ECE 39595 - Fundamentals of Quantum Technology

Course Details

Lecture Hours: 3 Credits: 3

Counts as:

  • EE Elective
  • CMPE Complementary Elective

Experimental Course Offered:

Fall 2022

Requisites:

ECE 20002 or [ECE 20200 and ECE 25500]; and [MA 26200 or [MA 26500 and MA 26600]]; PHYS 27200 or [PHYS 24100 + PHYS 25200];

Requisites by Topic:

Linear circuit analysis, linear algebra and differential equations, and electric and magnetic interractions

Catalog Description:

This course is intended to introduce the fundamental concepts of quantum physics needed to prepare engineers to work on the development of quantum technologies or pursue more advanced studies in this field. Focus is placed on developing an understanding of the basic behavior of quantum systems, the implications of which are discussed in the context of the popular experimental platform of quantized circuits where possible. Topics covered include the fundamentals of the Schrodinger equation and wavefunctions, the general mathematical framework of quantum mechanics, the use of approximate methods for analyzing quantum systems, the quantized interactions between (artificial) atoms and linear circuits, and the density matrix. The course concludes with an introduction to revolutionary quantum technologies such as quantum communication systems, quantum computers, and quantum sensing systems.

Required Text(s):

  1. Quantum Mechanics for Scientists and Engineers , 1st Edition , D. A. B. Miller , Cambridge University Press , 2008 , ISBN No. 978-0521897839

Recommended Text(s):

  1. Introduction to Quantum Mechanics , 3rd Edition , D. J. Griffiths and D. F. Schroeter , Cambridge University Press , 2018 , ISBN No. 978-1107189638
  2. Modern Quantum Mechanics , 3rd Edition , J. J. Sakurai and J. Napolitano , Cambridge University Press , 2020 , ISBN No. 978-1108473224

Learning Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:
  1. an ability to use the Schrodinger equation to analyze simple quantum systems. [1]
  2. an ability to utilize the mathematical framework of quantum mechanics to analyze the dynamics of quantized circuits. [1]
  3. an ability to mathematically describe basic quantum interactions between (artificial) atoms and circuit components. [1]
  4. an ability to use engineering judgement to assess the capabilities and challenges of revolutionary quantum technologies. [6]

Lecture Outline:

Week Topic
1 Brief history of quantum mechanics, overview of quantum technologies, introduction to Lagrangian and Hamiltonian mechanics
2 Lagrangian and Hamiltonian mechanics for simple mechanical and electrical systems
3 Time-independent Schrodinger equation, wavefunctions
4 Time-dependent Schrodinger equation, wavefunction collapse, uncertainty principle
5 Mathematical framework of quantum mechanics
6 Mathematical framework continued, quantum mechanics of simple circuits (quantum harmonic oscillator revisited, creation and annihilation operators, coherent states)
7 Quantum mechanics of simple circuits (Schrodinger and Heisenberg picture, driven quantum harmonic oscillator, capacitively coupled quantum harmonic oscillators)
8 Approximate methods in quantum mechanics
9 Introduction to (artificial) atoms, two-level systems
10 Introduction to circuit-atom interactions (formulation and semiclassical analysis)
11 Introduction to circuit-atom interactions (formulation and semiclassical analysis) 11 Introduction to circuit-atom interactions (the Jaynes-Cummings model, Rabi oscillations, spontaneous and stimulated emission)
12 Density matrix
13 Introduction to quantum communication
14 Introduction to quantum computing
15 Introduction to quantum sensing

Engineering Design Content:

  • Analysis

Assessment Method:

Homework and Exams