| Code |
14333
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Physics
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Entry requirements |
The student should have some elementary knowledge of mathematics, namely differential and integral calculus of one real variable, probability theory, linear algebra (vector and matrix calculus), and complex numbers.
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Learning outcomes |
The Curricular Unit has three main objectives:
a) Provide basic concepts of Newton's mechanics;
b) Introduce the foundations of Shannon's information theory;
c) Approach quantum theory in Dirac formalism to explore quantum computing.
It also has, as a complementary objective, to allow the student to increase his computational skills in solving physics problems, as well as his ability to correctly conceptualize problems.
At the end of the Curricular Unit the student should be able to solve basic problems in mechanics, deal with the basic concepts of information theory, and make calculations based on Dirac's formalism of quantum mechanics.
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Syllabus |
1 Basic concepts of mechanics. Kinematics in 1, 2 and 3 dimensions: position, velocity, acceleration. Projectile motion, circular motion. Dynamics: mass, force, Newton laws. Friction. Work and kinetic energy. Conservative forces, potential energy. Mechanical energy conservation. Impulse and linear momentum, centre of mass, collisions. Linear momentum conservation.
2 Information theory. Surprise and uncertainty (entropy): Shannon formula. Units. Information. Conditional entropy. Channel diagrams. Matrix method. Joint entropy. Mutual information. Channel capacity. Data compression.
3 Quantum computation. Vector spaces and linear operators in C; Dirac notation. External product, closure relation. Diagonalization in C. Hermitian and projection operators, spectral decomposition. Tensor product. Functions of operators. Simultaneous diagonalization. Quantum mechanics postulates. Qubits. Quantum gates, quantum circuits, applications.
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Main Bibliography |
1.1 Fundamentos de Física, vol 1, 10ª ed. D Halliday, R Resnick, J Walker. LTC, Rio de Janeiro (2016)
1.2 Beginning Math and Physics for Game Programmers. W Stahler. New Riders Pub., USA (2004)
1.3 Mathematics and Physics for Programmers, 2nd ed. JP Flynt, D Kodicek. Course Technology, Boston (2012)
1.4 Physics for Game Developers, 2nd ed. DM Bourg, B Bywalec. O'Reilly, Beijin (2013)
2.1 The Mathematical Theory of Communication. CE Shannon, W Weaver. Univ. of Illinois Press, Illinois (1949)
2.2 Elements of Information Theory, 2nd ed. TM Cover, JA Thomas. Wiley, New York (2006)
3.1 Quantum Mechanics, vol 1. C Cohen-Tannoudji, B Diu, F Laloë. Wiley, New York (1977)
3.2 Computação Quântica e Informação Quântica. MA Nielsen, IL Chuang. Bookman, Porto Alegre (2005)
3.3 Quantum Computing - From Linear Algebra to Physical Realizations. M Nakahara, T Ohmi. CRC Press, Florida (2008)
3.4 Quantum Computing for Computer Scientists. NS Yanofsky, MA Mannucci. Cambridge Univ. Press, Cambridge (2008)
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Teaching Methodologies and Assessment Criteria |
This curricular unit lasts one semester, and involves 60 hours of contact with the teacher, 92.5 hours of independent work and 7.5 hours for evaluation (total: 160 hours).
Classes are theoretical-practical - TP. The theoretical component involves the exposition of the syllabus and the resolution of some examples. The practical component consists of the application of the syllabus to the resolution of exercises taken from series of exercises created specifically for this curricular unit.
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Language |
Portuguese. Tutorial support is available in English.
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