Brachet (ENS) - included a three months stay in the Institute for Molecular Science as a JSPS fellow, in the Shikano group.  

June 2015

Paris School of Economics 

During my PhD I also got a Master in Theoretical Economics at Paris School of Economics, with a master thesis on agent based modeling, in particular concerning Macroeconomics agents.

June 2010

Università degli Studi di Roma, Sapienza

I obtained my B.Sc. at the Sapienza University under the supervision of Prof. Sergio Caprara, on "quantum decoherence and the emergence of the arrow of time".


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Septembre, 2016 - en cours

Une introduction à l'informatique, et les notions de base nécessaires pour écrire des programmes simples (instructions, variables et types simples, fonctions et passage de paramètres, fichiers) et notions d'algorithmique.

Septembre, 2016 - en cours

Principales techniques de conception et analyse d'algorithmes pour les problèmes polynomiaux et les problèmes NP-complets. Complexité de l'approximation, du comptage. Complexité paramétrée. Classes probabilistes.

Sept, 2018 - 2019

L’objectif de ce cours est de sensibiliser aux menaces et enjeux et d’initier aux principaux concepts de cybersécurité. Il s’agit de présenter un guide de bonnes pratiques applicables à l’ensemble des professionnels de l’informatique, qu’ils soient en formation ou en activité.

January, 2017 - en cours

Modèles de calcul naturel (Master 2 - IMD)

Présentation des chaînes de Markov, leurs algorithmes et applications. Réseaux Booléenne, sand piles models. Introduction aux automates quantiques cellulaires.

January, 2019 - en cours

Fondamentaux du calcul quantique I (linéarité de la théorie, q-bit, super-position, intrication); Fondamentaux du calcul quantique II (quantum gates et circuits) Algorithme quantique de Grover; Alorithme de Shor; Elements de crypto-quantique, protocole de Cryptage RSA.

Sept, 2019 - en cours

Les étudiants étudieront des notions élémentaires telles que les variables aléatoires, les distributions de probabilités, etc. avec des exercices sous la forme de travaux dirigés. À l'issue de ce cours, les étudiants seront à même de formuler des solutions probabilistes à des problèmes concrets, ce qui leur permettra de maîtriser l'utilisation des probabilités dans des cours plus avancés (algorithmes randomisés, machine learning, etc.)


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Recent publications 

December 14th, 2019 Quantum Information Processing 19: 47

A quantum walk with both a continuous-time and a continuous-spacetime limit


Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (aka Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (aka quantum walks or quantum cellular automata based) enjoying a relativistic continuous-spacetime limit. We provide a first example of a quantum simulation scheme that unifies both approaches. The proposed scheme supports both a continuous-time discrete-space limit, leading to lattice fermions, and a continuous-spacetime limit, leading to the Dirac equation. The transition between the two can be thought of as a general relativistic change of coordinates, pushed to an extreme. As an emergent by-product of this procedure, we obtain a Hamiltonian for lattice fermions in curved spacetime with synchronous coordinates.


December 17th, 2019 Scientific Reports volume 9 19292

Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps


We extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the variance grows cubicly with time, σ^2 ∝ t^3, and a Gaussian for the position of the walker. We investigate this proposal both locally and globally with the results showing that the time-dependent interplay between interference, memory and long-range hopping leads to multiple transitions between dynamical regimes, namely ballistic → diffusive → superdiffusive → ballistic → hyperballistic for non-hermitian coin whereas the first diffusive regime is quelled for implementations using the Hadamard coin. In addition, we observe a robust asymptotic approach to maximal coin-space entanglement.


November 22nd, 2019 Martín-Vide C., Pond G., Vega-Rodríguez M. (eds) Theory and Practice of Natural Computing. TPNC 2019. Lecture Notes in Computer Science, vol 11934. Springer, Cham 

Non-abelian Gauge-Invariant Cellular Automata

July 29th, 2019, Scientific Reports volume 9, 10904  


Gauge-invariance is a mathematical concept that has profound implications in Physics—as it provides the justification of the fundamental interactions. It was recently adapted to the Cellular Automaton (CA) framework, in a restricted case. In this paper, this treatment is generalized to non-abelian gauge-invariance, including the notions of gauge-equivalent theories and gauge-invariants of configurations.


From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks

A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries —whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)–dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices.


February 27th, 2019 Scientific Reports (Nature) volume 9 - 2989 

Quantum Walks Hydrodynamics

A simple Discrete-Time Quantum Walk (DTQW) on the line is revisited and given an hydrodynamic interpretation through a novel relativistic generalization of the Madelung transform. Numerical results show that suitable initial conditions indeed produce hydrodynamical shocks and that the coherence achieved in current experiments is robust enough to simulate quantum hydrodynamical phenomena through DTQWs. An analytical computation of the asymptotic quantum shock structure is presented. The non-relativistic limit is explored in the Supplementary Material (SM).


September 28th, 2018 Phys. Rev. A 98, 032333 

Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks

A Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories.  


September 12, 2018 Phys. Rev. A 97, 062112

Elephant Quantum Walk

We explore the impact of long-range memory on the properties of a family of quantum walks in a one-dimensional lattice and discrete time, which can be understood as the quantum version of the classical ‘Elephant Random Walk’ non-Markovian process. This Elephant Quantum Walk is robustly superballistic with the standard deviation showing a constant exponent, whatever the quantum coin operator, on which the diffusion coefficient is dependent. 



August 22, 2018 Quantum 2, 84 

Quantum Walking in curved spacetime: discret metrics

We characterise and construct QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we investigate whether a finite number of coins is enough to generate all speeds, and whether their arrangement can be controlled by background signals travelling at lightspeed. The interest of such a discretization is twofold: to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other. 


March 2, 2018 Phys. Rev. A 97, 062111

The Dirac equation as a quantum walk over the honeycomb and triangular lattices

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2+1)--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.


February 21, 2018 in Proceedings of AUTOMATA'2018, volume 10875 of LNCS, pages 1--12, 2018.

A gauge-invariant reversible cellular automaton

Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in terms of Cellular Automata. More precisely, we describe a step-by-step gauging procedure to enforce local symmetries upon a given Cellular Automaton. We apply it to a simple Reversible Cellular Automaton for concreteness. From a Computer Science perspective, discretized gauge theories may be applied to numerical analysis, quantum simulation, fault-tolerant (quantum) computation. From a mathematical perspective, discreteness provides a simple yet rigorous route straight to the core concepts.


© 2018 By Giuseppe Di Molfetta.