Introduction to quantum information processing
Weekly outline
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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 giovanni.ranieri@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.
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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- 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
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Math recap
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hmw with details of solutions
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- 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 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 Homework - Deadline Oct 3 midnight
- 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
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More advanced exercises for self-study
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entanglement, quantum teleportation, dense coding
Reading: Chap 6 sections 6.1, 6.3, 6.4
Graded Homework - Deadline
Oct 17 midnightextended Oct 21 8:00am -
Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)
Reading: chap 6 paragraph 6.2
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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)
Graded Homework - Deadline
Nov 7 midnightextended to monday 11th morning 11h59 am-
The deadline is November
7th at 23:59AMextended to monday morning 11h59 am. Submit the assignment on moodle as one unique pdf file. You can handwrite (clearly) or latex.
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No in presence class. 3 Videos for this week's lectures are available below.
Rabi oscillations, qubit manipulation, one-qubit quantum gates
Reading: Chap 15 (15.4 - 15.5) of Notes
Homeworks: Two hours in room INF 2 at 15h15-17h. Continuation of graded homework 7 (+ start playing with Pennylane and Qiskit for those who finished).
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Vidéo 1: Dynamics of spin 1/2 in a time dependent magnetic field - part I
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Video 2: Dynamics of spin 1/2 in a time dependent magnetic field - Part II
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Video 3: Application to Rabi oscillations. And realization of NOT and Hadamard quantum gates.
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Short hands-on exercise to discover PennyLane (Xanadu). The zip file contains a Jupyter notebook. The information for installing PennyLane is in the notebook.
This is to be done this and next couple of weeks together with a Qiskit hands-on exercise on the IBM platform (coming soon).
The goal is to familiarize yourselves with these platforms by using the, language, simulators (and possibly NISQ devices) they provide. This will prepare you for the final mini-project of the course.
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Heisenberg interaction, manipulation of qubit pairs
Reading: Chap 16 of notes
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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
Graded Homework 9 - deadline December 1st at 23h59 -
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This file contains the lectures of this and part of next week.
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Upload graded hmw 9 here. The deadline is December 1st at 23h59.
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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
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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.
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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
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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
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