Introduction to Quantum Computing

Course Number: COMS 4281
Date/Time: MW 10:10-11:25am
First meeting: September 7

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 for lectures and assignments. Here are some resources to help you get up to speed on writing Markdown, LaTeX, and code in a Jupyter Notebook.

Problem Sets

Please read this post for detailed instructions on running and submitting your Problem Set notebooks.

Schedule

  1. Week 1
  2. Week 2
    • September 12. Reversible computing. Basics of quantum info. [Slides] [No video this week, due to tech issues]
    • September 14. Basics of quantum info, continued. [Video from Spring 2021]
  3. Week 3
    • September 19. Partial measurements. Quantum teleportation. [Slides] [Video]
    • September 21. Measurements in other bases. Heisenberg's Uncertainty Principle. The EPR Paradox. [Slides] [Video]
  4. Week 4
    • September 26. Bell's Theorem. [Slides] [Video]
    • September 28. Holevo's theorem. Superdense coding. Universal gate sets. Deutsch algorithm. [Slides] [Video]
  5. Week 5
  6. Week 6
  7. Week 7
  8. Week 8
  9. Week 9
  10. Week 10
  11. Week 11
  12. Week 12
    • November 21. Quantum error correction and fault tolerance. [Slides]
  13. Week 13
    • November 28. Stabilizer formalism. [Slides]