[1] Gottesman, D. (1997). Stabilizer codes and quantum error correction. California Institute of Technology.
[2] Lidar, D. A., & Brun, T. A. (Eds.). (2013). Quantum error correction. Cambridge university press.
Quantum error correction
| Language of instruction | angličtina, čeština |
|---|---|
| Code | 460-4161 |
| Abbreviation | KOCH |
| Course title | Quantum error correction |
| Coordinating department | Department of Computer Science |
| Course coordinator | Ryszard Stefan Kukulski, Ph.D. |
Summary
Upon completion of this course, students will be able to:
Knowledge
- Understand quantum error correction - Students will understand the principles of quantum error correction theory, including quantum noise models, quantum correction codes, and stabilization codes.
- Quantum Error Correction Criteria - Students will become familiar with the Knill-Laflamme conditions and quantum error correction criteria that enable efficient detection and correction of quantum errors.
- Stabilization Codes and CSS Codes - Students will gain an understanding of Calderbank-Shor-Steane (CSS) codes and other stabilization codes that form the basis for advanced quantum correction methods.
- Fault-tolerant quantum error correction - Students will understand fault-tolerant quantum computation methods, including codes designed for quantum processors with high noise.
- Probabilistic quantum codes - Students will learn new approaches to quantum error correction using probabilistic methods and learn how to analyze their performance.
Skills
- Quantum Noise Modeling - Students will be able to simulate and analyze quantum noise and quantum error models in quantum computing environments.
- Implementing Quantum Correction Codes - Students will learn to program and test quantum correction codes, including stabilization codes and CSS codes, in the Qiskit and Cirq frameworks.
- Optimizing Quantum Correction Protocols - Students will be able to analyze and design quantum correction schemes adapted to different types of quantum processors.
- Application of probabilistic codes in quantum error correction - Students will learn probabilistic coding and error detection methods used in state-of-the-art quantum error correction approaches.
- Analyzing the performance of quantum error correction methods - Students will be able to compare the effectiveness of different error correction codes and evaluate their robustness to noise.
Competencies
- Analytical Thinking - Students will gain the ability to critically analyze quantum correction methods and their impact on the reliability of quantum computations.
- Independent Quantum Noise Problem Solving - Students will be able to develop their own approaches to mitigate noise and quantum errors in practical scenarios.
- Working with modern quantum technologies - The course will provide students with hands-on experience implementing quantum correction codes on simulators and real quantum devices.
- Research readiness in quantum error correction - Students will gain a solid theoretical foundation and practical skills that will enable them to engage in scientific research in quantum information security.
This course will prepare students for a deeper understanding of quantum error correction methods and enable them to implement quantum error correction in practice on modern quantum systems.
Knowledge
- Understand quantum error correction - Students will understand the principles of quantum error correction theory, including quantum noise models, quantum correction codes, and stabilization codes.
- Quantum Error Correction Criteria - Students will become familiar with the Knill-Laflamme conditions and quantum error correction criteria that enable efficient detection and correction of quantum errors.
- Stabilization Codes and CSS Codes - Students will gain an understanding of Calderbank-Shor-Steane (CSS) codes and other stabilization codes that form the basis for advanced quantum correction methods.
- Fault-tolerant quantum error correction - Students will understand fault-tolerant quantum computation methods, including codes designed for quantum processors with high noise.
- Probabilistic quantum codes - Students will learn new approaches to quantum error correction using probabilistic methods and learn how to analyze their performance.
Skills
- Quantum Noise Modeling - Students will be able to simulate and analyze quantum noise and quantum error models in quantum computing environments.
- Implementing Quantum Correction Codes - Students will learn to program and test quantum correction codes, including stabilization codes and CSS codes, in the Qiskit and Cirq frameworks.
- Optimizing Quantum Correction Protocols - Students will be able to analyze and design quantum correction schemes adapted to different types of quantum processors.
- Application of probabilistic codes in quantum error correction - Students will learn probabilistic coding and error detection methods used in state-of-the-art quantum error correction approaches.
- Analyzing the performance of quantum error correction methods - Students will be able to compare the effectiveness of different error correction codes and evaluate their robustness to noise.
Competencies
- Analytical Thinking - Students will gain the ability to critically analyze quantum correction methods and their impact on the reliability of quantum computations.
- Independent Quantum Noise Problem Solving - Students will be able to develop their own approaches to mitigate noise and quantum errors in practical scenarios.
- Working with modern quantum technologies - The course will provide students with hands-on experience implementing quantum correction codes on simulators and real quantum devices.
- Research readiness in quantum error correction - Students will gain a solid theoretical foundation and practical skills that will enable them to engage in scientific research in quantum information security.
This course will prepare students for a deeper understanding of quantum error correction methods and enable them to implement quantum error correction in practice on modern quantum systems.
Literature
Advised literature
[1] Nielsen, M. A. (1998). Quantum Information Theory (Doctoral dissertation, The University of New Mexico).
[2] E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A, vol. 55, no. 2, p. 900, 1997
[3] R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Physical Review Letters, vol. 77, no. 1, p. 198, 1996.
[4] A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A, vol. 54, no. 2, p. 1098, 1996.
[5] A. M. Steane, “Simple quantum error-correcting codes,” Physical Review A, vol. 54, no. 6, p. 4741, 1996.
[6] A. M. Steane, “Error correcting codes in quantum theory,” Physical Review Letters, vol. 77, no. 5, p. 793, 1996.
[2] E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A, vol. 55, no. 2, p. 900, 1997
[3] R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Physical Review Letters, vol. 77, no. 1, p. 198, 1996.
[4] A. R. Calderbank and P. W. Shor, “Good quantum error-correcting codes exist,” Physical Review A, vol. 54, no. 2, p. 1098, 1996.
[5] A. M. Steane, “Simple quantum error-correcting codes,” Physical Review A, vol. 54, no. 6, p. 4741, 1996.
[6] A. M. Steane, “Error correcting codes in quantum theory,” Physical Review Letters, vol. 77, no. 5, p. 793, 1996.