Summer term 2018

Summer term 2018:

Lecture: Quantum information theory
  • Lecturer: Jens Eisert
  • Date and time: Tuesday 8:00-10:00, Thursday 8:00-10:00

    We have tried to find a better time for the lecture later at the day, but this has turned out to be infeasible. The first lecture will hence be FRIDAY, April 20, 10:00-12:00 ("Hoersaal A"). From THEN on, we will follow the anticipated Tuesday and Thursday schedule. Apologies for the confusion.

  • Room: "Hoersaal B"
  • Tutors: Ingo Roth, Dominik Hangleiter
  • The exercise sheets will be made available here.
  • Exam: There will be an exam at the end of the course.
  • Re-take Exam: There will also be a re-take exam.
  • Topic of the lecture:

    This course provides an overview of an exciting emerging field of research, that of quantum information theory. The field is concerned with the observation that single quantum systems used as elementary carriers of information allows for entirely new modes of quantum information processing and communication, quite radically different from their classical counterparts. Quantum key distribution suggests to communicate in a fashion, secure from any eavesdropping by illegitimate users. Quantum simulators can outperform classical supercomputers in simulation tasks. The anticipated - but now rapidly developing - devices of quantum computers can solve not all, but some delicate computational problems that are intractable on classical supercomputers. This course will give an overview over these developments. At the heart of the course will be method development, setting the foundations in the field, building upon basic quantum theory. We will also make the point that quantum information is not only about information processing, but a mindset that can be used to tackle problems in other fields, most importantly in consensed matter research, with which quantum information is much intertwined for good reasons.

  • Content:

    1. Impossible machines

    2. A crash course on quantum theory
    2.1 Quantum states
    2.2 Postulates of quantum mechanics
    2.3 Composite quantum systems
    2.4 Schmidt decomposition

    3. Possible machines
    3.1 Dense coding
    3.2 Teleportation

    4. Quantum channels and operations
    4.1 Complete positivity
    4.2 Kraus theorem
    4.3 Local operations and classical communication

    5. Entanglement theory
    5.1 Criteria for entanglement
    5.2 Pure state entanglement and the magic of typical sequences
    5.3 Entanglement witnesses
    5.4 Entanglement measures
    5.5 Separability criteria

    6. Quantum Shannon theory
    6.1 Capacities as optimal rates
    6.2 A glimpse at quantum Shannon theory

    7. Quantum key distribution
    7.1 BB84 scheme
    7.2 Entanglement-based schemes
    7.3 Words on quantum technologies

    8. Quantum computing
    8.1 The idea of a quantum computer
    8.2 Quantum gates and universality
    8.3 Solovay Kitaev theorem
    8.4 Clifford gates
    8.5 Deutsch-Jozsa algorithm
    8.6 Shor algorithm
    8.7 Models for quantum computing

    9. Quantum error correction
    9.1 The sentiment of fighting noise with noise
    9.2 Topological codes
    9.3 Fault tolerance
    9.4 Majorana fermions and codes

    10. Quantum simulation
    10.1 Elements of quantum simulation
    10.2 Quantum advantages

    11. Intersection of quantum information and condensed-matter physics
    11.1 Quantum lattice models
    11.2 Area laws
    11.3 Tensor networks
    11.4 Topological order

  • Literature: M. A. Nielsen, I Chuang, "Quantum Computation and Quantum Information", Cambridge University Press.