Foundations of quantum computer science
Academic year: 2024/25
Semester: 1
CFU: 6
Hours: 45
Teachers
Syllabus
Quantum phenomenology (2 CFU)
- Blackbody radiation. Wien’s Law. Stefan-Boltzmann Law. Planck’s hypothesis. Photoelectric effect. Einstein’s theory. The concept of the photon. Experimental determination of Planck’s constant (ℏ) via Millikan’s experiment (on the photoelectric effect): interactive classroom demonstration.
- Compton effect. Photons. Compton wavelength of the electron. Relativistic dispersion relation.
- Interference. Young’s experiment (double-slit experiment). Bragg’s experiment. Wave-particle duality. De Broglie relation.
- Brownian motion. Plum pudding model (jellium model). Rutherford model. Atomic spectroscopy. Spectral series (Balmer, Paschen, Lyman, Rydberg). Bohr atomic model. Bohr radius: quantization of angular momentum. Energy spectrum of the hydrogen atom. Rydberg formula.
- Matter waves: standing waves. Probability amplitude. Wave function.
- Magnetic interactions. Zeeman effect. Orbital magnetic moment. Stern-Gerlach experiment. Spin. Quantum statistics. Spin-statistics theorem (introduction). Fermions and bosons.
Quantum mechanics for computation (3+1 CFU)
- Operators and observables (RvN2). Unitary operators.
- Single-qubit gates.
- Schrödinger equation (RvN3): Majorana and Rabi oscillations.
- Measurement (RvN4-5). Density matrix.
- Composite systems, entangled states, and two-qubit gates.
- Vector spaces and linear operators. Hilbert spaces.
- Conceptual differences between classical and quantum mechanics. Postulates of Quantum Mechanics.
- Compatible and incompatible observables. Uncertainty principle. Stern-Gerlach experiment. Symmetry transformations and unitary operators.
- Introduction to quantum computing via Quantum Mechanical formalism. C-bits and Q-bits. Quantum gates.
Bibliography
- J. J. Brehm, W. J. Mullin, Introduction to the structure of matter: a course in modern physics (J. Wiley & Sons, 1989)
- K. S. Krane, Modern physics (J. Wiley & Sons, 2019)