Course Description – Quantum information science (QIS) is a rapidly developing field that aims to revolutionize computation and communication technology. This course introduces the basic principles of quantum mechanics and its applications in quantum information science. The experimental and mathematical concepts of quantum mechanics are introduced in terms of quantum bits, or qubits, and the students will learn how qubits are used for computing and communication. Topics include: wave-particle duality, interferometry and quantum sensing, spin systems, atomic transitions and Rabi Oscillations, bra/ket notation, quantum communication and entanglement, quantum computation and algorithms, and continuous systems. The primary objective is to provide the conceptual and quantitative foundations for higher-level courses in quantum information science and nanoelectronics.
Format and Schedule – Live lectures will be given in person M/W/F 1:00PM – 1:50PM.
Prerequisites – Math 257, PHYS 214 (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 | |
| Linear operators | Matrix representations of linear operators | ||
| Unitary and hermitian operators | |||
| spectral decomposition | |||
| Observables | expectation values | ||
| incompatible observables | |||
| uncertainty principle | |||
| Quantum measurements and evolution | Quantum communication | The projection axiom and state discrimination | |
| Quantum key distribution | |||
| Quantum Dynamics | Unitary evolution | ||
| Schrodinger's equation | |||
| Quantum entanglement | Entanglement | Tensor products | |
| Interactions | |||
| Quantum Steering | |||
| Bell's Theorem | |||
| Quantum Computation | Quantum Circuits | Algorithms | |
| Physical Implementations | NMR quantum computing | ||
| decoherence | |||
| spin-echo effect | |||
| 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 | |||
| Harmonic oscillator |