Introduction to Quantum Computing

Course Number: COMS 4281
Zoom link: https://columbiauniversity.zoom.us/j/94433279768 (Passcode: available on CourseWorks, or e-mail me)
Piazza link: http://piazza.com/columbia/spring2021/comsw4281
Date/Time: MW 2:40-3:55pm
First meeting: January 11

Syllabus

This Week’s Office Hours

Description

This class is an introduction to the theory of quantum computing and quantum information. Topics covered include:

  • The fundamental postulates of quantum information theory
  • Entanglement and nonlocality
  • The quantum circuit model
  • Basic quantum protocols, such as quantum teleportation and superdense coding
  • Basic quantum algorithms, such as Simons’ algorithm, the Quantum Fourier Transform, Phase Estimation, Shor’s Factoring algorithm, Grover search, amplitude amplification
  • Quantum error correction and fault-tolerance
  • (Time permitting) Quantum cryptography, quantum advantage/quantum supremacy, quantum complexity theory

The goal of the course is to provide a rigorous foundation for future research/studies in quantum computing and quantum information, and along the way provide students with an understanding of the state of the field, and where it’s headed.

No background in quantum physics is required. However, having familiarity and comfort with abstract linear algebra is a must.

Problem Sets

All problem sets can be found at this Overleaf link. Problem Set $n$ is in the file “ps$n$.tex”. You can also use the tex file as your LaTeX template for your solutions.

  • Problem Set 0 - due January 19, 11:59pm EST

Schedule

  1. Week 1
    • January 11. Overview of the quantum computing and quantum information; class administrivia, and basic postulates of quantum information. [Slides] [Video]
    • January 13. Classical versus quantum bits. How to safely test a bomb (with high probability). Composite quantum systems. No-cloning. [Slides] [Video]
    • Supplementary reading: Nielsen and Chuang, Sections 2.1 and 2.2.