Introduction to quantum information processing
Weekly outline

Course Wednesdays CHANGE OF ROOM now at: 14h1516h Room CO 3 till next notice
and as usual on Thursdays 15h1516h Room INF 2.
Exercices Thursdays 16h1517h. Room INF 2.
Instructor: nicolas.macris@epfl.ch
Teaching assistants: anastasia.remizova@epfl.ch and dina.abdelhadi@epfl.ch
Student assistants: mehrad.sahebi@epfl.ch and florian.delavy@epfl.ch and victor.braun@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 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 miniproject will start in the second part of the semester.
FINAL EXAM: one cheatsheet recto verso A4 is allowed. Handwritten or latex with readable sized characters
Saturday: 03.02.2024 from 09h15 to 12h15 (Room PO01)
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

Double slit experiment. Concept of wave function and quantum state. The Born rule. Examples of interference phenomenon: e.g. MachZehnder interferometer
Reading: Chapter 1 in notes, Feynman lectures vol III Chap 1, Articles above "Double slit experiment: old and new" and "Interference of C60 molecules"

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..."

The deadline is OCTOBER 6th at 7:00AM. Submit the assignment on moodle as one unique pdf file. You can handwrite (clearly) or latex.


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.

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)

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

The deadline is OCTOBER 27th at 7:00AM. Submit the assignment on moodle as one unique pdf file. You can handwrite (clearly) or latex.

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

CHANGE OF ROOM FOR WEDNESDAY: room CO3 till next notice
Thursday is as usual in INF2
QKD, BB84, B92
Reading: Chap 5 of notes and in Nielsen and Chuang Chap 12 section 6

entanglement, quantum teleportation, dense coding
Reading: Chap 6 sections 6.1, 6.3, 6.4

The deadline is extended to MONDAY 20th Nov at 23h59 PM. Submit the assignment on moodle as one unique pdf file. You can handwrite (clearly) or latex.


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

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

Hmw 10 is graded and the deadline is Friday December 1st at 07:00 AM.


von Neumann entropy, entanglement revisited
Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1  7.3
Presentation of project (this thursday).
You will upload one short pdf with your analysis of the theoretical part and the completed jupyter notebook provided here.
Form teams of two students: find your partner! Indicate both family names in name of your uploaded files as name1name2.pdf, ect...
Sharp deadline: Thursday 21 December midnight.

This is the jupyter notebook to complete for the practical parts of the project

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.
Homework: work on project

Here a proof of Schmidt theorem that was sketched on the blackboard. With all indices at correct places ect!


This week: Wednesday and thursday classes replaced by work on project

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

