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Circuit Quantum Processing of Information and Bioinformatics

Subcategories:

Fundamentals of quantum processing of information

Annotation:
Learning outcomes of the course unit The aim is to acquire basic terms of quantum processing of information and basic methods of their use.

Warp:
Hilbert's space, clean and mixed states. Unitary operators and superoperators. Density matrix. Bondage and nonlocality. Bell's inequalities. Selected terms of quantum theory of information. Quantum circuits.

Basic study material:
MA Nielsen, IL Chuang: Quantum computation and quantum information, Cambridge University Press, Chapters 1, 2 and 4.

J. Gruska: Quantum computing, McGraw-Hill, Chapters 1 and 2.

Tutor: prof. Jozef Gruska, doc. Mário Ziman.

Other Recommended Literature:
ND Mermin: Quantum Computer Science, Cambridge University Press.

T. Heinosaari, M. Ziman: Mathematical language of quantum theory: From Uncertainty to Entanglement, Cambridge University Press.

Quantum automata, algorithms and complexity

Annotation:
The first objective is the acquisition of basic models of quantum automata; their strengths, properties, relationships and relationships to classical (especially probabilistic) models.

The second objective is to acquire the key methods of designing quantum algorithms and communication protocols and proving the lower bounds of complexity of related computational and communication problems.

The third objective is to master the basic classes of quantum complexity, their properties and relationships to classical complexity classes.

Warp:
Quantum universal models (Turing machines, cellular automata). Models of quantum finite automata. Reduction results and properties of corresponding language classes.

Basic techniques for designing quantum algorithms and protocols and their complexity. Basic communication protocols and their complexity: Lower search methods for quantum algorithms and communication protocols.

Basic classes of quantum complexity, their properties and relationships to classical complexity classes. Quantum interactive proof systems and corresponding complexity classes.

Basic study material:
J. Gruska: Quantum computing, McGraw-Hill, 1999, Chapter 4.

J. Gruska, D. Qiu, L. Li, P. Mateus; Quantum finite automata, CRC Handbook on Finite State Models and Applications, 31 pages.

P. Kaye, R. Laflame and M. Mosca; An introduction to quantum computing, Oxford University Press, 2007.

MA Nielsen, IL Chuang: Quantum computation and quantum information, Cambridge University Press, Chapters 4, 5 and 6.

Selected articles from the quantum archive.

Tutor: prof. Jozef Gruska, doc. Libor Polák.

Other Recommended Literature:
J. Gruska: Quantum Automata - An Invitation, Recent advances in Formal Languages ​​and Applications, Studies in Computational Intelligence, V 25, Springer Verlag, 81-117.

ND Mermin: Quantum Computer Science, Cambridge University Press.

S. Aaronson: Quantum computing from Democritos, Cambridge, 2012.

Quantum cryptography

Annotation:
Learning outcomes of the course unit The aim is to acquire basic methods of quantum generation of classical keys and quantum versions of basic classical cryptographic protocols and primitives. Methods of Generating Quantum Randomness and Improving Random Properties.

Warp:
Generating quantum randomness and its evaluation. Quantum Generation of Classical Keys. Quantum encryption methods. Basic quantum protocols. Quantum Sharing Secrets. Quantum teleportation and its applications.

Basic study material:
G. Gilbert, YS Weinstein, M. Hamrick: Quantum Cryptography, World Scientific, 2013.

J. Gruska: Quantum computation, McGraw-Hill, Chapter 6.

Selected articles from the quantum archive.

Tutor: prof. Jozef Gruska, dr. Jan Bouda.

Other Recommended Literature:
ND Mermin: Quantum Computer Science, Cambridge University Press.

S. Aaronson: Quantum computing from Democritos, Cambridge, 2012.

Methods of combating decoherence

Annotation:
Dekoherence is considered the main obstacle to performing long-term and highly accurate quantum processing of information. Learning outcomes of the course unit The aim is to get acquainted with the basic methods of fighting decoherence such as quantum correction codes, fault-proof quantum computation as well as methods using special physics systems.

Warp:
Decoherence - its resources, properties and consequences. Error models. Quantum correction codes. Stabilizer and CSS codes. Quantum fault-tolerant computations. Versatile sets of quantum fault tolerant counting. Adiabatic and topological quantum counting.

Basic study material:
MA Nielsen and IL Chuang: Quantum computation and quantum information, Cambridge University Press, Chapter 10.

J. Gruska: Quantum computing: McGraw-Hill, 1999, Chapter 7.

Selected articles from the quantum archive.

Tutor: prof. Jozef Gruska, doc. Mário Ziman.

Other Recommended Literature:
ND Mermin: Quantum Computer Science, Cambridge University Press.

Quantum theory of information, coherence and correlation

Annotation:
The first objective is to master the basics of quantum theory of information.

The second objective is to acquire basic knowledge about interconnection, its properties, strength and applications in computing, communication and cryptography.

Warp:
Quantum noise and its properties. Quantum information and its properties. Quantum channels and their capacities.

Definition and design of linked states. Classification of multilateral interconnection. Purification of mixed interconnected states. Detection, measurement and witness ties. Discord. Non-quantum quantum correlation. Computational and communication power of interconnection. Bell's inequalities.

Basic study material:
J. Gruska, Quantum computing, McGraw-Hill, 1999, Chapter 8.

T. Heinosaari, M. Ziman: Mathematical language of quantum theory: From Uncertainty to Entanglement, Cambridge University Press.

R. Horodecki, P. Horodecki and M. Horodecki: Quantum entanglement Rev. Mod. Phys. 81 (2): 865-942.

AD Aczel: Entanglement, the greatest mystery in pysics, Four Walls and Eight Windows, 2002.

Selected articles from the quantum archive.

Tutor: doc. Mário Ziman, prof. Jozef Gruska.

Other Recommended Literature:
M. Hayashi: Quantum Information Theory, Springer, Chapters 1-4.

Computational methods in systemic biology

Annotation:
The student will be acquainted at the expert level with the latest scientific knowledge from the field of computational methods for modeling and analysis of biological systems and corresponding applications.

Warp:
Formalities and languages ​​for modeling biological processes, techniques and tools for verification, validation, analysis and simulation of biological systems, parallel and high performance computational methods in system biology.

Basic study material:
3-4 articles from recent lectures of Computational Methods in Systems Biology, Briefings in Bioinformatics, PLOS one, BMC Systems Biology and others as recommended by the Examiner. The articles will be individually specified for the student.

Tutor: prof. Luboš Brim, dr. David Šafránek

Other Recommended Literature:


Digital System Biology

Annotation:
Students will be acquainted with basic methods and techniques from the field of computational methods for modeling and analysis of biological systems and corresponding applications.

Warp:
Basic concepts of system approach to biological systems, specification of biological system, dynamics of biochemical reactions, stochastic modeling and simulation, modeling of cellular communication networks and pathways, modeling of cell cycle, validation of model, formal methods and techniques for systemic biology.

Basic study material:
The examiner sets out a selection of chapters in the range of 100-200 pages of the textbooks: Olaf Wolkenhauer: Systems Biology - Dynamic Pathways Modeling, Rostock University, 2012 (can be obtained with the author's permission as an electronic copy from the examiner) Marco Bernardo, Erik de Vink, Alessandra Di Pierro , Herbert Wiklicky (Eds.): Formal Methods for Dynamic Systems, SFM 2013. Springer. Bertinoro, Italy, June 17-22, 2013 Bernardo, Marco; Degano, Pierpaolo; Zavattaro, Gianluigi (Eds.): Formal Methods for Computational Systems Biology. SFM 2008 Bertinoro, Italy, June 2-7, 2008. Springer. Chapters will be specified individually for the student.

Tutor: prof. Luboš Brim, dr. David Šafránek, dr. Matej Lexa

Other Recommended Literature:
Uri Alon: An Introduction to Systems Biology - Design Principles of Biological Circuits. Boca Raton: Chapman & Hall / CRC, 2007.
CHOI, Sangdun. Introduction to Systems Biology. 1st ed. Totowa: Humana Press, c2007, xvi, 542 pp. ISBN 9781588297068.