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Winter term 2022/23

Quantum computing

Quantum computing

Lecture: Quantum information theory (20110401)

  • Lecturer: Jens Eisert

  • On-site format: The lecture will be held on-site and in flesh and blood.

  • Feedback: You can evaluate the lecture and the tutorials here.

  • Place: 1.1.16 FB-Raum (Arnimallee 14)

  • Exam: The exam will take place in person on February 15, 2023, 8am.
  • Retake Exam: The retake exam will be on Monday April 17th 2023, 10am.
  • Results of the first exam: Results
  • Results of the repeat Exam: Results
    If you want to have a look at your graded exam, please email one of the tutors to agree on a time and date.
  • There will be another lecture/Q&A on Mon 13.2.

  • Date and time:

    Monday 8:15-10:00
    Wednesday 8:15-10:00

  • Tutorials: We offer four tutorials, by Alexander Townsend-Teague, Antonio Mele, Janek Denzler, Ansgar Burchards. Hand in the homework in the tray in front of room 1.3.14. 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.
  • Tutorial 1:

    - Time: Monday 10:15-12:00
    - Tutor: Ansgar Burchards (ansgarburchards(at)gmail.com)
    - Room: 1.1.53 Seminarraum E2

  • Tutorial 2:

    - Time: Tuesday 8:15-10:00
    - Tutor: Antonio Mele (antoniomele.p(at)gmail.com)
    - Room: 1.1.53 Seminarraum E2

  • Tutorial 3:

    - Time: Thursday 14:15-16:00
    - Tutor: Janek Denzler (j.denzler(at)fu-berlin.de)
    - Room: 1.1.53 Seminarraum E2

  • Tutorial 4:
    - Time: Thursday 12:15-14:00
    - Tutor: Alex Townsend-Teague (alex.townsend-teague(at)outlook.com)
    - Room: 1.1.53 Seminarraum E2

Problem sheets: The exercise sheets will be made available here:

     Problem sheet 0

     Problem sheet 1

     Problem Sheet 2

     Problem Sheet 3

     Problem Sheet 4

     Problem Sheet 5

     Problem Sheet 6

     Problem Sheet 7

     Problem Sheet 8

     Problem Sheet 9

     Problem Sheet 10

     Problem Sheet 11

     16.12: There is no problem sheet this week. Enjoy your holidays!

  • 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.

Seminar: Recent advances in tensor networks: from condensed matter physics to machine learning (20123011)

  • Lecturer: Jens Eisert
  • Date and time: Mondays 14:15-16:00
  • Room: 1.3.48 Seminarraum T3 (Arnimallee 14)
  • Tutors: Alexander Nietner will be the head tutor, but we will take turns and have several experts involved in this, to make this a collective and fun effort

    • Jan Naumann
    • Philipp Schmoll
    • Andreas Bauer
    • Steven Thomson and others

  • Topic of the research seminar:

    To understand the intricated behavior of quantum systems of many constituents is one of the main aims of modern physics. This is because they exhibit a wide range of interesting and exotic phenomena with no parallel in classical physics, including phase transitions at zero temperature, superconductivity, or topological effects. Yet, the very same complexity that is responsible for the rich physics is at the same time a road block in their study. The dimension of Hilbert space, so the configuration space of quantum mechanics, scales exponentially with the system size, rendering naive methods often inapplicable.

    This research seminar introduces to notions of tensor networks that are designed to capture natural properties of interacting quantum many-body systems and beyond. We will look at area laws for entanglement entropies, matrix product states, projected entangled pair states, notions of parent Hamiltonians and of topologically ordered systems. We will turn to numerical techniques to tackle interacting quantum many-body systems in and out of equilibrium. But also look at fresh applications in machine learning, where similar ideas increasingly move into the focus of attention.

    • During the first day, October 17, an overview will be given by Jens Eisert. 
    • Then we will distribute topics to students so that every participant can give a talk on an exciting topic in its own right:

      00    17.10.2022    Introduction
              24.10.2022    No session
      01    31.10.2022    Area law and entanglement entropies (Philipp Schmoll)       
      02    07.11.2022    Matrix product states, canonical and parent Hamiltonians (Shozab Qasim)
      03    14.11.2022    Time dependent tensor network methods (Alex Nietner)
      04    21.11.2022    Density matrix renormalization group (Jan Naumann)    
      05    28.11.2022    Time dependent variational principle (Frederik Wilde)     
      06    05.12.2022    Projected entangled pair states and simple update (Jan Naumann)     
      07    12.12.2022    Toric Code and topological order (Andreas Bauer)    

          19.12.2022    X-mas holidays           

              02.01.2023    No session
      08    09.01.2023    AKLT and SPT (Jonáš Fuksa)       
      09    16.01.2023    Fermionic tensors and MPS (Andreas Bauer)       
      10    23.01.2023    Multiscale entanglement renormalization (Shozab Qasim)       
      11    30.01.2023    MPS Sampling and machine learning (Frederik Wilde)         
      12    06.02.2023    Tensor networks and AD (Jan Naumann)         
      13    13.02.2023    Closing session           

Group seminar: Recent advances in quantum many-body theory (20010416)