**Thomas Vidick** is professor in computer science and mathematics at California Institute of Technology and laureate of the FSMP's 2020 Research Chair of Excellence. During his stay in Paris, he will work at IRIF, Inria and DI-ENS, and give a course entitled **Interactive proofs with quantum devices**.

Thomas Vidick is also the author of a blog (read here).

### Where and when?

The lectures will take place on tuesday from **10:00 to 12:00 from septembre 22 ^{nd} 2020** at

**Institut Henri Poincaré**(11 rue Pierre et Marie Curie, 75005 Paris).

#### Lectures from November 10 will be held at the scheduled time but online. For login details, please check this page later.

**Tuesday 22^{nd} September 2020: Introduction. Testing quantum systems. What is a qubit? (Amphithéâtre Hermite)**

**29**

TuesdayTuesday

^{th}September 2020:*Formalizing the setup for testing: Interactive proofs. Operational measures of distance.***(Salle 314)**

**Tuesday**6**October 2020:**^{th}

**Using non-locality for testing: The Magic Square****(Amphithéâtre Hermite)**

**Tuesday**13**October 2020:**^{th}*Using computational advantage for testing: A qubit from computational assumptions***(Amphithéâtre Hermite)**

**Tuesday**20**October 2020:**^{th}

*Overview of approaches to delegated computation*

**(Amphithéâtre Hermite)**

**Tuesday**27**October 2020:**^{th}

*The Mahadev delegation protocol*(1/2)

**(Amphithéâtre Hermite)**

**Tuesday**10**November 2020:**^{th}

*The Mahadev delegation protocol*(2/2)

**(online)**

**Tuesday**17**November 2020:**^{th}

**Overview of complexity of quantum multi-prover interactive proofs**

**(online)**

**Tuesday**24**November 2020:**^{th}

*Quantum linearity testing and quantum low-degree testing*

**(online)**

**Tuesday**1**December 2020:**^{st}

**Towards MIP* = RE**

**(online)**

### Abstract of the course

**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.

### Lectures notes and videos

**Lecture #1 - 09/22/2020: Introduction. Testing quantum systems. What is a qubit?Click here to find the lecture notes or here on overleaf.**

**Lecture #2 - 09/29/2020: Formalizing the setup for testing: Interactive proofs. Operational measures of distance.Click here to find the lecture notes or here on overleaf.**

**Lecture #3 - 10/06/2020: Using non-locality for testing: The Magic SquareClick here to find the lecture notes or here on overleaf.**

**Lecture #4 - 10/13/2020: Using computational advantage for testing: A qubit from computational assumptionsClick here to find the lecture notes or here on overleaf.**

**Lecture #5 (20/10/2020): Overview of approaches to delegated computation**

Click here to find the lecture notes.

Click here to find the slides.

**Lecture #6 (27/10/2020): The Mahadev delegation protocol (1/2)**

Click here to find the lecture notes.