Seminar on Quantum Capacities and Quantum Algorithms

Julien Schanz
Dr. Simon Schmidt
Prof. Dr. Moritz Weber

Contents

In this seminar, we are learning basics in Quantum Information Theory from the book of Watrous, The Theory of Quantum Information. We are then going to look at the features of Quantum Entropy and Quantum (Channel) Capacities; these are tools measuring how „quantum“ a system is, in some sense. Also, if there are enough people interested in this direction, we will take a look at Quantum Algorithms, which are the software of quantum computers. Here, the algorithms by Shor, Deutsch or Grover may be studied.

Talks

• 1) 19.4. Mathematical Foundations of QIT 1, Registers and states, entanglement, Watrous Ch 2.1, LL
• 2) 26.4. Mathematical Foundations of QIT 2, Quantum channels, Stinespring, Watrous Ch 2.2, MW
• 3) 3.5. Mathematical Foundations of QIT 3, Quantum measurement, Watrous Ch 2.3, RK
• 4) 10.5. Quantum Entropy, Classical entropy, Watrous Ch 5.1, S
• 5) 17.5. Quantum Entropy 2, Quantum entropy, Watrous Ch 5.2, LS
• 24.5. - fällt aus
• 31.5. Quantum Entropy 3, Source Coding, Watrous Ch. 5.3, YN
• 6) 7.6. Quantum Capacity 1, Classical information over quantum channels, Watrous Ch. 8.1, DZ
• 7) 14.6. Quantum Capacity 2, Quantum information over quantum channels, Watrous Ch. 8.2, evtl. 8.3, AB
• 8) 21.6. Quantum Algorithm 1, Quantum gates and quantum versions of classical computations, quantum algorithms, ggf Deutsch’s algorithm, Rieffel-Polak, Ch 5+ggf 7 (+ Kaye-Laflamme-Mosca, Ch 4-6, + ggf 7-8), MK
• 9) 28.6. Quantum Algorithm 2, Grover’s Algorithm, Rieffel-Polak, Ch 9 (+ Kaye-Laflamme-Mosca, Ch 7+8), NF
• 10) 5.7. Quantum Algorithm 3, Shor's Algorithm, Rieffel-Polak, Ch 8, PB

References

• J. Watrous, The Theory of Quantum Information, 2018, Chapters 1-3, 5, 8
• M. Wilde, Quantum Information Theory, 2013, Part IV
• E. Rieffel, W. Polak, Quantum Computing: A Gentle Introduction, 2011, Chapters 5, 7-9
• P. Kaye, R. Laflamme, M. Mosca, An Introduction to Quantum Computing, 2007, Chapters 4-8
• M. Nielsen, I. Chuang, Quantum Computation and Quantum Information

These books can also be found in the Semesterapparat of the seminar.