# 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 –**

Topics | Subtopics | ||
---|---|---|---|

Part I | Foundations | 1. 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 | |||

Topics | Subtopics | ||

Part II | Perturbations and Light-Matter Interaction | 7. 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 | |||

Topics | Subtopics | ||

Part III | Atomic Qubits | 13. Density matrices, Bloch sphere | |

14. Decoherence and coherent manipulations | |||

Quantum Information Applications | 15. Quantum entanglement generation and characterization | ||

16. Quantum algorithms | |||

17. Quantum superdense coding and teleportation | |||

18. Quantum key distribution |