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!

*looking for a more serious profile picture!

 
 

( 01 )

Education

2010-2015

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".

 

( 02 )

Teaching

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.)

 

( 03 )

Recent publications 

Avril 16th, 2020 Physical Review Letters, in production 

 

We provide the first evidence that under certain conditions, electrons may naturally behave like a Grover search, looking for defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e. local unitary matrices that drive the evolution of a single particle on the lattice. Some of these are well-known to recover the (2+1)--dimensional Dirac equation in continuum limit, i.e. the free propagation of the electron. We study two such Dirac QW, one on the square grid and the other on a triangular grid reminiscent of graphene-like materials. The numerical simulations show that the walker localises around a defect in O(N^1/2) steps with probability O(1/logN). This in line with previous QW formulations of the Grover search on the 2D grid. But these Dirac QW are `naturally occurring' and require no specific oracle step other than a hole defect in a material.

[arXiv][Journal]

April,3rd, 2020, Electronic Proceedings in Theoretical Computer Science 315, pp. 38–47

Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more established techniques. We propose two variations of a model to grow random graphs and trees, based on continuous-time quantum walks on the graphs. After a random characteristic time, the position of the walker(s) is measured and new nodes are attached to the nodes where the walkers collapsed. Such dynamical systems are reminiscent of the class of spontaneous collapse theories in quantum mechanics. We investigate several rates of this spontaneous collapse for an individual quantum walker and for two non-interacting walkers. We conjecture (and report some numerical evidence) that the models are scale-free.

[arXiv][Journal]

Quantum simulation of quantum relativistic diffusion via quantum walks

Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: The diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.

[arXiv][Journal]

Janaury 8th, 2020 Symmetry 12(1), 128

Dynamical Triangulation Induced by Quantum Walk

We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2− manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as t^α e^(−βt2) , where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.

[arXiv][Journal]

© 2018 By Giuseppe Di Molfetta.