COMS 4281: Introduction to Quantum Computing

Fall 2024

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

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.

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

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

Problem Sets

Pset0, due Friday, September 13, 11:59pm.
Pset1, due Sunday, October 6, 11:59pm. Download the Jupyter notebook and run it on the qBraid platform (NOT Google Colab!). [PDF Preview]
Pset2 (Theory), due Wednesday, December 4, 11:59pm. [PDF Preview]
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