Lecture: Quantum information theory (20110401)

• Lecturer: Jens Eisert
  
  
• On-site format: The lecture will be held on-site.
  
  
• Place: 0.1.01 Hörsaal B (Arnimallee 14)
• Date and time:
  Tuesday 8:15-10:00
  Thursday 8:15-10:00

• Tutorials: We offer three tutorials. Hand in the homework in the tray in front of room 0.1.01. The deadline for the submission of the exercises is agreed upon with the tutor of each tutorial. You can also mark the questions you would like to have corrected and marked in detail.
  
  
  • Monday 14-16, room 1.1.53
  • Monday 16-18, room 1.4.31
  • Tuesday 16-18, room 1.1.16
  The tutors are Clara Wassner, Simon Cichy, Yifan Tang, Jacopo Rizzo. We have decided to hold one tutorial on 22.04 16-18 in room 1.1.16 introducing regulations and answering questions. We will discuss exercise sheets from the week starting on 28.04.
  
  
• Problem sheets: The exercise sheets will be made available here.
  
  
  • Problem sheet 0.
• 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 a comprehensive 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. Introduction
  1.1 Some introductory words
  1.2 Quantum information: A new kind of information?
  
  2. Elements of quantum (information) theory
  2.1 Quantum states and observables
  2.2 Unitary time evolution
  2.3 Composite quantum systems
  
  3. Two possible machines
  3.1 Quantum teleportation
  3.2 Dense coding
  
  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 Pure state entanglement
  5.2 Mixed state entanglement
  
  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. Elements of quantum computing
  8.1 Why quantum computing?
  8.2 From classical to quantum computing
  8.3 Gottesman-Knill and Solovay-Kitaev theorems
  
  9. Quantum algorithms
  9.1 Deutsch and Deutsch-Jozsa algorithm
  9.2 Grover’s database search algorithm
  9.3 Exponential speed-up in Shor’s factoring algorithm
  9.4 Some thoughts on quantum algorithmic primitives
  
  10. Quantum computational models
  10.1 Adiabatic quantum computing
  10.2 Measurement-based quantum computing
  10.3 Further models of quantum computing
  
  11. Notions of computational complexity
  11.1 Cost functions
  11.2 Complexity classes
  
  12. Non-universal quantum computers
  12.1 Quantum simulators
  12.2 Variational quantum computers
  12.3 Final thoughts
  
  13. Quantum error correction
  13.1 Peres Code
  13.2 Shor code
  13.3 Elements of a theory of quantum error correction
  13.4 Stabilizer codes and the toric code
  
  
• Literature: See the script.

• Lecturer: Jens Eisert
• Date and time: Contact the lecturer.