Quantum Information
Code: 104408 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| Computational Mathematics and Data Analytics | OB | 3 |
Contact
- Name:
- Alessio Celi
- Email:
- alessio.celi@uab.cat
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
It is advisable to have a good command of algebra, especially of vector spaces and, preferably, of complex Euclidean spaces. It is advisable also to be familiar with the basic concepts of classical information, as delivered in the course “Teoria de la informació” of the first semester.
Objectives and Contextualisation
The course is an introduction to the current perspective of quantum mechanics and its paradigms. With today’s technology, many of the most paradoxical quantum effects are no longer just academic curiosities — they have become powerful resources forming the foundation of quantum technologies, which have numerous and surprising practical applications. Some of these applications will be presented in this course, particularly quantum cryptography and quantum computing.
The course is aimed at mathematics students with a strong interest in computer science and data analysis. Therefore, it will be necessary to provide the essential physical background through an introduction to the fundamentals of quantum mechanics, classical cryptography, and classical computing. Some basic concepts from classical information theory will also be reviewed.
The goal of the course is not only to provide an overview of recent advances in quantum information but also to equip students with the basic tools they need to pursue postgraduate studies in this field, should they wish to do so.
Learning Outcomes
- CM30 (Competence) Explain the hypotheses of quantum physics, applying them to information processing problems.
- KM26 (Knowledge) Identify the impact of quantum technologies on computing, cryptography and other communication protocols in the environment.
- SM32 (Skill) Apply the concept of quantum measurement to optimisation problems in simple quantum discrimination, estimation and communication problems.
Content
0. Review of linear algebra and complex numbers
- Real vector spaces
- Complex numbers
- Complex vector spaces
1. Elements of quantum theory
- Basic principles
- Mixed states
- Unitary operators
- Qubits
- Entangled states
- von Neumann measurement
2. Quantum cryptography
- Information security
- Quantum communications
- Quantum key Distribution
3. Generalized Measurements and Entanglement
-
POVM vs. von Neumann -
Bell states and non-locality
4. Quantum information processing
- Digital electronics
- Quantum gates
- Quantum circuits
5. Quantum computation
- Elements of computer science
- Principles of quantum computation
- Deutsch-Jozsa algorithm and other examples
Some of these arguments will be dealt with in the form of seminars
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Seminars of specific topics | 10 | 0.4 | CM30, KM26, SM32, CM30 |
| Theoretical lessons | 28 | 1.12 | CM30, KM26, CM30 |
| Type: Supervised | |||
| Projects with online quantum computers | 12 | 0.48 | |
| Type: Autonomous | |||
| Homework exercises | 36 | 1.44 | CM30, KM26, SM32, CM30 |
| Numerical resolutions of excercises | 36 | 1.44 | SM32, SM32 |
| Study of the theoretical background | 20 | 0.8 | CM30, KM26, CM30 |
The course is structured around theoretical classes, problem-solving sessions, and continuous assessment activities.
The theoretical classes are delivered on the blackboard. Some lectures or seminars on specific course topics will generally be given in English and may be presented either on the blackboard or as PowerPoint presentations.
The problem-solving sessions are usually conducted on the blackboard and consist of solving the most significant exercises, whose statements will be made available to students through the Virtual Campus.
There will be three assignments. Their objective is to deepen, consolidate, and expand students’ knowledge of the topics and results covered throughout the course. These assignments may include problems and questions of greater complexity and scope. They must be submitted periodically during the course and on pre-agreed dates. These activities aim to encourage independent work.
All materials — problem sets, additional teaching resources, detailed solutions to selected exercises, and announcements related to the course — will be made available to students through the Virtual Campus.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Assessment of computational aspects | 20 | 1.5 | 0.06 | SM32 |
| Attendance and participation in specialized seminars | 5 | 0 | 0 | |
| Delivery of exercises (autonomous work) | 30 | 0 | 0 | CM30, KM26, SM32 |
| Evaluation exam of theoretical concepts | 45 | 2.5 | 0.1 | CM30, KM26 |
| Retaken exam of theoretical and computational aspects | 65 | 4 | 0.16 | CM30, KM26, SM32 |
The assessment is structured to favor students who follow regularly and deliver assignments without penalizing students who opt for the single assessment. The 3 deliveries correspond to the arguments developed during the theory classes and worked on in the problem classes. The grade of the deliveries will be: LL= (LL1+LL2+LL3)/3. There will be a final exam (and if necessary a supplementary exam) solely on the arguments discussed in the theory and problem classes.
The final assessment will consist of the performance of the exam (or the supplementary exam) Ex and the LL assignments according to the formula: 0.4 * LL + Ex (10 - 0.4* LL)/10 This formula does not penalize those who take the final exam alone but favors those who do the assignments.
Only the students who did the exam can do the supplementary exam.
Bibliography
The students wil have access to the lessons in pdf format and copies of the Keynote / Powerpoint of the course. For further information, the following bibliography is advisable:
Theory
- S.M. Barnett, Quatum Information, Oxford University Press, 2009.
- J. Preskill. Lectures notes on Quantum Computation. Es pot obtenir gratuïtament a la direcció: http://www.theory.caltech.edu/people/preskill/ph229.
- M.A. Nielsen; S.L. Chuang. Quantum Computation and Quantum Information. Cambridge Univ. Press, Cambridge 2000.
• A. Peres. Quantum Theory: Concepts and Methods. Kluwer, Dordrecht 1995.
• D. Applebaum. Probability and Information. Cambridge Univ. Press, Cambridge 1996.
• D. Boumeester; A. Eckert; A. Zeilinger. The Physiscs of Quantum Information. Springer 2000.
• D. Heiss. Fundamentals of Quantum Information. Springer 2002.
Problems
- Steeb, Willi-Hans, and Yorick Hardy. Problems and solutions in quantum computing and quantum information. World Scientific Publishing Company, 2018.
- C. P. Williams; S. Clearwater. Exploration in Quantum Computing. Springer 1998
Software
IBM quantum composer
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PLAB) Practical laboratories | 1 | Catalan | second semester | morning-mixed |
| (SEM) Seminars | 1 | Catalan | second semester | morning-mixed |
| (TE) Theory | 1 | Catalan | second semester | morning-mixed |