ECE 398EC: Quantum Systems I, SP 2023

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 –

IntroductionBits and InformationBinary encoding, entropy, source compression
Quantum Systems and Wave-Particle DualityYoung's Double Slit Experiment
de Brogile wavelength, Planck-Einstein relation
QubitsThe Mach-Zehnder InterferometerMatrix description of an interferometer
Quantum sensing
Spin 1/2 ParticlesThe Stern-Gerlach Experiment
Bra-ket notation
Two-level atomsThe Hamiltonian and time evolution
Transition probabilities
Mathematical structure of quantum mechanicsHilbert spaceComplex vector spaces, inner products
Operators and ObservablesMatrix representations of linear operators
Unitary and hermitian operators
Observables and expectation values
Spectral DecompositionEigenvalues and Eigenvectors
The spectral decomposition theorem
Compatible and incompatible observables
Quantum measurements and evolutionQuantum communicationThe projection axiom and state discrimination
Communication capacity
Quantum DynamicsUnitary evolution
Schrodinger's equation
Quantum entanglementEntanglementTensor products
Quantum nonlocalityQuantum Steering
Bell's Theorem
Wave functions and continuous-variable systemsContinuous systemsPosition and momentum of quantum particles
Wave packets
Dynamics of a free particleSchrodinger's equation
Particle in a box