Introduction to quantum information processing
Aperçu des semaines
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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 and yihui.quek@epfl.ch
Teaching assistant: perrine.vantalon@epfl.ch
Student assistants: gopal.dahale@epfl.ch, cherilyn.christen@epfl.ch, timothe.jobin@epfl.ch, ekaterina.pankovets@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)
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.)
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 sometime during the second part of the semester.
Final exam is during official exam session: one cheat-sheet recto verso A4 is allowed. Handwritten or latex with readable sized characters
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. 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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- 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.
Instructor Nicolas Macris
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Math recap on complex numbers and linear algebra.
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hmw with details of solutions for the math recap
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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; Exercises Thursday 15h15 - 17hInstructor Nicolas Macris -
Wed regular class: 14h15 - 16h Room CE1 3
Thursday: only exercises: 15h15 - 17h Room INF2- 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.
Graded HW1
Instructor Nicolas Macris
- Physical examples of qubits: photon polarization, spin 1/2, two level systems
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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
Instructor Yihui Quek
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Entanglement, quantum teleportation, dense coding
Reading: Chap 6 sections 6.1, 6.3, 6.4
Graded HW2
Instructor Yihui Quek
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Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)
Reading: chap 6 paragraph 6.2
Instructor: Yihui Quek
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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
Instructor Nicolas Macris
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Density matrices continued, partial DM, von Neumann entropy
Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1 - 7.3
Instructor Nicolas Macris
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Schmidt theorem, Entanglement entropy, Examples
Reading: Notes of last week and/or parts of chap 7.
Graded HW3
Instructor Yihui Quek
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- Pauli group and why Pauli errors are a universal error basis.
- Recognsize common quantum noise models (bit/phase flip, depolarizing, amplitude damping).
- Connect classical linear codes to quantum codes.
- Work through encoding, error dtection, and decoding for the 3-qubit repetition code.Reading:
Instructor Yihui Quek
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- Stabilizer operators.
- Logical operators.
- CSS codes from classical codes.
- Steane [[7, 1, 3]] code
Reading:
Instructor Yihui Quek
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- Recap of fault tolerant models.
- Error propagation and why FT matters.
- Threshold theorem and code-concatenation.
Graded HW4
Instructor Yihui Quek
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- Introduction to magnetic moments, spin, Bloch sphere representation, Larmor precession
- Rabi oscillations
- Application to elementary gates (NOT and Hadamard logical gates)
Reading: Chap 2 (2.5 - 2.10) and Chap 15 (15.1 - 15.3 - 15.4 - 15.5) 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)
Instructor Nicolas Macris
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Heisenberg interaction, manipulation of qubit pairs
Reading: Chap 16 of notes
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