ECE 398EC: Quantum Systems I, SP 2024

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 –

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
Linear operatorsMatrix representations of linear operators
Unitary and hermitian operators
spectral decomposition
Observablesexpectation values
incompatible observables
uncertainty principle
Quantum measurements and evolutionQuantum communicationThe projection axiom and state discrimination
Quantum key distribution
Quantum DynamicsUnitary evolution
Schrodinger's equation
Quantum entanglementEntanglementTensor products
Quantum Steering
Bell's Theorem
Quantum ComputationQuantum CircuitsAlgorithms
Physical ImplementationsNMR quantum computing
spin-echo effect
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
Harmonic oscillator