| Study programme competencies |
| Code | Study programme competences |
| A13 | CON_13 Have knowledge of the physical and technical limitations of implementing quantum information processing systems: noise, decoherence, etc., as well as the mitigation or correction strategies that are proposed. |
| B13 | HD24 Actively participate in face-to-face activities in the classroom. |
| C1 | C1. Adequate oral and written expression in the official languages. |
| C2 | C2. Mastering oral and written expression in a foreign language. |
| C3 | C3. Using ICT in working contexts and lifelong learning. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Ability to understand the construction, analysis and applications of quantum error control codes in communication systems and quantum computers. Error control codes in communication systems and quantum computers. Knowledge of the main specific specific codes. | AJ13 |
BJ13 |
CJ1 CJ2 CJ3 |
| Contents |
| Topic | Sub-topic |
| Quantum errors | - Overview of quantum errors and their sources - Decoherence and noise in open quantum systems - Types of errors and error channel models - Digitization of quantum noise. Error operators |
| Fundamentals of quantum error correction error correction |
- From Classical to Quantum Error Correction - The three-qubit error correction code - The nine-qubit Shor code - Conditions of quantum error correction - The quantum Hamming limit |
| Construction of quantum codes | - Classical linear block codes - Calderbank-Shor-Steane Codes (CSS) |
| Stabilizer codes | - The stabilizer formalism - Measurement in the stabilizer formalism - Constructions of stabilizer codes - Quantum circuits for coding, decoding and correction |
| Topological stabilizing codes | - The Z2 chain complex - Surface codes on a torus: toric codes - Flat surface codes - Topological quantum error correction |
| Fault-tolerant quantum computing | - Fault tolerance in quantum computing - Fault-tolerant error correction - Fault-tolerant coded operations |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Problem solving | B13 | 5 | 27 | 32 |
| Oral presentation | C1 C2 C3 | 2 | 0 | 2 |
| Guest lecture / keynote speech | A13 | 18 | 23 | 41 |
| Personalized attention | 0 | 0 | 0 | |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||
| Methodologies |
| Methodologies | Description |
| Problem solving | Typical quantum error code design and analysis problems will be solved, in order to learn how to use the methods seen in the lectures. |
| Oral presentation | An oral presentation of evaluation work will be made |
| Guest lecture / keynote speech | The main elements of quantum error codes, their applications and limitations will be presented. limitations. |
| Personalized attention |
|
|
| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Problem solving | B13 | Resolution of exercises in an autonomous and individual way, delivery in writing. Two sets with a value of 30% each. | 60 |
| Oral presentation | C1 C2 C3 | Submission of a roll-up work by the student | 40 |
| Assessment comments | |||
| Sources of information |
| Basic |
M. A. Nielsen, I. L. Chuang (2010). Quantum Computation and Quantum Information. Cambridge University Press
Ivan B. Djordevic (2021). Quantum Information Processing, Quantum Computing. and Quantum Error Correction. Academic Press |
|
|
|
| Complementary |
Giuliano Gadioli La Guardia (2020). Quantum Error Correction. Springer
D. A. Lidar, T. A. Brun (2013). Quantum Error Correction. Cambridge University Press
Frank Gaitan (2013). Quantum Error Correction and Fault Tolerant Quantum Computing. Taylor & Francis |
|
|
| Recommendations | |||
| Subjects that it is recommended to have taken before | |||
|
| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus |
| Other comments | |