Introduction to Topological Quantum Computation
This course provides an introduction to topological quantum physics for students with little background in topology. It builds intuition for topological invariants, manifolds, and fundamental groups, then moves to anyons, braid groups, and topological quantum field theory (TQFT). The central model, Kitaev's toric code, is used to illustrate topological order, degenerate ground states, and fault-tolerant quantum memory. Finally, non-Abelian anyons and braiding operations are introduced as the basis for topological quantum computation.
All concepts are presented through physical examples and diagrams; category theory is deliberately avoided.
All concepts are presented through physical examples and diagrams; category theory is deliberately avoided.
Lecturer
Date
21st September ~ 21st December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 10:40 - 12:15 | A3-1-301 | Zoom 15 | 204 323 0165 | BIMSA |
| Wednesday | 13:30 - 15:05 | A3-1-301 | Zoom 15 | 204 323 0165 | BIMSA |
Prerequisite
Basic quantum physics
Syllabus
1. Topology basics – invariants, manifolds, fundamental groups (intuitive level)
2. Particle statistics in 2+1D – braid groups, Abelian vs. non-Abelian anyons, fractional statistics
3. TQFT essentials – metric-independence, Chern–Simons theory, cobordism ideas (no category language)
4. Toric code – lattice model, vertex/plaquette operators, anyonic excitations (e and m particles), ground‑state degeneracy and topological protection
5. Topological quantum computation – encoding qubits in fusion spaces, braiding as unitary gates, fault tolerance, and brief outlook on physical realizations
2. Particle statistics in 2+1D – braid groups, Abelian vs. non-Abelian anyons, fractional statistics
3. TQFT essentials – metric-independence, Chern–Simons theory, cobordism ideas (no category language)
4. Toric code – lattice model, vertex/plaquette operators, anyonic excitations (e and m particles), ground‑state degeneracy and topological protection
5. Topological quantum computation – encoding qubits in fusion spaces, braiding as unitary gates, fault tolerance, and brief outlook on physical realizations
Reference
1.Topological Quantum: Lecture Notes and Proto-Book, Steven H. Simon
2.Introduction to Topological Quantum Computation, JIANNIS K . PACHOS
2.Introduction to Topological Quantum Computation, JIANNIS K . PACHOS
Audience
Undergraduate
, Advanced Undergraduate
Video Public
Yes
Notes Public
Yes
Language
Chinese
Lecturer Intro
Hao Dai received her Ph.D. from the Chinese Academy of Sciences in 2020. Following that, from 2020 to 2023, she worked as a postdoctoral fellow at Tsinghua University. In 2023, she has become an Assistant Professor at BIMSA. Her primary research interests encompass the domains of quantum information and computation.