Aperçu des semaines

  • Généralités

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    Course: Wednesdays 14h15 - 16h room CE13 and Thurdays 15h15 - 16h room INF2

    Exercices: Thursdays 16h00-17h. Room INF2

    Instructor:  nicolas.macris@epfl.ch  

    Teaching assistants: anastasia.remizova@epfl.ch  and perrine.vantalon@epfl.ch

    Student assistants:  pablo.rodenas@epfl.ch and lenny.delzio@epfl.ch and thomas.brunet@epfl.ch and khurshed.fitter@epfl.ch

    Description: Information is stored and processed in hardware components. With their miniaturization the concept of classical bit must be replaced by the notion of quantum bit. After having introduced the basics of quantum physics for "discrete" systems, the basic spin 1/2 qubit and its manipulation on the Bloch sphere are illustrated. This course then develops the subjects of communications, cryptography, quantum correlations, and introduces elementary concepts  of quantum physics with applications in information theory such as the density matrix and von Neumann's entropy. The course is intended for an audience with no knowledge of quantum physics and elementary knowledge of classical physics and linear algebra. Practical exercises, simulations and implementations on NISQ machines will also be covered during the semester. This course prepares students for more advanced quantum information classes.

    Course and exercices are in presence. Videos of class will be accessible here VIDEOS (these only serve as an aid and are not meant to replace in class presence. The material and order of classes and videos might also differ.)

    Lecture notes  (in french - to be translated - we treat only a subset of these notes this semester)

    Grading scheme: 4 graded homeworks 20%, miniproject 10%, final exam 70%. You will upload your homeworks on the moodle page.  The mini-project will start in the second part of the semester.

    BIBLIOGRAPHIE

    Michel Le Bellac: A short introduction to quantum information and quantum computation, Cambridge University press 2006. A small pedagogical book introducing physical aspects of the subject.

    N. David Mermin: Quantum Computer Science, An introduction, Cambridge University press 2007. An introduction written by a physicist for computer scientists.

    Neil Gershenfeld, The Physics of Information Technology, Cambridge University Press 2000, An introduction to various phenomena, classical and quantum, underpinning information technologies.

    Michael A. Nielsen and Isaac Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000. Un livre complet et d’un niveau plus avance.

    OTHER

    * For an introduction to QM read chapters 1 et 2 of Feynman Lectures vol III.

    * Double slit experiment: old and new

    * Interference of C60 molecules

    * From Cbits to Qbits: Teaching computer scientists quantum mechanics, by D. Mermin

    * There is plenty of room at the bottom a historical conference of R. Feynman on miniaturization

    * http://physicsworld.com/cws/article/news/2014/nov/13/secure-quantum-communications-go-the-distance

    * QKD-history.pdf an article by Gilles Brassard: Brief History of Quantum Cryptography: A Personal Perspective

  • 11 - 12 Sept: Introduction and interference experiments

    • Introduction and overview of class
    • Phenomenological illustration of strange quantum behaviors through interference experiments: Double slit experiment, Mach-Zehnder interferometer, Photon polarization experiments
    • Classical physics prediction versus experiment. Quantum prediction.
    • A first (qualitative) encounter with the concepts of quantum state, and Born rule.


    Reading: Chapter 1 in notes, paragraphs 1.1 - 1.3. Chapter 3 paragraph 3.1.

    Feynman lectures vol III Chap 1, Articles above "Double slit experiment: old and new" and "Interference of C60 molecules"

    Extra reading to go further: rest of chapter 1

  • 18 - 19 Sept: Mathematical principles of Quantum Mechanics

    Cette semaine
    • A recap of linear algebra in finite Hilbert spaces. The Dirac notation.
    • Principles of QM
    • Qubits and their Hilbert space (single and many qubit systems, product and entangled states)
    • Bloch sphere representation. Elementary unitary operations on single qubits
    • Physical examples of qubits: photon polarization, spin 1/2, two level systems

    Reading: Chap 3 of Notes. 

    Extra reading: Article above "From Cbits to Qbits..."


  • 25 - 26 Sept: Application of the principles to the interference experiments

    25 Sept regular class

    26 Sept No class only exercises from 15h15 - 17h

    • Application of principles to the Mach-Zehnder interferometer and the double slit experiment
    • Application of principles to photon polarization experiments
    • Quantum versus classical prediction (revisited)

    Reading: Chap 2 of notes for extra information.

    Graded Homework - Deadline Oct 3 midnight

  • 2 - 3 Oct: cryptography quantique

    Secret Key Distribution (QKD) protocols: BB84, B92

    Reading: Chap 5 of notes and in Nielsen and Chuang Chap 12 section 6

  • 9 - 10 Oct: entanglement I

    entanglement, quantum teleportation, dense coding

    Reading: Chap 6 sections 6.1, 6.3, 6.4

    Graded Homework - Deadline Oct 17 midnight

  • 16 - 17 Oct: entanglement II

    Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)

    Reading: chap 6 paragraph 6.2

  • 23 - 24 October Holiday fall break

  • 30 - 31 Oct: Spin 1/2 and dynamics in magnetic fields I

    Introduction to magnetic moments, spin, Bloch sphere representation, Larmor precession

    Reading: Chap 2 and Chap 15 of notes.

    Homework 3 continued & Homework 4

    For more advanced material on the Stern-Gerlach experiments Feynman Lectures vol III, chap 5 & 6 (will not be needed in this class)

    Graded Homework - Deadline Nov 7 midnight

  • 6 - 7 Nov: dynamics of spin in magnetic fields II

    Rabi oscillations, qubit manipulation, one-qubit quantum gates

    Reading: Chap 15 of Notes

  • 13 - 14 Nov: Heisenberg interaction

    Heisenberg interaction, manipulation of qubit pairs

    Reading: Chap 16 of notes

  • 20 Nov - 21 Nov: density matrix

    statistical mixtures, system+environment, generalization of the notion of quantum state and the density matrix

    parts of the chapter are in the tablet notes in next week's posting

    Reading: parts of Chap 4 of notes: paragraphs 4.1 - 4.3

    Graded Homework - Deadline Nov 21 midnight


  • 27 Nov - 28 Nov: von Neumann entropy I

    von Neumann entropy, entanglement revisited

    Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1 - 7.3


  • 4 - 5 Dec: von Neumann entropy II

    Continuation on Von Neumann entropy: recap, Schmidt theorem, purification, entropy of entanglement, examples

    Wednesday: regular class 14h15-16h

    Thursday: 2hours of homework on the project from 15h15 to 17h

    Reading: parts of chap 7.



  • 11 - 12 Dec: von Neumann entropy III

    Continuation: discussion main inequalities satisfied by entropy: convexity, subadditivity, strong subadditivity. 

    Entanglement entropy. Araki-Lieb inequality. 

    Measurements and Holevo bound.

    Reading: chapter 7 (parts)

    Wednesday: regular class

    Thursday: hmw work on project 15h15-17h


  • 18 - 19 Déc: Selected topics/Project

    This could be about qubit platform technologies overview or a topic in quantum information and communication or an overview of  quantum computation and simulation. Or this could be an introduction to the Jaynes-Cummings Hamiltonian

  • Extra material on NISQ devices

  • Exams of last years

  • Old projects