Introduction to quantum information processing

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.

• 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

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

Secret Key Distribution (QKD) protocols: 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

Graded Homework - Deadline Oct 17 midnight extended Oct 21 8:00am

Entanglement swapping, Bell inequalities, (if time allows: Ekert 1991 protocol for QKD)

Reading: chap 6 paragraph 6.2

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 midnight extended to monday 11th morning 11h59 am

• 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).

Heisenberg interaction, manipulation of qubit pairs

Reading: Chap 16 of notes

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 -

Density matrices continued, partial DM, von Neumann entropy

Reading: parts of chap 4 and 7: paragraph 4.4 and 7.1 - 7.3

Homework: continuation of graded Homework 9

Schmidt theorem, Entanglement entropy, Examples

Reading: Notes of last week and/or parts of chap 7.

Homeworks: hmw 10 is to train of entropy and related concepts. You can also work on the mini-project.

Continuation: discussion main inequalities satisfied by quantum entropy: convexity, subadditivity, strong subadditivity. 

Purification and Araki-Lieb inequality.

Non-signaling

Reading: chapter 7 (mainly paragraph 7.4 and a discussion of 7.5)

Wednesday: regular class

Thursday: 15h15-17h work on mini-project

Wed class: Holevo bound and accessible information when we measure

Reading: paragraphs 7.6 and 7.7

Thursday: 15h15-17h work on mini-project