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Quantum Information and Quantum Many-Body Theory (4EU+)
Provider: Faculty of Science

Activity no.: 7008-24-07-31There are no available seats
Enrollment deadline: 01/03/2024
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time07.03.2024, at: 08:00 - 28.06.2024, at: 16:00
Regular seats120
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJan Philip Solovej    E-mail address: solovej@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockSpring Block 4
Block noteThe course will consist of three phases: Phase 1: March 7-May 2, 2024 Online lectures (approximately one two hour lectures every other week, in total 7 lectures) Phase 2: May2-May 31, 2024: Students work on assignments which will be presented at a poster session at the physical meeting. Phase 3: June 24-June 28, 2024: Physical Master Class (Approximately 24 hours of lectures plus 5 hours exercises).
Exam requirementsThe students must through their active participation in the group work and the presentation at the master class show that they have acquired the necessary understanding and skills.
Exam formContinuous assessment
Exam detailsThe students will be evaluated on the group work, which will be presented during the master class
Exam aidsAll aids allowed
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures36.00
Preparation140.00
Exercises5.00
Project work20.00
Seminar5.00
Sum206.00
Content
We are currently witnessing the second quantum revolution and with it the advent of quantum technological devices for information processing purposes. Understanding these systems and their capabilities as well as developing robust algorithms for them, requires a fundamental understanding of complex quantum many-body systems as well as ways to characterize their properties efficiently. Within this course, we will help the participants to obtain proficiency in all of these aspects of quantum theory. A tentative list of topics include:

Entanglement/Non-Locality:
Lecture 1: States, Measurement, Tensor Product, Maximally Entangled State
Lecture 2: Tensor Product (contd.), Density Matrices, Reduced States, Entropy, Entanglement Entropy.
Lecture 3: Bell-inequalities, Bell’s Theorem, Non-local Games/Protocols.

Quantum Spin-System
Lecture 1: Spin Hamiltonians, Spin-½ Heisenberg Model, SU(2), Ground States, Ground State Energy
Lecture 2: Free Energy, Thermodynamic Limit, Thermal State
Lecture 3: Symmetry Breaking, Mermin-Wagner
Lecture 4: AKLT, Matrix Product States

For each of these topics, we will provide introductory lectures to get students acquainted with the topics before entering into the in-person phase, where experts and practitioners of these fields will give further insight.

Formel requirements
Expected minimal requirements: Linear algebra some elementary quantum knowledge, e.g., elementary quantum computing or elementary quantum mechanics.

Learning outcome
The goal is to provide the students with a blended learning approach to the course content on the mathematics of quantum theory with special emphasis on complex quantum many-body systems and quantum information theory. The main intended learning outcomes include an overview over the latest developments in those fields. Furthermore, the course will help the participants to develop competencies to engage in self-organized cross-university and interdisciplinary collaborations via online groupwork as well as to give an receive peer-feedback on results. Inviting external experts in the field will also give young researchers in the field the opportunity to grow their professional network considerably.

Literature
Research papers and lecture notes.

Target group
Master students and PhD students. The course is open to all interested students, also students outside the 4EU+ Alliance. Travel grants are, however, only available to students from within the alliance. Priority will be given to students from our partner universities, University of Milan, University of Warsaw, University of Geneva, Heidelberg University, Sorbonne University and Charles University.

Teaching and learning methods
The course will consist of three phases:
Phase 1: March 7-May 2, 2024 Online lectures (approximately one two hour lectures every other week, in total 7 lectures)
Phase 2: May2-May 31, 2024: Students work on assignments which will be presented at a poster session at the physical meeting.
Phase 3: June 24-June 28, 2024: Physical Master Class (Approximately 24 hours of lectures plus 5 hours exercises).

Remarks
Co-organiser: Albert Werner, werner@math.ku.dk
4EU+ contact person: Suzanne Andersen, suzanne@math.ku.dk

Centre for the Mathematics of Quantum Theory (QMATH) organizes the course together with the University of Milan and the University of Warsaw. The course is open to Danish and international PhD students and master students within MATH, Physics and Computer Science.

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