Linear Algebra

- To understand the basic principles of the quantum formalism and their mathematical formulation in terms of linear algebra and matrix theory. To know how to apply them in the context of computation and of basic protocols of information processing. - To understand the formulation of a quantum algorithm in the circuit model. - To be familiar with the main quantum gates and the basic rudiments for their concatenation to give rise to universal computation. - To understand the formulation of two basic quantum algorithms (Grover's and Shor's) and the computational advantage they provide with respect to classical models of computation for the problems of database search and factorization. According to the master's documentation the students will obtain in this course the following basic, general and specific competences (see additional documentation in the application "Reina"). CB6, CB7, CB8, CB9, CB10 CG2, CG4, CG5, CG6, CG7 CE1, CE2, CE3, CE4, CE6, CE8, CE11, CE12, CE15

1. Quantum theory 1.1 Matrix theory notions and Dirac notation 1.2 The axioms of quantum mechanics 1.3 Some toy quantum algorithms 2. The circuit model for quantum computation 2.1 Quantum gates 2.2 Universality 3. Quantum algorithms 3.1 Database search: Grover's algorithm 3.2 Factorization: Quantum Fourier transform and Shor's algorithm

Learning activities: - Theoretical lessons. - Practical lessons. - Office hours. - Group work. - Individual student work. Methodology: - In class presentations by the teacher with computer and audiovisual support, in which the main concepts of the course are developed. Bibliography is provided to complement the students' learning. - Critical reading of texts recommended by the course teacher to expand and consolidate knowledge of the course and to complete and deepen the understanding of those topics in which the students are more interested. - Resolution of problems raised by the teacher individually or in a group. - Elaboration of works individually or in group. Office hours: An office-hours schedule of 2 hours per week will be established so that the students can ask questions and discuss with the teacher the content of the theoretical lessons, the assigned problems and the works to be elaborated.