Description and contextualization of the subject

Este curso optativo ofrece al estudiante contenido avanzado sobre computación cuántica, extendiendo el temario ofrecido en la asignatura obligatoria quantum Information and quantum computing. En particular se abordarán temas actuales en desarrollo de protocolos de computación cuántica como la eliminación de la decoherencia presente en todo plataforma, el desarrollo de algoritmos cuánticos (quantum Fourier transform, Shor algorithm) y también protocolos de comunicación cuántica como el quantum key distribution (QKD). Finalmente se abordarán temáticas sobre metrología cuántica desde un punto de vista teórico.

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.

RCO12. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Technologies.





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

Advanced quantum computing: Simple proof of universality in quantum circuit model, Equivalent quantum computations, Divincenzo¿s criteria, Physical Realizations.



Fighting with decoherence: Decoherence free subspace, Dynamical decoupling, Quantum error correction code (QECC).



Quantum algorithms: Quantum Fourier transformation, Quantum phase estimation, Shor¿s Algorithm, Quantum Simulations, Grover algorithm, Self-protected algorithms.



Quantum Communication: Quantum cryptography, One-time Pad, Quantum money, BB84 protocol, Ekert protocol (E91), the role of entanglement, QKD protocols using continuous-variable systems, Quantum random-number generation, Quantum secret sharing



Quantum Entanglement: EPR paradox, Bell inequalities, Separability, Entanglement, Entanglement criteria such as Partial transposition, entanglement witnesses, entanglement measures, experiments



Quantum sensing, and quantum metrology: Quantum parameter estimation, Bayesan vs. frequentist approach, Quantum Cramer Rao bound,

Quantum Fisher information and related quantities, the use of quantum entanglement for metrology, spin-squeezing, experiments

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).

Journals

List of relevant journal references provided by the lecturers.