Introduction to quantum information processing
Résumé de section
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Wednesdays Room CE1 3 at 14h15 - 16h Course lectures
Thursdays Room INF2 at 15h15 -17h exercises and sometimes first hour 15h15-16h dedicated to class and/or discussion (announced on moodle page day before).
Instructors: nicolas.macris@epfl.ch
Teaching assistant: perrine.vantalon@epfl.ch aviv.taller@epfl.ch
Student assistants: francesca.fino@epfl.ch gabriel.jouveaux@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.
Lecture notes (in french - we treat only a subset of these notes this semester)
Extra references for reading will also be given for some of the lectures (see in weekly schedule below)
Grading scheme: 1 midterm 20%, miniproject 10%, final exam 70%. The mini-project will start sometime during the second part of the semester.
BIBLIOGRAPHYMichel 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. Complete reference probably somewhat more advanced than these lectures.
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
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This fall we treat material corresponding to a subset of these notes. Namely in the following order chapters 1, 2 (parts of them) and chapter 3; then chapters 5 and 6; then chapter 7; then chapters 15 and 16.
Note that chapters on quantum compuation (9, 10, 11, 12, 13, 14) are to large extent independent and treated in spring in class CS-308.
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- Introduction and general overview of class
- Phenomenological illustration of strange quantum behaviors through interference experiments: Double slit experiment, Mach-Zehnder interferometer, (and photon polarization experiments if time permits).
- Classical physics prediction versus experiment. Quantum prediction.
- A math recap of linear algebra done in Dirac's notation.
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
This week class Wed 14h15 - 16h and Thursday 15h15 - 16h. Exercises Thursday 16h - 17h.
Note: I will complete Wed's class the first 15 minutes on Thursday
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- 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..."Class Wednesday 14h15 - 16h room CE 1 3; Exercises Thursday 15h15 - 17h room INF2-
In this handout you can already solve the math of the problems just from the principles taught in class. Physical interpretations of what "polarization" and "interferometers" are will be discussed in the next class.
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Wed regular class: 14h15 - 16h Room CE1 3
Thursday: We finish class from 15h15 to 15h30++ and discussion/questions Room INF2. Exercises start immediately after (till 17h).- Physical examples of qubits: photon polarization, spin 1/2, two level systems
- 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 2.1 -2.4 of notes for extra information. Paragraphs 2.5 - 2.7 on spin will be treated later on during the semester.
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Secret Key Distribution (QKD) protocols: BB84, B92
Reading: Chap 5 of notes and in Nielsen and Chuang Chap 12 section 6
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Entanglement, quantum teleportation, dense coding
Reading: Chap 6 sections 6.1, 6.3, 6.4
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Bell inequalities, Ekert 1991 protocol for QKD
Reading: chap 6 paragraph 6.2
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Wednesday 28th at 8h15-10h MIDTERM
Thursday hmw session for discussion and questions
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statistical mixtures, system+environment, generalization of the notion of quantum state and the density matrix
Reading: parts of Chap 4 of notes: paragraphs 4.1 - 4.3
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von Neumann entropy
Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1 - 7.3
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Schmidt theorem, Entanglement entropy, Examples
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Main inequalities satisfied by quantum entropy: convexity (proof), subadditivity (proof), strong subadditivity (review).
Purification and Araki-Lieb inequality (proof). Entanglement revisited.
Mutual information acquired by measurements and Holevo bound (review)
Reading: chapter 7 (mainly paragraph 7.4 and a discussion of 7.5)
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- Introduction to magnetic moments, spin, Bloch sphere representation, Larmor precession
Reading: Chap 2 (2.5 - 2.10) and Chap 15 (15.1 - 15.3) of notes.
If you want to read more on the Stern-Gerlach experiments see Feynman Lectures vol III, chap 5 & 6 (will not be needed in this class)
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Class of Wednesday
- Rabi oscillations
- Application to elementary gates (NOT and Hadamard logical gates)
- Heisenberg spin-spin interactions if time permits (and CNOT gate)
Reading: Chap 15 (15.4 - 15.5) of notes.
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Heisenberg interaction, manipulation of qubit pairs
Reading: Chap 16 of notes
