Thomas Vidick, professeur en sciences informatique et mathématique au California Institute of Technology, lauréat 2020 de la Chaire d'excellence de la FSMP, accueilli à l'IRIF, à Inria et au DI-ENS, a donné dans le cadre de sa chaire un cours intitulé Interactive proofs with quantum devices.
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Résumé du cours
Interactive proofs with quantum devices
Quantum mechanics distinguishes itself by such phenomena as superpositions and the uncertainty principle, entanglement, and the no-cloning principle. These uniquely quantum oddities all have "classical signatures" that can be witnessed by the end user and have served to validate the theory from an experimental physics point of view (e.g. a double-slit experiment, or a Bell test).
In recent years computer scientists have built on such experimental setups to go much further than testing specific features of quantum mechanics: they have developed protocols that allow one to (1) test that a black-box device must operate non-classically, (2) certify that it generates intrinsically random bits, (3) verify that it contains a specific quantum state, (4) verify that it implements a desired quantum computation, and more.
The goal for this course is to lay the foundations for an emerging research area of "hybrid classical-quantum protocols" and build towards a concrete understanding of some of the most important results of the past few years. These include Mahadev's celebrated protocol for classical delegation of quantum computation (arXiv:1804.01082) and the recent complexity-theoretic result MIP* = RE (arXiv:2001.04383). Towards a self-contained presentation of these results we will develop the required foundations in quantum information, complexity theory, and cryptography. Time allowing and depending on the participants' interests we will present connections with the field of operator algebras.
Notes de cours et vidéos
Cours n°1 (22/09/2020) : Introduction. Testing quantum systems. What is a qubit?
Cours n°2 (29/09/2020) : Formalizing the setup for testing: Interactive proofs. Operational measures of distance.
Cours n°3 (06/10/2020) : Using non-locality for testing: The Magic Square
Cours n°4 (13/10/2020) : Using computational advantage for testing: A qubit from computational assumptions
Cours n°5 (20/10/2020) : Overview of approaches to delegated computation
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Cours n°6 (27/10/2020) : The Mahadev delegation protocol (1/2)
Cours n°7 (10/11/2020) : The Mahadev delegation protocol (2/2)
Cours n°8 (17/11/2020) : Overview of complexity of quantum multi-prover interactive proofs
Cours n°9 (24/11/2020) : Compression of nonlocal games
Cours n°10 (02/12/2020) : Quantum linearity testing