NAT3045: Quantum Error Correction and Fault Tolerance (MPQ/TUM)
NAT3045: Quantum Error Correction and Fault Tolerance (MPQ/TUM)
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. The following concepts and methods will be taught in this course:
1. Description of noisy systems and dynamics.
2. Fundamental of error correction - detectability and correctability of errors.
3. Strategies to design error correcting codes.
4. Fault tolerance in quantum computation.
References
Nielson and Chuang, Quantum Computation and Quantum Information.
Daniel Gottesman, Surviving as a quantum computer in a classical world (U. Maryland).
John Wright, Quantum coding theory (lecture notes, U. Berkeley).
Venue
MPQ, B2.46 (Theory Seminar Room).
Wednesday/Thursday, 15:00 - 16:30 (Lectures)
Monday/Tuesday, 16:00 - 17:00 (Exercises)
Zoom for Lectures (only with previous permission): https://eu02web.zoom-x.de/j/3598685293
Lectures
Prereq: Linear Algebra Basics
Notes (Taken from Ignacio's QI course from 2021, written by Sirui Lu)
Introduction, States, Distance between states
Notes, In-class slides (Lecture 1, Lecture 2).
Channels, Distance between channels
Notes, In-class slides (Lecture 3)
Shor's 9 qubit code, Knill Laflamme conditions
Notes, In-class slides (Lecture 4, Lecture 5).
Classical Linear codes, Stabilizer formalism
Notes, In-class slides (Lecture 6, Lecture 7).
Stabilizer formalism, CSS codes
Notes, In-class slides (Lecture 8, Lecture 9).
Classical GF(4) codes
Notes, In-class slides (Lecture 10)
Stabilizer codes from GF(4) codes, Concatenated codes
Notes, In-class slides (Lecture 11, Lecture 12)
Toric code
Notes, In-class slides (Lecture 13)
Planar codes, Fault tolerance
Notes, In-class slides (Lecture 14, Lecture 15)
Fault tolerance, Threshold theorem
Notes, In-class slides (Lecture 16, Lecture 17)
Clifford Unitaries, Universal computation with magic states
Notes, In-class slides (Lecture 18, Lecture 19)
Transversal gates,Fault tolerant error correction and state preparation
Notes, In-class slides (Lecture 20, Lecture 21, Lecture 22)
Tutorials
Tutorial 1: Problems, Solutions
Tutorial 2: Problems, Solutions
Tutorial 3: Problems, Solutions
Tutorial 4: Problems, Solutions
Tutorial 5: Problems, Solutions
Tutorial 6: Problems, Solutions
Tutorial 7: Problems, Solutions
Tutorial 8: Problems, Solutions
Tutorial 9: Problems, Solutions
Practice Final exam: Problems, Solutions