M2 Degree in Quantum, Mathematics, and Computer Science
The QMI M2 offers 14 courses covering all of the theoretical aspects of quantum computing and quantum technologies, a unique curriculum in terms of breadth.
The curriculum is split into two periods. The first period (P1) runs from October to December, and the second (P2) from January to March. Two courses (noted P1.5) are on a shifted schedule and run from December to February. The program also includes crash courses in Quantum Information in September (for students with no quantum background), and a research internship from April to August.
Validation: In order to obtain their degree, students must validate 30 ECTS in courses, and the internship's 30 ECTS. This means they must validate at least 10 courses in the curriculum.
Description: This course provides a graphical approach to represent and study quantum information and computation. After exploring general features of quantum information in a graphical yet formal way, we introduce the more specific ZX-calculus, that can be used to represent and manipulate states and operators at an atomic level. We will show some important results about quantum information in this setting, and will further demonstrate its use in applications ranging from verication to simulation.
Period: P1 ECTS: 3
Lecturers: Renaud Vilmart
Syllabus: Click here
Description: Quantum information theory seeks to understand the absolute limits of information processing using quantum systems. This course will explore a variety of information processing tasks including data compression, channel coding and entanglement distillation. For each task, we will develop the necessary tools to analyse their properties and demonstrate how their rates can be characterised in terms of entropic quantities. We will also cover recent major advances in the field and discover so-called one-shot information theory which examines the rates of protocols within the non-asymptotic regime.
Period: P1 ECTS: 3
Lecturers: Peter Brown, Cambyse Rouzé
Syllabus: Click here
Description: This course explores the theory and applications of tensor computations, ranging from the basic operations on tensors to the numerical algorithms for the formation and manipulation of tensor decompositions and networks. After providing all theoretical fundamentals for the tensor algebra, the course focuses on the state-of-the-art research work that leverages tensor decompositions and networks in the domains of quantum computing, high performance computing, and AI/data analysis.
Period: P1 ECTS: 3
Lecturers: Oguz Kaya
Syllabus: Click here
Description: Coming soon!
Period: P1 ECTS: 3
Lecturers: Augustin Vanrietvelde
Description: Coming soon!
Period: P1 ECTS: 3
Lecturers: Titouan Carette, Cambyse Rouzé
Description: Coming soon!
Period: P1 ECTS: 3
Lecturers: Romain Alléaume
Description: Coming soon!
Period: P1.5 ECTS: 3
Lecturers: Benoît Valiron
Description: Coming soon!
Period: P1.5 ECTS: 3
Lecturers: Matt Wilson
Description: What are the mathematical structures encapsulating the weirdness of quantum theory? How can they be formally pinned down to ease their handling? How, in particular, can the crucial notion of causal structure be salvaged within a theory that seems to disregard it in such a careless way? Can one also superpose causal influences? These are the questions that this course will answer. We will show how recently developed mathematics (based in particular on category theory) help us to reformulate quantum theory from the ground up as a process theory, by taking its peculiar properties (first and foremost entanglement) as axioms. This opens to a renewed perspective on the notion of causal structure. Going to higher-order quantum processes – processes that map a quantum evolution to another quantum evolution –, we will discover that even causal structures might be put in a superposition in a quantum computer, leading to new speedups and applications.
Period: P2 ECTS: 3
Lecturers: Titouan Carette, Augustin Vanrietvelde
Syllabus: Click here
Description: This course explores quantum information processing through the lens of quantum correlations. We will develop an understanding of quantum correlations and the main mathematical tools to characterise them: from the well-known Bell-nonlocality and self- testing to new techniques based on graph inflation. We will discover direct applications and insights that can be gained from this approach, including results on communication complexity and non-local computation. We will further explore deep problems that leverage variations of the acquired techniques, such as parallel repetition theorems, Tsirelson's problem and marginal problems in general.
Period: P2 ECTS: 3
Lecturers: Mirjam Weilenmann, Marc-Olivier Renou
Syllabus: Click here
Description: Convex optimization has emerged as a critical tool for quantum information scientists, leveraging the natural convexity of quantum theory to offer powerful techniques for solving a variety of complex problems in the field. In this course we will develop these tools, with a focus on semidefinite optimization, analysing their mathematical properties and discussing their practical usage. The course will be driven by applications throughout quantum information science, using the tools we develop to solve important problems and provide new powerful perspectives on the field.
Period: P2 ECTS: 3
Lecturers: Peter Brown
Syllabus: Click here
Description: Quantum cryptography can be seen as the first, perhaps most natural consequence of the difference between classical and quantum information. The course will base its approach on quantum information theory to present the main principles related to quantum cryptographic constructions. It will also connect and discuss the practical developments, technologies, and applications of quantum cryptography, and its positioning with respect to classical cryptography.
Period: P2 ECTS: 3
Lecturers: Romain Alléaume
Syllabus: Click here
Description: Many-body quantum systems are ubiquitous in theoretical and experimental quantum information processing, from the simulation of condensed matter systems to the development of good quantum error-correcting codes. Recent years have seen major developments in our mathematical understanding of these systems' intricacies. In these lectures, we will explore the complexity of physically motivated models of many-body quantum systems, from ground and thermal states of matter to outputs of short-time quantum evolutions. We will consider two notions of complexity: (i) the computational hardness of simulating properties of the system (a.k.a. forward problem); and (ii) the learnability of classical descriptions of the system from access to samples (a.k.a inverse problem).
Period: P2 ECTS: 3
Lecturers: Cambyse Rouzé, Marco Fanizza
Syllabus: Click here
Description: Coming soon!
Period: P2 ECTS: 3
Lecturers: Marc Baboulin, Simon Martiel