Quantum information processing
Weekly outline
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Course Wednesdays 8h15-10h Room INF1 and Thursdays 15h15-16h Room ELD 020. Exercices Thursdays 16h15-17h. Room ELD 020.
Instructor: nicolas.macris@epfl.ch
Teaching assistants: antoine.bodin@epfl.ch and dina.abdelhadi@epfl.ch
Student assistants: ahmed.ezzo@epfl.ch and florian.delavy@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 on IBM Q 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 serve as an aid and are not meant to replace in class presence)
NOTES (in french - to be translated - we teat 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 (dates to be announced as we go). The mini-project 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/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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Double slit experiment. Concept of wave function and quantum state. The Born rule. Interference in two different contexts: Mach-Zehnder interferometer,
Josephson junction and SQUID.Reading: Chapter 1 in notes, Feynman lectures vol III Chap 1, Articles above "Double slit experiment: old and new" and "Interference of C60 molecules"
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Polarization degree of freedom for photons, notion of qubit, polarization observable.Reading: Chap 2 of Notes, for Dirac's and component notation: Article above "From Cbits to Qbits..."
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Graded homework deadline October 6 midnight
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Principles of quantum physics. Product and entangled states.
Reading: Chap 3 of notes, for Dirac's notation and tensor product see also Article above "From Cbits to Qbits..."
See also Nielsen and Chuang's book Chapter 2 Sections 2.1 and 2.2.
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Introduction to magnetic moments, spin, Bloch sphere representation, Larmor precession
Reading: Chap 2 and Chap 15 of notes.
For more advanced material on the Stern-Gerlach experiments Feynman Lectures vol III, chap 5 & 6 (will not be needed in this class)
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Rabi oscillations, qubit manipulation, one-qubit quantum gates
Reading: Chap 15 of Notes
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Deadline of graded homework is thursday 27 Oct midnight
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Heisenberg interaction, manipulation of qubit pairs
Reading: Chap 16 of notes
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QKD, 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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Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)
Reading: chap 6 paragraph 6.2
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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
Homework 10 is graded: deadline extended Sunday December 4th midnight.
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von Neumann entropy, entanglement revisited
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Continuation on Von Neumann entropy: recap, Schmidt theorem, purification, subadditivity, Araki-Lieb inequality. Entropy of entanglement
Homework: continuation of hmw 11 and/or start of project
Graded mini-project with deadline on Dec 23rd at 23h59: implementation on an NISQ device on the IBM Q platform. For this project find a team mate and hand-in a common upload.
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Creation and annihilation operators, algebraic approach
Wednesday: regular class.
Thursday: regular class 15h15--> 16h. Then project.
Homework: project
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Coupling of two level system with harmonic oscillator mode, Rabi oscillations revisited.
Perspectives: cavity electrodynamics, circuit electrodynamics and superconducting qubit platforms.
Wednesday: regular class
Thursaday: only project 15h15-17h
Homework: project deadline friday 23 Decembre 23h59
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