QC809: Quantum Computation and Phases of Quantum Matter
The Study Board for Science
Teaching language: English
EKA: N310093102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master
STADS ID (UVA): N310093101
ECTS value: 10
Date of Approval: 22-10-2025
Duration: 1 semester
Version: Archive
Entry requirements
Academic preconditions
Students are expected to have prior knowledge of the postulates of quantum mechanics and their application to quantum computing, including familiarity with quantum circuits, universal gate sets, and basic quantum algorithms (e.g., from QC801 and QC802).
Course introduction
This course explores the connections between quantum condensed matter physics and quantum computation, focusing on how various phases of quantum matter—particularly topological phases—can serve as resources for quantum computing. Students will learn about the topological classification of gapped quantum phases of matter, with special emphasis on phases that are useful for quantum information processing.
The course will examine specific examples of topological phases, including:
- Symmetry-protected topological (SPT) phases, whose ground states support measurement-based quantum computing
- Topologically ordered phases, like the toric code, which are foundational to topological quantum error correction
Students will also study quantum dualities—non-trivial correspondences between seemingly distinct quantum systems—and how these can be leveraged to develop algorithms for efficiently preparing resource states for computation.
Beginning with seminal work in topological quantum computing and topological phases of matter, the course will bring students to the forefront of current research in the field.
Expected learning outcome
By the end of the course, students should be able to
- Demonstrate a comprehensive understanding of core terminology and concepts in topological quantum matter.
- Explain and apply foundational results and principles related to topological phases of matter.
- Critically engage with current literature in the fields of topological phases of matter and topological quantum computing.
Content
Topics covered in this course will include:
- Topological Classification: An introduction to the classification of gapped quantum phases across various spatial dimensions (d+1 dimensions, with d = 1, 2, 3), incorporating both algebraic topology and quantum field theory methods
- Quantum Lattice Models: Analysis of quantum lattice models representing topological phases, including their ground states, order parameters, and topological operators
- Stabilizer Codes from Lattice Models: Development of stabilizer quantum codes derived from quantum lattice models
- Generalized Symmetries and Dualities: Exploration of generalized gaugings and symmetries, including their interpretation as dualities, and investigation of their algorithmic implementation on quantum circuits
Literature
See itslearning for syllabus lists and additional literature references.
It is expected that the following literature will be used:
- Steve Simon: Topological Quantum
- Lecture Notes on Quantum Information by John Preskill
- Anyons in an exactly solved model and beyond – Aleksei Kitaev
Examination regulations
Exam element a)
Timing
Spring/June
Tests
Project with oral exam
EKA
N310093102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Duration
30 minutes, no preparation
Examination aids
All common aids allowed
ECTS value
10
Indicative number of lessons
Teaching Method
Planned lessons:
Total number of planned lessons: 60
Hereof:
Common lessons in classroom/auditorium: 60
Generally, in each week there will be 2 hours of ordinary lectures, where the lecturer covers the syllabus, and 2 hours of exercise sessions, where the students will present homework solutions to problems announced during the course.
Other planned teaching activities:
The students will work on the weekly homework problems, and on the exam project.
Hereof:
Common lessons in classroom/auditorium: 60
Generally, in each week there will be 2 hours of ordinary lectures, where the lecturer covers the syllabus, and 2 hours of exercise sessions, where the students will present homework solutions to problems announced during the course.
Other planned teaching activities:
The students will work on the weekly homework problems, and on the exam project.
Teacher responsible
| Name | Department | |
|---|---|---|
| Apoorv Tiwari | apoorvtiwari@imada.sdu.dk | Institut for Matematik og Datalogi |
| William Elbæk Mistegård | wem@imada.sdu.dk | Institut for Matematik og Datalogi |
Timetable
Administrative Unit
Team at Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.