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ECE 305 - Quantum Systems I

Last offered Spring 2025

Official Description

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. Course Information: Prerequisite: Math 257 and Phys 214, or junior standing.

Related Faculty

Course Director

Goals

The goal of this course is to introduce the undergraduate student to the physical and mathematical concepts underlying quantum computing and quantum engineering. Students can take this course relatively early in their degree program (Sophmore or Junior year) with only basic pre-requisites. By the end of the semester, the student should be equipped with the conceptual and technical foundation necessary to pursue advanced 400-level quantum science courses or independent studies.

Topics

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.

Detailed Description and Outline

Introduction

Lecture 1

Bits and Information


Lecture 2

Quantum Systems and Wave-Particle Duality
(complementarity, quantum probabilities)



Qubits

Lecture 3

The Mach-Zehnder Interferometer
(phase shifters, beam splitters, matrix representations, quantum sensing)




Lecture 4

Spin 1/2 particles
(Stern-Gerlach experiment, bra-ket notation, Bloch sphere, measuring spin)




Lecture 5

Atomic Qubits
(time evolution, unitary operators and the Hamiltonian, transition probabilities)



Mathematical structure of quantum states and observables

Lecture 6

Hilbert space and Linear Operators

(Pauli matrices, eigenvalues, spectral decomposition)


Lecture 7

Observables
(Expectation values, incompatible observables, uncertainty principle)





Quantum entanglement and computation

Lecture 8

Entanglement
(Tensor products, interaction Hamiltonians, nuclear spin entanglement, quantum steering, and Bell's theorem)





Lecture 9

Quantum Computation
(Quantum circuits and algorithms, NMR quantum computing, decoherence, spin-echo effect)





Wave functions and continuous-variable systems

Lecture 10

Continuous Systems
(The continuum limit, wave functions, continuous observables, position and moment, Fourier transformations)





Lecture 11

Dynamics of a free particle
(Schrodinger equation, Heisenberg uncertainty principle, wave packets, particle in a box, quantum harmonic oscillator)




Texts

B. Schumacher and M. Westmoreland, Quantum Processes Systems, and Information, 2010 (Primary).

References

D. Miller, Quantum Mechanics for Scientists and Engineers, Cambridge, 2008 (Supplemental).

Required, Elective, or Selected Elective

Math 257 and Phys 214, or junior standing.

Course Goals

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.

Instructional Objectives

By the end of the course, the student should be able to:

1. Principles

  • Use matrices and matrix multiplication to represent the behavior of qubits and finite-dimensional quantum systems (1, 6).
  • Apply principles of quantum mechanics to analyze the Mach-Zehnder Interferometer, spin 1/2-systems, and two-level atomic systems (1, 7).
  • Compute expectation values and variance of different quantum observables (1, 7).
  • Evaluate the time evolution of quantum systems under different Hamiltonians using Schrodinger’s equation (1, 6).
  • Differentiate between entangled and unentangled quantum systems and identify different methods for generating entanglement between quantum systems (1, 2).
  • Compute the effects of partial measurements on entangled systems and explain their connection to the problem of quantum error correction (1, 3).
  • Construct use-cases of quantum entanglement in terms of remote-state preparation, Bell nonlocality, or quantum computation (3, 5).
  • Apply principles of quantum computation to design simple quantum circuits (3, 5).
  • Identify the different components of NMR quantum computing and explain how they realize quantum logical gates (1, 3).
  • Compute the wave function for a continuous system under different types of Hamiltonians (1, 7).
  • Analyze the quantum harmonic oscillator using second-quantization formalism (1, 7).
  • Describe how information can be encoded and decoded into bits (3).
  • Illustrate the geometry of qubit systems using the Bloch sphere (1, 3).
  • Explain principles of quantum measurement using sequential Stern-Gerlach experiments (3, 5).
  • Explain the difference between discrete and continuous quantum systems and how the two are related (3).

Schedule and Instructors

TitleSectionCRNTypeHoursTimesDaysLocationInstructor
Quantum Systems IQS77402LEC31400 - 1520 T R  3017 Electrical & Computer Eng Bldg Eric Chitambar