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Quantum information processing

Subheadings:

Basics of quantum information processing

Annotation:
The aim is to master the basic concepts of quantum information processing and basic ways of their use.

Warp:
Hilbert space, pure and mixed states. Von Neumann measurement and POVM. Unitary operators and superoperators. Entanglement and nonlocality. Bell inequalities. Quantum teleportation. Quantum circuits.

Basic study material:
  • MA Nielsen, IL Chuang: Quantum Computation and Quantum Information, Cambridge University Press, Chapters 1, 2 and 4.
  • J. Gruska: Quantum computing, McGraw-Hill, chapters 1 and 2.
  • John Preskill’s quantum computation and physics lecture notes
  • John Watrous’s “Theory of Quantum Information” lecture notes
Examiner: doc. RNDr. Jan Bouda, Ph.D. prof. RNDr. Jozef Gruska, DrSc. , doc. Mgr. Mário Ziman, Ph.D.

Other recommended literature:
  • ND Mermin: Quantum Computer Science, Cambridge university Press.
  • T. Heinosaari, M. Ziman: Mathematical language of quantum theory: From Uncertainty to Entanglement, Cambridge University Press.

Quantum computational complexity, quantum communication complexity, basic quantum algorithms

Annotation:
The first goal is to master the key methods to design quantum algorithms and communication protocols, as well as proving complexity bounds of computation and communication problems.
The second goal is to understand basic quantum complexity classes, their mutual relationship and relationship to classical complexity classes.

Warp:
Basic quantum algorithms. Shor and Grover algorithms. Algorithms based on random walks.
Quantum computational complexity. Quantum circuit model. Basic complexity classes - BQP, QMA.
Quantum communication complexity. Quantum fingerprinting.

Basic study material:
  • P. Kaye, R. Laflame and M. Mosca; An introduction to quantum computing, Oxford University Press, 2007.
  • John Preskill’s quantum computation and physics lecture notes
  • John Watrous’s “Quantum Computation” lecture notes
  • Selected articles from the quantum archive.
Examiner: doc. RNDr. Jan Bouda, Ph.D. prof. RNDr. Jozef Gruska, DrSc.

Other recommended literature:
  • MA Nielsen, IL Chuang: Quantum Computation and Quantum Information, Cambridge University Press, Chapters 4, 5 and 6.
  • J. Gruska: Quantum computing, McGraw-Hill, 1999, chapter 4.
  • ND Mermin: Quantum Computer Science, Cambridge University Press.
  • S. Aaronson: Quantum computing from Democritos, Cambridge, 2012.

Quantum cryptography

Annotation:
The aim is to master the basic methods of quantum keys distribution and quantum versions of basic cryptographic protocols and primitives. Methods of generating quantum randomness and improving the properties of randomness.

Warp:
Generation of quantum randomness. Quantum keys distribution. Encryption of quantum information. Basic quantum protocols. Quantum secret sharing. Impossibility of quantum bit commitment and coin tossing. Secure multi-party computation. Device-independent protocols.

Basic study material:
  • John Watrous’s “Quantum Computation” lecture notes
  • G. Gilbert, YS Weinstein, M. Hamrick: Quantum Cryptography, World Scientific, 2013.
  • Selected articles from the quantum archive.
Examiner: doc. RNDr. Jan Bouda, Ph.D. prof. RNDr. Jozef Gruska, DrSc. , doc. Mgr. Mário Ziman, Ph.D.

Other recommended literature:
  • ND Mermin: Quantum Computer Science, Cambridge university Press.
  • S. Aaronson: Quantum computing from Democritos, Cambridge, 2012.
  • MA Nielsen, IL Chuang: Quantum Computation and Quantum Information, Cambridge University Press.
  • J. Gruska: Quantum Computation, McGraw-Hill, Chapter 6.

Quantum decoherence and error correction

Annotation:
Decoherence is considered to be a major obstacle to the implementation of long-running and high-precision quantum information processing. The aim is to get acquainted with the basic methods of combating decoherence such as quantum error correction codes and fault-tolerant quantum computing.

Warp:
Decoherence - sources, properties and consequences. Error models. Quantum error correction codes. Stabilizer and CSS codes. Quantum fault-tolerant computing. Universal gate sets for fault-tolerant quantum computing.

Basic study material:
Examiner: doc. RNDr. Jan Bouda, Ph.D. prof. RNDr. Jozef Gruska, DrSc. doc. Mgr. Mário Ziman, Ph.D.

Other recommended literature:
  • ND Mermin: Quantum Computer Science, Cambridge University Press.
  • MA Nielsen and IL Chuang: Quantum Computation and Quantum Information, Cambridge University Press, Chapter 10.
  • J. Gruska: Quantum computing: McGraw-Hill, 1999, chapter 7.

Quantum information theory, entanglement and correlations

Annotation:
The first goal is to master the basics of quantum information theory.
The second goal is to acquire basic knowledge about entanglement, its properties, power and applications in computation, communication and cryptography.

Warp:
Quantum noise and its properties. Quantum information and its properties. Quantum channels and their capacities. Von Neumann entropy (quantum Shannon entropy).
Definition and design of entangled states. Classification of entangled states. Purification of mixed entangled states. Detection and measurement of entanglement. Discord. Nonlocal quantum correlations. Computational and communication power of entanglement. Bell inequalities.

Basic study material:
  • J. Watrous: The Theory of Quantum Information, Cambridge University Press 2018.
  • S. Mancini, A. Winter: A Quantum Leap in Information Theory. World Scientific 2020.
  • John Preskill’s quantum computation and physics lecture notes
  • John Watrous’s “Theory of Quantum Information” lecture notes
  • Selected articles from the quantum archive.
Examiner: doc. RNDr. Jan Bouda, Ph.D. prof. RNDr. Jozef Gruska, DrSc. doc. Mgr. Mário Ziman, Ph.D.

Other recommended literature:
  • T. Heinosaari, M. Ziman: Mathematical language of quantum theory: From Uncertainty to Entanglement, Cambridge University Press.
  • R. Horodecki, P. Horodecki and M. Horodecki: Quantum entanglement Rev. Mod. Phys. 81 (2), 865-942.
  • M. Hayashi: Quantum information theory, Springer, chapters 1-4.
  • J.Gruska, Quantum computing, McGraw-Hill, 1999, chapter 8.

Optimization and advanced quantum information theory

Annotation:
The goal is to learn basic techniques for (non-iid) analysis of security of quantum protocols, hypothesis testing, as well as optimization methods used in quantum information processing e.g. to calculate smooth entropies.

Warp:
Semi-definite programming. Navascuez-Pironio-Acin hierarchy. Semi-definite programming and smooth min/max-entropies. Entropy accumulation techniques.

Basic study material:
Examiner: doc. RNDr. Jan Bouda, Ph.D. doc. Mgr. Mário Ziman, Ph.D.

Randomness, pseudorandomness, and derandomization in quantum information processing

Annotation:
The goal is to learn basic techniques that use randomness and probability in quantum information processing.

Warp:
Randomness techniques in quantum information processing. Random states, random matrices, random (unitary) channels. Concentration of measure. Haar measure. Quantum pseudorandomness and its applications - state and unitary designs. Derandomization using pseudorandom structures.

Basic study material:
  • J. Watrous: The Theory of Quantum Information, Cambridge University Press 2018.
  • Selected articles from the quantum archive.
Examiner: doc. RNDr. Jan Bouda, Ph.D. doc. Mgr. Mário Ziman, Ph.D.