Introduction to Quantum Computing (Fall 2024)

Jan 1, 0001

Course Number: COMS 4281
Date/Time: MW 10:10am-11:25am
Room: 209 Havemayer Hall
First meeting: September 4

Syllabus

This Week’s Office Hours (updated every Sunday)

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.

Jupyter Resources

We will be using Jupyter the problem sets. Here are some resources to help you get up to speed on writing Markdown, LaTeX, and code in a Jupyter Notebook.

Practice Worksheets

  1. Worksheet 1 - covering material up to Sept 18.
  2. Worksheet 2 - covering material up to Sept 23.
  3. Worksheet 3 - covering material up to Oct 2.
  4. Worksheet 4 - covering material up to Oct 7.
  5. Worksheet 5 - covering material up to Oct 9.
  6. Worksheet 6 - covering material up to Oct 28.
  7. Worksheet 7 - covering material up to Nov 13.

Problem Sets

  1. Pset0, due Friday, September 13, 11:59pm.

  2. Pset1, due Sunday, October 6, 11:59pm. Download the Jupyter notebook and run it on the qBraid platform (NOT Google Colab!). [PDF Preview]

  3. Pset2 (Theory), due Wednesday, December 4, 11:59pm. [PDF Preview]

  4. Pset2 (Coding), due Sunday, December 15, 11:59pm. Tutorial on signing up for IBM’s Quantum API access.

Schedule

Week Date Topic Slides
1 Sept 4 Overview of quantum computing and the class. [Slides]
2 Sept 9 Reversible computing. [Slides]
Sept 11 Basics of quantum info. [Slides]
3 Sept 16 Basics of quantum info, continued. [Slides]
Sept 18 Entanglement, quantum teleportation, and more. [Slides]
4 Sept 23 Heisenberg Uncertainty Principle, EPR Paradox. [Slides]
Sept 25 EPR Paradox and Bell’s Theorem. [Slides]
5 Sept 30 Holevo’s Theorem and Introduction to Quantum Computation. [Slides]
Oct 2 Simon’s Algorithm. same as above
6 Oct 7 The Quantum Fourier Transform. [Slides]
Oct 9 Phase Estimation, and the Factoring Problem. [Slides]
7 Oct 14 Midterm review.
Oct 16 Shor’s Factoring algorithm. [Slides]
8 Oct 21 Midterm.
Oct 23 Midterm recap.
9 Oct 28 Grover search. [Slides]
Oct 30 Grover recap and Quantum counting. [Slides]
10 Nov 6 Intro to quantum complexity theory. [Slides]
11 Nov 11 More quantum complexity theory. [Slides]
Nov 13 Introduction to Hamiltonians. [Slides]
12 Nov 18 Hamiltonian simulation. [Slides]
Nov 20 Introduction to quantum error correction. [Slides]
13 Nov 25 Quantum error correction and fault tolerance. [Slides]
14 Dec 4 Final exam review
15 Dec 9 Final