Introduction to quantum information processing
Weekly outline

Course: Wednesdays 14h15  16h room CE13 and Thurdays 15h15  16h room INF2
Exercices: Thursdays 16h0017h. 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 miniproject will start in the second part of the semester.
BIBLIOGRAPHIEMichel 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/securequantumcommunicationsgothedistance
* QKDhistory.pdf an article by Gilles Brassard: Brief History of Quantum Cryptography: A Personal Perspective

 Introduction and overview of class
 Phenomenological illustration of strange quantum behaviors through interference experiments: Double slit experiment, MachZehnder 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

Math recap

hmw with details of solutions

 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
Reading: Chap 3 of Notes. For the Bloch sphere representation see also paragraphs in chap 2.8  2.10Extra reading: Article above "From Cbits to Qbits..." 
25 Sept regular class
26 Sept No class only exercises from 15h15  17h
 Physical examples of qubits: photon polarization, spin 1/2, two level systems
 Application of principles to the MachZehnder interferometer and the double slit experiment
 Application of principles to photon polarization experiments
 Quantum versus classical prediction (revisited)
Reading: Chap 2.1 2.4 of notes for extra information. Paragraphs 2.5  2.7 on spin will be treated later on during the semester.
Graded Homework  Deadline Oct 3 midnight
 Physical examples of qubits: photon polarization, spin 1/2, two level systems

Secret Key Distribution (QKD) protocols: BB84, B92
Reading: Chap 5 of notes and in Nielsen and Chuang Chap 12 section 6

More advanced exercises for selfstudy

entanglement, quantum teleportation, dense coding
Reading: Chap 6 sections 6.1, 6.3, 6.4
Graded Homework  Deadline Oct 17 midnight

Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)
Reading: chap 6 paragraph 6.2


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 SternGerlach experiments Feynman Lectures vol III, chap 5 & 6 (will not be needed in this class)
Graded Homework  Deadline Nov 7 midnight

Rabi oscillations, qubit manipulation, onequbit quantum gates
Reading: Chap 15 of Notes

Heisenberg interaction, manipulation of qubit pairs
Reading: Chap 16 of notes

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

von Neumann entropy, entanglement revisited
Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1  7.3

Continuation on Von Neumann entropy: recap, Schmidt theorem, purification, entropy of entanglement, examples
Wednesday: regular class 14h1516h
Thursday: 2hours of homework on the project from 15h15 to 17h
Reading: parts of chap 7.

Continuation: discussion main inequalities satisfied by entropy: convexity, subadditivity, strong subadditivity.
Entanglement entropy. ArakiLieb inequality.
Measurements and Holevo bound.
Reading: chapter 7 (parts)
Wednesday: regular class
Thursday: hmw work on project 15h1517h

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 JaynesCummings Hamiltonian


