Lectures:
1. From classical to quantum error correction. We will showhow ideas from classical coding theory (like parity checks) carry over to quantum, but with added challenges like no-cloning and superposition
2. Noise models. We will describes how quantum information degrades (bit-flip, phase-flip, depolarizing noise).
3. Noise measure and description of quantum silarity measures (fidelity, trace distance, diamond norm).
4. Quantum Operations and Kraus Representations of Error Channels
5-6. Quantum error correction criteria. The topic is concetrated on the Knill-Laflamme conditions.
7. Introduction to stabilizer codes and application of Group Theory to QEC.
8. Examples of error correction codes and stabilizer codes.
9. Concatinating quantum error correction codes
10. QEC based on classical codes - CSS codes.
11. Introduction to probabilistic quantum error correction.
12. Introduction to fault-tolerant quantum error correction.
Seminars:
1-2. Review of classical parity checks using bit strings. Introduction to quantum bit representation and the no-cloning theorem.
Description of a single qubit in superposition and demonstrate error introduction. Analyzis of Shor's code.
3-4. Problem solving on noise modeling on quantum architecture and quantum channels description.
5-6. Modelling error correction codes and stabilizer codes to quantum architecture.
7-8. Implementation of 3-qubit bit-flip, 5-qubit perfect, and 7-qubit Steane code.
Measurement of code performance under different noise channels. Analyzis of trade-offs between
error suppression and circuit depth.
9-10. Exercises concerining construction of CSS codes using classical linear codes, encoding, noise analyzis and
decoding operations.
11-12. Problem solving on the topic: analysis of quantum fault-tolerant error correction codes.
1. From classical to quantum error correction. We will showhow ideas from classical coding theory (like parity checks) carry over to quantum, but with added challenges like no-cloning and superposition
2. Noise models. We will describes how quantum information degrades (bit-flip, phase-flip, depolarizing noise).
3. Noise measure and description of quantum silarity measures (fidelity, trace distance, diamond norm).
4. Quantum Operations and Kraus Representations of Error Channels
5-6. Quantum error correction criteria. The topic is concetrated on the Knill-Laflamme conditions.
7. Introduction to stabilizer codes and application of Group Theory to QEC.
8. Examples of error correction codes and stabilizer codes.
9. Concatinating quantum error correction codes
10. QEC based on classical codes - CSS codes.
11. Introduction to probabilistic quantum error correction.
12. Introduction to fault-tolerant quantum error correction.
Seminars:
1-2. Review of classical parity checks using bit strings. Introduction to quantum bit representation and the no-cloning theorem.
Description of a single qubit in superposition and demonstrate error introduction. Analyzis of Shor's code.
3-4. Problem solving on noise modeling on quantum architecture and quantum channels description.
5-6. Modelling error correction codes and stabilizer codes to quantum architecture.
7-8. Implementation of 3-qubit bit-flip, 5-qubit perfect, and 7-qubit Steane code.
Measurement of code performance under different noise channels. Analyzis of trade-offs between
error suppression and circuit depth.
9-10. Exercises concerining construction of CSS codes using classical linear codes, encoding, noise analyzis and
decoding operations.
11-12. Problem solving on the topic: analysis of quantum fault-tolerant error correction codes.