Parisian Master of Research in Computer Science
Master Parisien de Recherche en Informatique (MPRI)

Quantum information and applications (24h, 3ECTS)

Person in charge: Sophie Laplante (Université Paris Cité, IRIF)

Teachers for 2023-24

Presentation and objectives

Each year computing machines become faster and faster, but they use still use at their base the same Newtonian physics. Feynman in 1982 already asked about the necessity of this restriction to classical physics. The idea behind quantum computation is to use quantum phenomena to solve tasks that conventional machines cannot achieve.

Historically the first result that showed the superiority of the quantum model was in cryptography. Bennett and Brassard in 1984 gave a first quantum protocol for perfectly secure key distribution. Such an unconditional security does not exist in the classical world.

At present many important concepts of theoretical computer science have been extended to quantum computation, from communication to algorithms and error correcting codes.

The aim of this course is to present the bases of several concepts about quantum computation. The emphasis will be on quantum algorithms and communication. We will describe the basics of Quantum Computation and its applications in algorithms, communication complexity and nonlocality.

Prerequisites

Algorithms, basic notions in computational complexity, basic notions in linear algebra and probability.

Organisation

Lectures

Lectures take place Thursdays 12:45, room 1004. Unless specified otherwise lectures are in the 3-hour format. Lectures will take place in French, English upon request. (In the past all lectures have been in English.) References in brackets refer to Ronald de Wolf's (RdW) and John Watrous' (JW) lecture notes.

Basic notions (order and contents subjects to change)

  • Sept 14 SL: States, measurements, entanglement. Mermin-GHZ game, CHSH [RdW: Chapter 1.1-1.4 + 16.1-16.2] [JW: Lectures 1&2, Lecture 3 pp.6-8, Lecture 20]
  • Sept 21 SL: Quantum non-locality. Local, quantum and non-signaling sets. Bell inequalities. Tsirelson inequalities. Gates and circuits, superdense coding.
  • Sept 28 SL: density matrices, Entropy and Holevo's theorem. no-cloning theorem, teleportation. BPP in BQP. [RdW: 1.5] [JW Lecture 3, Lecture 4 pp. 1-3]
  • Oct 5 SL: Quantum query model, Deutsch-Jozsa, Bernstein-Vazirani [RdW: 2.1, 2.4] [JW Lecture 4 pp. 3-6, Lecture 5 ]. Simon's algorithm. [RdW: 3.1-3.2] [JW: Lecture 6]

Algorithms and complexity (order and contents subjects to change)

  • Oct 12 FM: Quantum Fourier Transform, Phase Estimation, Period Finding [RdW: 4, 5]
  • Oct 19 NO CLASS but HOMEWORK by SL (see homework section)
  • Oct 26 FM: Factorization, Discrete Logarithm, Hidden Subgroup Problem [RdW : 5, 6]
  • Nov 2 NO CLASS but HOMEWORK by FM (see homework section)
  • Nov 9 FM: Grover's algorithmm, Amplitude Amplification, Quantum Counting [RdW: 7]
  • Nov 16 FM: Lower bounds for query complexity: polynomial methods. [RdW: 11.1-11.2]

QuanTech Seminars

This course is also part of the Quantum technologies Graduate School of Université Paris Cité. As a consequence, a joint QuanTech seminar is offered to MPRI students by IRIF and MPQ, which you are welcome to attend.

Homework

Final exam

(Subject to change) The final exam will take place on Nov 23, 12:45-15:45. Handwritten and printed lecture notes (your own, Ronald de Wolf, or others) are allowed for the exam.

Please make sure to have your student ID with you for the exam.

Sample exams:

  • Exam from 2013. Be aware that the content varies from year to year and in particular there is no crypto in the course this year.
  • Part of exam from 2014, with an example of a quantum algorithm to design.

References and Lecture Notes

We recommend the following lecture notes to use alongside the lectures:

- Ronald de Wolf Quantum Computing lecture notes

- John Watrous Quantum Computation Lecture notes

- John Preskill Lecture notes for PH219/CS219 mainly for information theory (10.1, 10.2.1) and Holevo's bound (10.6.2)

- Qiskit (open-source SDK) Textbook mixing quantum computation explanations and source codes

The following textbooks are also suggested.

- Quantum Computer Science: An Introduction. N. David Mermin. Cambridge University Press, 2007.

- Quantum Computation and Quantum Information. M. Nielsen et I. Chuang. Cambridge University Press, 2000.

Related Courses

This course is a prerequisite for the course Quantum information and cryptography which covers advanced algorithms, quantum cryptography and post-quantum cryptography.

The following courses are strongly recommended.

  • 2.11.1 Advanced algorithms
  • 2.11.2 Randomness in Complexity

If you are interested in Algorithms and Complexity, we recommend taking courses from the following list.

1st quarter courses

  • 2-11-1 Advanced Algorithms
  • 2-11-2 Randomness in Complexity
  • 2-12-1 Techniques in Cryptography and Cryptanalysis
  • 2-18-2 Algorithmique distribuée avec mémoire partagée
  • 2-38-1 Algorithms for embedded graphs

1st and 2nd quarter courses

  • 2-13-2 Error correcting codes and applications to cryptography
  • 2-18-1 Distributed algorithms for the networks
  • 2-24-1 Optimisation
  • 2-29-1 Graph algorithms
  • 2-33-1 Theory of Computations

If you are particularly interested in quantum computing you can also take courses from the Physics masters program Dispositifs quantiques

 
Universités partenaires Université Paris-Diderot
Université Paris-Saclay
ENS Cachan École polytechnique Télécom ParisTech
ENS
Établissements associés Université Pierre-et-Marie-Curie CNRS INRIA CEA