Fundamentals of Quantum Mechanics and Quantum Computers (4 Cfu)

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FUNDAMENTALS OF QUANTUM MECHANICS AND QUANTUM COMPUTERS (4 CFU) PROF. ANTONIO FEOLI DESCRIPTION The course covers the main ideas of quantum physics and their application to quantum computers. Topics include: Atomic spectra and the crisis of classical physics – The photoelectric effect – Bohr’s atomic model – de Broglie’s hypothesis of matter waves – Schroedinger’s equation – The continuity equation and Schroedinger’s interpretation of wave mechanics – Born’s probabilistic interpretation – The double slit experiment – Bohr’s complementarity principle – The principle of superposition of states – The collapse of the wavefunction – The paradox of Schroedinger’s cat – Heisenberg’s uncertainty principle – Simple examples of applications of the Schroedinger’s equation - Hilbert space and the postulates of quantum mechanics – The interpretation of quantum mechanics of de Broglie and Bohm – Polarization and Malus’ law – The “entangled states” – The paradox of Einstein, Podolsky, Rosen (EPR) – Einstein’s boxes and the instantaneous action at a distance – Bell’s theorem and the quantum non-locality – The problem of decoherence – Quantum computers – Difference between classical and quantum computers – The Qubit – Bloch’s sphere – Quantum registers – Quantum logic gates - Quantum parallelism – Computational complexity – Shor’s algorithm. TEXTS, READINGS, MATERIALS Paul Adrien Maurice Dirac: “The principles of Quantum Mechanics” (Oxford University Press, 1930) Albert Einstein, Boris Podolsky and Nathan Rosen: “Can quantum-mechanical description of physical reality be considered complete?” Physical Review vol. 47, p. 777 (1935) Richard Phillips Feynman, Robert B. Leighton and Matthew Sands: “The Feynman lectures on physics” vol. III (Addison – Wesley, 1964) John Stewart Bell: “Speakable and unspeakable in quantum mechanics” (Cambridge University Press, 1987) Jim Baggott: “The meaning of quantum theory” (Oxford University Press, 1992) David J. Griffiths: “Introduction to quantum mechanics” (Prentice Hall, Upper Saddle River, New Jersey, 1995) .

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