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 Diderot, IRIF)

Teachers for 2021-22

Organisation

Lectures take place Thursdays 16:15. We will have 5 x 2.5 hours during the first half of the course followed by 4 x 3 hours.

In case you are awaiting test results, or tested positive for COVID, or have any symptoms, please do stay at home and keep us informed of your situation by email.

Lectures will take place in French, English upon request. (In the past all lectures have been in English.)

Basic notions

  • Sept 16 SL States, measurements, entanglement, CHSH
  • Sept 23 SL Evolution, circuits, superdense coding
  • Sept 30 SL Holevo's theorem, teleportation, no-cloning, BQP
  • Oct 7 SL BPP vs BQP, Quantum query model, Deutsch-Jozsa, Bernstein-Vazirani
  • Oct 14 SL Grover's algorithm, Simon's algorithm

Algorithms and complexity

  • Oct 21 FM Qiskit, Grover extensions
  • Oct 28 FM Amplitude amplification, phase estimation, applications
  • Nov 4 FM Lower bounds, complexity
  • Nov 11 no class (public holiday)
  • Nov 18 FM Query complexity of total functions, BQP included in PSPACE

FINAL EXAM

The final exam will take place on Nov 25 or Dec. 2nd at the usual time. Handwritten and printed lecture notes (your own, Ronald de Wolf, Iordanis Kerenidis, etc.) are allowed for the exam.

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

Sample 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.

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.

Lecture Notes

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

- Ronald de Wolf Quantum Computing lecture notes

- Iordanis Kerenidis lecture notes

Related Courses

This course is a prerequisite for the course Quantum information and cryptography which covers 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

Student seminar

In the QuanTech masters there is a student seminar which you are welcome to attend. (Web page forthcoming)

  • 15.10 Thierry Debuisschert - 12h - 454A Condorcet
  • 22.10 Iordanis Kerenidis - 12h - 454A Condorcet
  • 12.11 Luca Guidoni - 12h - 646A Condorcet
  • 19.11 Julien Laurat - 12h - 483A ou 366A Condorcet (salle à confirmer)

References

  • 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.
 
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