ECE 398EC: Quantum Systems I, SP 2022

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.

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 – G. Grynberg, A. Aspect, C. Fabre, Introduction to Quantum Optics, Cambridge, 2010 (Primary).
D. Miller, Quantum Mechanics for Scientists and Engineers, Cambridge, 2008 (Supplemental).

Grading – This course will have homework assignments given every two weeks, two midterm exams, and a final exam. Their relative contribution to the overall grade is as follows:

Homework: 25%
Midterm Exams 1 &2: 25% each
Final Exam: 25%

Outline –

Part IFoundations1.       Time-dependent and time-independent Schrödinger’s equation; solutions in different potentials
2.       Hilbert space, finite vs. infinite-dimensional systems, bras/kets, quantum numbers, qubits and qudits
3.       Quantum measurements, observables, uncertainty relation, Pauli measurements
4.       The quantum harmonic oscillator; Dirac solution, coherent states, squeezed states
5.       The quantum circuit model, gates, measurements
6.       Review and problem solving
Part IIPerturbations and Light-Matter Interaction7.       Electric and magnetic dipole interactions, the Hamiltonian for a quantum particle in a classical field
8.       Time-independent perturbation theory
9.       Time-dependent perturbations; pulses and oscillating perturbations, Fermi’s Golden Rule
10.       Two-level systems, Rabi Oscillations
11.       Optical Bloch equations
12.       Review and problem solving
Part IIIAtomic Qubits13.       Density matrices, Bloch sphere
14.       Decoherence and coherent manipulations
Quantum Information Applications15.       Quantum entanglement generation and characterization
16.       Quantum algorithms
17.       Quantum superdense coding and teleportation
18.       Quantum key distribution