ESQuisses2024 summer school - Sciencesconf.org

ABOUT THE SCHOOL

The ANR project ESQuisses is glad to announce a summer school to be held from June 10th to June 14th in Porquerolles, France. The lectures will start on Monday (June 10th) morning, and will end on Friday (June 14th) at noon. Participants are expected to arrive on Sunday (June 9th) and depart on Friday (June 14th).

This summer school aims at gathering mathematicians, physicists and computer scientists interested in stochastic methods in quantum mechanics.

Several introductory lectures will be given by leading researchers in the field. The topics covered include classical and quantum optimal transportation, non-local correlations in networks, stochastic quantum dynamics, and quantum error correction. The lectures shall be complemented by additional, more focused, research talks. Young researchers as well as confirmed researchers are welcome to participate. Poster sessions for Phd and post-doctoral students will be organized during the week.

Ample time for discussion and exchanges will be set aside, allowing for an interactive and inclusive in-person event.

REGISTRATION AND FEES

Please register here unitl Friday, May 3rd 2024. Note that the number of places is limited, so please register as soon as possible.

Financial aid, covering local expenses (accommodation and meals) is available upon application when registering before Friday, April 19th 2024.

Only participants that have payed the fees or have received the Financial aid will have their registration validated.

The conference fees, which cover local expenses (full board accommodation), are as follows:

Masters and PhD students, postdocs: 300 EUR
Faculty and industry participants: 450 EUR

We ask you to pay these fees (or chose the "Invited speaker - 0 €" option if you received financial aid) here, before Friday, May 3rd 2024.

LECTURES

Denis Bernard (LPENS, Paris) - Stochastic quantum dynamics in and out of equilibrium (for and by amateurs)

I will use the opportunity of discussing coherent fluctuations in mesoscopic many-body systems to address some simple but useful concepts and tools of modern (quantum) statistical physics.This will include basics of large deviation functions or of macroscopic fluctuations theory, in the classical framework, as well as elements of many-body open quantum systems or of quantum stochastic dynamics -- particularly the quantum symmetric exclusion process -- in the quantum domain.
No prerequisite, except basic knowledge of statistical mechanics and quantum mechanics (as, I guess, any student has).

Roberto Bondesan (Imperial College London) - Introduction to quantum error correction

Quantum computers promise to revolutionise the simulation of quantum systems and to implement better algorithms for optimisation and cryptography. However, quantum devices are noisy and error suppression is a critical component of quantum computation and quantum communication. In this lecture, you will learn about quantum error correction. I will describe how to characterise quantum noise, how quantum codes work, and what are the outstanding open problems in the field to achieve quantum advantage. No prerequisite knowledge of quantum computing will be required.

Reda Chhaibi (IMT Toulouse) - Probabilistic and computational aspects of classical optimal transport

This lecture is intended as an introduction to the topic of optimaltransport (OT).The non-commutative (or quantum) version of OT is entirely left for thecourse of G. De Palma.
From that point of view, the usual theory we present is commutative (orclassical).Starting from the Monge Problem, we will introduce and study therelaxation proposed by Kantorovich. Further we will discuss the entropic relaxation, which paves the waytowards the Sinkhorn algorithm. This is now the reference method fornumerically solving optimal transport.Such a plan will allow us to discuss both the theoretical andcomputational aspects of OT.

References:
Cédric Villani. Topics in Optimal Transport.
Gabriel Peyré, Marco Cuturi. Computational Optimal Transport.

Marc-Olivier Renou (INRIA, CPHT, Paris) - Quantum correlations in Bell scenarios and quantum networks: Foundations and Applications

I will introduce the quantum correlations which can be obtained in the Bell scenario (in which several parties measure a single shared quantum source), and their generalisation to quantum networks (which involve several independent quantum sources). I will present several of their applications, notably for the foundations of Quantum Information Theory (Bell theorem ruling out Local Hidden Variable models, quantum network correlations ruling out Real Quantum Theory, ...) and for practical quantum devices (Device Independent quantum information processing). In particular, I will present the Navascues-Pironio-Acín (NPA) hierarchy and its generalised NPA-inflation hierarchy which can be used to characterise quantum correlations in quantum networks and quantify their applicability to concrete information processing tasks.

Giacomo De Palma (University of Bologna) - The quantum Wasserstein distance of order 1

Quantum optimal transport is a rapidly growing field at the intersectionof quantum mechanics and optimal transport theory. Optimal transporttheory searches for the most efficient way to transport resources fromone location to another, and non-commutativity makes the quantum versionof the problem extremely challenging. We will focus on thegeneralization of the Wasserstein distance of order 1 to qudits andquantum spin systems of [De Palma et al., IEEE Trans. Inf. Theory 67,6627 (2021)], which recovers the Hamming distance for the states of thecanonical basis. We will prove the basic properties of the distance andhint at some of its applications in quantum computing and quantumstatistical mechanics.

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