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.

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

Schedule

  1. Week 1
    • September 4. Overview of quantum computing and the class. Class organization. [Slides]
  2. Week 2
    • September 9. Reversible computing. [Slides]
    • September 11. Basics of quantum info. [Slides]
  3. Week 3
    • September 16. Basics of quantum info, continued. [Slides]
    • September 18. Entanglement, quantum teleportation, and more. [Slides]
  4. Week 4
    • September 23. Heisenberg Uncertainty Principle, EPR Paradox. [Slides]
    • September 25. EPR Paradox and Bell's Theorem. [Slides]
  5. Week 5
    • September 30. Holevo's Theorem and Introduction to Quantum Computation. [Slides]
    • October 2. Simon's Algorithm. [Slides]
  6. Week 6
    • October 7. The Quantum Fourier Transform. [Slides]
    • October 9. Phase Estimation, and the Factoring Problem. [Slides]
  7. Week 7
    • October 14. Midterm review.
    • October 16. Shor's Factoring algorithm.
  8. Week 8
    • October 21. Midterm.