Course Description – Quantum information science (QIS) is a rapidly developing field that aims to revolutionize computation and communication technology. This course will provide an introduction to physical quantum systems with an emphasis on QIS applications. The primary objective is to provide the conceptual and quantitative foundations for higher-level courses in quantum information science and nanoelectronics. A heavy emphasis will be placed on the roles that information and communication play in quantum mechanics.
Format and Schedule – Live lectures will be given in person M/W/F 1:00PM – 1:50PM.
Prerequisites – PHYS 214, ECE 329 (Overrides are possible).
Textbook – B. Schumacher and M. Westmoreland, Quantum Processes Systems, and Information, 2010 (Primary).
D. Miller, Quantum Mechanics for Scientists and Engineers, Cambridge, 2008 (Supplemental).
Grading – This course will have homework assignments given every two weeks, three midterm exams, and a final exam. Their relative contribution to the overall grade is as follows:
Homework: 25%
Midterm Exams 1, 2, & 3: 25% each
Final Exam: 25%
Outline –
| Topics | Subtopics | ||
|---|---|---|---|
| Introduction | Bits and Information | Binary encoding, entropy, source compression | |
| Quantum Systems and Wave-Particle Duality | Young's Double Slit Experiment | ||
| de Brogile wavelength, Planck-Einstein relation | |||
| Qubits | The Mach-Zehnder Interferometer | Matrix description of an interferometer | |
| Quantum sensing | |||
| Spin 1/2 Particles | The Stern-Gerlach Experiment | ||
| Bra-ket notation | |||
| Two-level atoms | The Hamiltonian and time evolution | ||
| Transition probabilities | |||
| Mathematical structure of quantum mechanics | Hilbert space | Complex vector spaces, inner products | |
| Operators and Observables | Matrix representations of linear operators | ||
| Unitary and hermitian operators | |||
| Observables and expectation values | |||
| Spectral Decomposition | Eigenvalues and Eigenvectors | ||
| The spectral decomposition theorem | |||
| Compatible and incompatible observables | |||
| Quantum measurements and evolution | Quantum communication | The projection axiom and state discrimination | |
| Communication capacity | |||
| Quantum Dynamics | Unitary evolution | ||
| Schrodinger's equation | |||
| Quantum entanglement | Entanglement | Tensor products | |
| Interactions | |||
| Quantum nonlocality | Quantum Steering | ||
| Bell's Theorem | |||
| Wave functions and continuous-variable systems | Continuous systems | Position and momentum of quantum particles | |
| Wave packets | |||
| Dynamics of a free particle | Schrodinger's equation | ||
| Particle in a box |