Description and contextualization of the subject

Esta asignatura obligatoria contiene conceptos fundamentales sobre información cuántica y computación cuántica. Entre ellos, la teoría clásica de la información y su unión con conceptos utilizados en el ámbito de la información cuántica como matrices densidad, esferas de Bloch, entrelazamiento etc. En un segundo bloque de esta asignatura, se analizará de la misma manera, conceptos de computación clásica y su relación con la metodología actual en computación cuántica como los modelos de circuitos cuánticos y algunos algoritmos. Los conocimientos adquiridos en esta asignatura se podrán completar con la asignatura optativa computación cuántica y aplicaciones.

Learning outcomes of the subject

Knowledge or content:

RCO1. Demonstrate the ability to explain the fundamental principles of the quantum world, both at a basic and technical level.

RCO2. Have a basic knowledge of the relevant literature in quantum mechanics and be capable of effectively reading and understanding research articles.

RCO3. Be able to initiate the development of original ideas and applications within the context of quantum physics research.

RCO4. Possess the capacity for independent research, synthesis, and be able to present in a clear and structured way complex issues related to the various areas of quantum mechanics addressed in this Master¿s program.

RCO5. Under supervision, demonstrate the ability to write and defend original work that meets the quality standards required for publication in high-impact indexed journals.

RCO6. Be able to identify opportunities for innovation and technology transfer in the field of quantum science and technology.

RCO7. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Information and Computation.



Competencies:

RC1. Possess and understand knowledge that provides a basis or opportunity for developing and/or applying original ideas, often in a research context.

RC2. Apply acquired knowledge and problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

RC3. Demonstrate the ability to integrate knowledge and address the complexity of formulating judgments based on incomplete or limited information, including reflection on social and ethical responsibilities linked to the application of their knowledge and judgments.

RC4. Communicate conclusions, as well as the underlying knowledge and rationale, clearly and unambiguously to both specialized and non-specialized audiences.

RC5. Possess learning skills that enable continued study in a largely self-directed or autonomous manner.



Abilities or skills:

RHE1. Demonstrate proficiency in using tools for bibliographic resource searches.

RHE2. Exhibit critical capacity to read research articles and incorporate their findings into one¿s own work.

RHE3. Write and present original work in one of the official languages and in English.

RHE4. Communicate scientific concepts and results clearly and effectively to both specialized and non-specialized audiences, through presentations and publications.

RHE5. Demonstrate the ability for autonomous learning and staying current with scientific and technological advances.





RHT1. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in basic research in quantum science.

RHT2. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in quantum technology.

RHT3. Effectively integrate into a fundamental or applied research project involving quantum aspects, and solve problems in multidisciplinary environments.

RHT5. Evaluate and select appropriate tools and techniques for the development of technological applications based on quantum physics.

RHT6. Join a company focused on the development of quantum technologies, contributing both to research and development and to the implementation of new strategies based on the principles of quantum mechanics.

Temary

Quantum information:

Classical Information theory: Probability, Shannon entropy and channels, Correlations, Kullback-Leibler divergence, mutual information, Subadditivity and related properties, data processing inequality

Information and the quantum: Density matrix, von Neumann entropy, purity, Bloch sphere. Bipartite systems, partial trace, Schmidt decomposition, Entanglement, Entanglement entropy, Fidelity for initial pure state

Quantum Information theory: Quantum relative entropy, mutual information, basic properties, Accessible information and the Holevo bound, The no-cloning theorem. Shannon and Schumacher channel coding theorems, Quantum data processing inequality. Quantum channels. Kraus representation theorem. Choi¿Jamio¿kowski isomorphism. Properties of quantum channels.

Computing with quantum

Theory of classical computation: Boolean functions. Turing machine, circuit model and gates. Universality. Reversible computation. Complexity.

Circuit model of quantum computing: Unitary representation of classical computation. The quantum circuit model. Universality. Algorithms: Deutsch, Deutsch-Jozsa, QFT. Quantum complexity. Clifford group. Gottesman-Knill theorem.

Bibliography

Basic bibliography

M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information, ¿Cambridge University Press, 2010.

J. Preskill, The Physics of Quantum Information, arXiv:2208.08064

I. Bengtsson and K. Zyczkowski, Geometry of Quantum States, An Introduction to Quantum Entanglement, Cambridge University Press, 2009.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).

In-depth bibliography

List of relevant journal references provided by the lecturers.