Information and Quantum Computation

Instance: 2024/2025 - 1S

Cycles of Study/Courses

Teaching language

Objectives

This curricular unit introduces basic concepts of

Quantum Mechanics in the context of systems with

discrete Hilbert spaces, using the language of

quantum information. Students will know how to apply

fundamental notions of the quantum description of

reality. The elementary results of quantum

information theory will be exposed, such as the

non-cloning theorem, quantum key distribution,

entanglement, dense coding and Bell inequalities.

Students will be able to understand the basic

functioning of a quantum computer and why quantum

computing may have an advantage over classical

computing. Some of the most common quantum

algorithms will be introduced, such as the Bernstein-

Vazirani, Simon de Grover and Shor algorithms.

Students will also learn to program quantum

computations in suitable languages. Finally,

they will have the opportunity to experimentally

observe quantum information effects through a set of

laboratory demonstrations.

Learning outcomes and competences

Not assuming students' prior knowledge in Quantum Mechanics, and with limited training in Physics, students will be exposed to the fundamental principles of the theory from the perspective of quantum information. The introduction of simple effects in quantum information should contribute to the solidification of the understanding of quantum theory itself. The exercises solved in theoretical-practical classes, as well as the assessed homework, of a conceptual, analytical and computational nature, will be an important tool for learning. Finally, experimental demonstrations should help students to better understand the content taught, developing physical intuition.

Working method

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Program

1. General principles of Quantum Mechanics: Dirac 
Notation, Quantum States, Operators, Measurements, 
Examples of physical systems.

2. Elementary concepts of quantum information: Qubit,
 Quantum Logic Gates, Quantum Circuits, Reversibility.

3. Quantum encryption: Non-cloning theorem, Quantum 
key distribution.

4. Entanglement: EPR Pairs, Dense Coding, Quantum 
Teleportation, Entanglement Measurements.

5. Non-local games: CHSH game and/or GHZ-Mermin game,
 Bell Inequalities.

6. Simple quantum algorithms: Bersntein-Vazirani 
Algorithm and/or Deutsch-Jozsa Algorithm, Simon Algorithm.

7. Brief introduction to computational complexity the
ory: Turing machines and decidability, Computational complexity, Randomness, Quantum complexity classes.

8. Quantum model of circuits: Controlled operations, 
Sets of universal gates, Approximation of general units.

9. Quantum Research: Oracle Formulation, Grover's 
Algorithm, Applications

10. Hidden subgroup problems: Quantum FourierTransformrm, Period determination, Factorization.

11. Real quantum computers: DiVincenzo Criteria, 
Examples of quantum computers, Shor Code.

12. Computer simulation of quantum circuits

Mandatory literature

Teaching methods and learning activities

Evaluation Type

Assessment Components

Amount of time allocated to each course unit

Eligibility for exams

Calculation formula of final grade

Normal (first) period of examination:


Combined assessment of home exercises (30%) and final
 exam (70%).

 final grade = 0.7 x final exam grade + 0.3 x 
continuous assessment grade.

Appeal (second) period of examination:

final grade =  final exam grade 

Examinations or Special Assignments

Internship work/project

Special assessment (TE, DA, ...)

Classification improvement

Observations