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## Quantum information and applications (24h, 3ECTS)Person in charge: Sophie Laplante (Université Paris Diderot, IRIF) ## Teachers for 2020-21## Organisation
Lectures take place Wednesdays
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 information - Oct 21 AC
**NO CLASS THIS WEEK** - Oct 28 AC
- Nov 4 AC
- Nov 18 AC
- Nov 25 AC
## FINAL EXAMThe final exam will take place on Dec. 2nd at the usual time. The exam will be 2 hours. Handwritten and printed lecture notes (your own, Ronald de Wolf, Iordanis Kerenidis, etc.) are allowed for the exam. The exam will be online at the following link BBB . We will ask you to turn off your microphone and turn on your camera during the exam. We will be available to answer questions by private chat. Please make sure to have your student ID with you for the exam and that you have the ability to scan or photograph your exam in good enough quality so that it is legible. The exam will be made available on this page as a PDF file at the beginning of the exam. Please handwrite the answers as you would normally do, and use separate sheets for parts I and II. Please send your answers to the emails given on the exam at the end of the allotted time. 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 objectivesEach 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. ## PrerequisitesAlgorithms, basic notions in computational complexity, basic notions in linear algebra and probability. ## Course outlineIntroduction - Model of quantum computation
- EPR paradox, teleportation, superdense coding.
- Holevo's theorem
Basic algorithms - Deutsch-Jozsa, Simon's algorithm, Grover search
Advanced Algorithms - Period finding, quantum Fourier transform, Shor's factoring algorithm.
- Amplitude amplification, collision algorithms
- Other quantum algorithms relevant in cryptography
Quantum complexity - Basics of quantum complexity theory
## Lecture NotesWe recommend the following lecture notes to use alongside the lectures: - Ronald de Wolf Quantum Computing lecture notes - Iordanis Kerenidis lecture notes ## Related CoursesThis 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
## References- Quantum Computer Science: An Introduction. N. David Mermin. Cambridge University Press, 2007.
- Quantum Computing: Lecture Notes. R. de Wolf
- Quantum Computation and Quantum Information. M. Nielsen et I. Chuang. Cambridge University Press, 2000.
## InternshipsInternships in the area of Complexity Theory are available. Please contact the Algorithms and Complexity group of IRIF or PCQC |