NAT3045 (2026): Quantum Error Correction and Fault Tolerance

NAT3045: Quantum Error Correction and Fault Tolerance (MPQ/TUM, Summer 2026)

Course Description:

Introduction to the theory of quantum error correction and fault tolerance, especially in the context of how these techniques enable quantum technologies with noisy devices. There will be an emphasis of both fundamentals of designing error correction codes and protocols, as well as their applications to quantum computation.

Course Outline

Part 1: Error correction fundamentals

Shor’s 9-qubit code, constructing encoders, decoders. Entropy removal.
Knill-Laflamme conditions for correctability and detectability of errors, implications.
Classical linear codes and Stabiliser Formalism.

Part 2: Constructing error correcting codes

CSS codes.
GF(4) codes, Quantum Hamming codes.
Topological codes - Toric code, Surface codes with boundaries, defects.
Product codes and Hypergraph product codes, Introduction to quantum LDPC codes.

Part 3: Encoded computation and Fault tolerance

Fault tolerant gates, encoder and decoders.
Logical operations in planar codes, lattice surgery.
Threshold theorem.
Recent implementations of fault tolerant computation.

References

Daniel Gottesman, Surviving as a quantum computer in a classical world (U. Maryland).

Nielson and Chuang, Quantum Computation and Quantum Information.

John Wright, Quantum coding theory (lecture notes, U. Berkeley).

When and where
Lectures: Monday/Thursday, 15:00 - 16:30 @ MPQ, Herbert Walther Lecture Hall.
Exercises: Tuesday/Wednesday, 16:00 - 17:00 @ MPQ, Theory seminar room (B2.46)
Zoom for Lectures (only with previous permission): https://eu02web.zoom-x.de/j/3598685293