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Lecture: Quantum information theory (20110401)
- Lecturer: Jens Eisert
- On-site format: The lecture will be held on-site.
- Rating: Please rate the course here.
- Times: Mon 16:15-18:00, Wed 16:15-18:00
Note that the course will start on October 23, 2023
- Place: 1.3.21 Seminarraum T1 (Arnimallee 14)
- Tutorials: We offer three tutorials. If a Monday tutorial does not take place, the students are kindly asked to distribute themselves among the other tutorials at the same time. For Tuesday tutorials, a replacement will be provided. Submission of the exercise sheets on paper is preferred, digital submissions can be made via e-mail to all tutors (see below).
- Tutors: Elies Gil-Fuster (e.gilfuster@fu-berlin.de), Johannes Jakob Meyer (jjmeyer@zedat.fu-berlin.de), Matthias Caro (matthias.caro@fu-berlin.de), Simon Cichy (simon.cichy@fu-berlin.de)
- Tutorial 1:
- Time: Monday 10:15-12:00
- Room: 1.3.21 Seminarraum T1
- Tutorial 2:
- Time: Monday 10:15-12:00
- Room: 1.3.48 Seminarraum T3 (Arnimallee 14)
- Tutorial 3:
- Time: Tuesday 8:15-10:00
- Room: Seminarraum E3 (Arnimallee 14)
- Problem sheets: The exercise sheets will be made available here:
- Exam: The exam will take place in person in Lecture Hall A during the regular timeslot of the lecture on the 14th of February. The exam starts at 16:15h, please be there at 16:00h. No notes or auxiliary materials may be used.
- Exam grades (password protected, we send you the password via email). You can come see your exam on Monday, February 26th, between 11h and 12:30h, in room 1.3.12. If you want to see the exam but this slot does not suit you, please write the tutors an email proposing a viewing time before Friday, March 1st.
- Retake exam: The retake exam will take place in person in Lecture Hall A on the 11th of April. The retake exam starts at 14:15h, please be there at 14:00h. No notes or auxiliary materials may be used.
- Retake exam grades (password protected, we send you the password via email). You can come see your exam on Wednesday, May 22nd, between 15h and 16h, in room 1.3.12. If you want to see the exam but this slot does not suit you, please write the tutors an email proposing a viewing time before Friday, May 24th.
- 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.
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