Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 267: Quantum Information Theory

Approved: 2023-02-28, Fraas, Kuperberg, Nachtergaele
Units/Lecture:
4
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Quantum Computation and Quantum Information by Nielsen and Chuang, Cambridge University Press
Prerequisites:
Graduate standing in Mathematics or Applied Mathematics, or consent of instructor
Course Description:
This course provides an introduction to the mathematical formulation of quantum theory as relevant for quantum information theory and applications to quantum computation. Topics covered include observables and states, quantum dynamics, quantum gates and circuits, quantum channels, entropies and related inequalities, entanglement, quantum coding theorems, and error correction.
Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

Chapter 1

Introduction

2-3

Chapter 1, 2.1

The math of quantum models

4-5

Chapter 2.2, 2.4, 2.5

States, observables, time evolution

6

Chapter 2.3, 2.6

Quantum teleportation, superdense coding, Bell inequalities

7-8

Chapter 8.2, 8.3

Quantum Channels, complete positivity

9-10

Chapter 9

Distance measures for quantum information

11

Chapters 11.1, 11.2

Classical information, shannon's source coding theorem

12-13

 Chapter 11.3, 11.4

Quantum entropy, relative entropy

14-15

Chapter 12

Quantum data compression, channel capacity, HSW theorem

16-17

Chapter 10.1-4

Quantum error correction                       

 

Additional Notes:
Suggested Lecture Schedule is based on 20 1.5 hour lectures. The syllabus leaves three classes for student presentations or special topics. Possible special topics include stabilizer codes, toric code, quantum estimation, quantum noises, quantum cryptography.