COMS 4281: Introduction to Quantum Computing
Fall 2025
Course Number: COMS 4281
Date/Time: Tu Th 10:10am - 11:25am
Room: 209 Havemeyer Hall
First meeting: September 2
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
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.
Practice Worksheets
- Worksheet1 (week of Sept 8).
- Worksheet2 (week of Sept 15).
- Worksheet3 (week of Sept 22).
- Worksheet4 (week of Sept 29).
- Worksheet5 (week of Oct 28).
- Worksheet6 (week of Nov 11).
- Worksheet7 (week of Nov 18).
Problem Sets
- Pset0, due Friday, September 12, 11:59pm. Jupyter notebook files here.
- Pset1, due Friday, October 10, 11:59pm. PDF Preview.
- Pset2 - Theory, due Wednesday, November 26, 11:59pm. You must type your solutions in LaTeX using the provided template.
Schedule
| Week | Date | Topic | Slides |
|---|---|---|---|
| 1 | Sept 2 | Overview of quantum computing and the class. | Slides |
| Sept 4 | Reversible computing. | Slides | |
| 2 | Sept 9 | Basics of quantum info. (Lecturer: Vince Mutolo) | Slides |
| Sept 11 | Basics of quantum info, continued. | ||
| 3 | Sept 16 | Quantum math, quantum vs classical information, Dirac notation. | Slides |
| Sept 18 | Quantum math, no-cloning, partial measurements. | Slides | |
| 4 | Sept 23 | Outer products, teleportation, measurements in other bases. | Slides |
| Sept 25 | Nonstandard measurements, Heisenberg's Uncertainty, EPR Paradox | Slides | |
| 5 | Sept 30 | EPR Paradox and Bell's Theorem. (Lecturer: Natalie Parham) | Slides |
| Oct 2 | Superdense coding, Holevo's Theorem, Quantum Circuits, Universal Gatesets, Deutsch's Problem. (Lecturer: Natalie Parham) | Slides | |
| 6 | Oct 7 | Deutsch's and Simon's algorithms. | Slides |
| Oct 9 | Simon's algorithm. | Slides | |
| 7 | Oct 14 | Quantum Fourier Transform, and midterm review. | Slides |
| Oct 16 | Midterm | ||
| 8 | Oct 21 | Quantum Fourier Transform. | Slides |
| Oct 23 | Phase Estimation Algorithm. | Slides | |
| 9 | Oct 28 | Phase Estimation Algorithm, continued. | Slides |
| Oct 30 | RSA Cryptosystem. Shor's algorithm. Order Finding. | Slides | |
| 10 | Nov 4 | No class. | |
| Nov 6 | Quantum algorithms for search and counting. | Slides | |
| 11 | Nov 11 | Quantum algorithms for search and counting continued. | Slides |
| Nov 13 | Introduction to quantum error correction. | Slides from previous year | |
| 12 | Nov 18 | Quantum error correction, continued. | |
| Nov 20 | Quantum error correction, continued. | ||
| 13 | Nov 25 | Quantum complexity theory. | |
| 14 | Dec 2 | Review. | |
| Dec 4 | Final |