Degree | Type | Year | Semester |
---|---|---|---|
2503740 Computational Mathematics and Data Analytics | OB | 3 | 2 |
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.
The course is an introduction to the current view of quantum mechanics and its paradigms. With the technology we have today, many of the most paradoxical quantum effects have ceased to be an academic curiosity and have become very powerful resources that will be the basis of many amazing practical applications in the not too distant future. This course introduces some of them: teleportation, dense coding, Bell inequalities, cryptography, quantum computing, and more. The course is aimed at mathematicians with a strong vocation for data analysis, therefore, it will be necessary to provide essential physical training with an introduction to the fundamentals of quantum mechanics, classical cryptography and computing. The basic concepts of classical information theory are also reviewed. The course has also a computational component: numerical simulations of various phenomena will be done and prototypes of quantum computers will be used to program various protocols. The aim of the subject is not only to give a description of the advances that have taken place in quantum information, but also to provide the student with the basic tools to be able to continue his postgraduate training in this field, if this is their interest.
0. Review of linear algebra and complex numbers
1. Elements of quantum theory
2. Generalized measurements
3. Quantum cryptography
4. Entanglement
5. Quantum information processing
6. Quantum computation
7. Quantum information theory
The course is structured into theory lectures, exercises lectures, and continuous assessment activities.
The theory lectures are in keynote/powerpoint presentation format. There will be some classes/seminars on some course topics that will be presented by researchers in the field of Quantum Information. These seminars will generally be in English.
The exercises lectures are usually made on the blackboard and consist of solving the most significant problems, the statements of which are made available to students through the Virtual Campus.
There will be 6 deliveries. The objective is to deepen, consolidate and extend the students' knowledge about aspects and results explained throughout the course. Thus, the deliveries may contain problems and issues of greater complexity and extension. These should be delivered periodically throughout the course and on previously agreed dates. The aim of these activities is to encourage autonomous work.
All the material: lists of problems, additional teaching material, detailed resolution of some exercises, as well as news related to the course, are made available to the 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.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Seminars of specific topics | 10 | 0.4 | 8 |
Theoretical lessons | 28 | 1.12 | 8, 2, 3 |
Type: Supervised | |||
Projects with online quantum computers | 12 | 0.48 | 9, 8, 2 |
Type: Autonomous | |||
Homework exercises | 36 | 1.44 | 1, 9, 8, 4, 3 |
Numerical resolutions of excercises | 36 | 1.44 | 1, 9, 8, 6, 3 |
Study of the theoretical background | 20 | 0.8 | 1, 8, 2, 6, 3 |
The evaluation consists of the following activities
Students who have been assessed in at least 66% of the total activities may take the rehearsal tests for activities 1 and 2. A student who has only completed activities 3, 4 will be considered non-assessable.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Assessment of computational aspects | 20 | 1.5 | 0.06 | 8, 4, 7, 5, 3 |
Attendance and participation in specialized seminars | 5 | 0 | 0 | 1, 8, 4, 2, 7, 5, 3 |
Delivery of exercises (autonomous work) | 30 | 0 | 0 | 1, 9, 8, 4, 5, 6, 3 |
Evaluation exam of theoretical concepts | 45 | 2.5 | 0.1 | 1, 8, 4, 2 |
Retaken exam of theoretical and computational aspects | 65 | 4 | 0.16 | 1, 8, 4, 2, 3 |
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
• 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
IBM quantum composer