CSE439

This course covers both introductory numerical linear algebra and quantum algorithms, which are phrased in linear algebraic terms. Students will cover linear operators and matrix representations, operator norms, orthogonalization, the SVD and QR factorizations, conditioning and stability. The course provides a mathematical foundation for subsequent study in Quantum Computing, and covers several quantum algorithms in depth, including Deutsch's Algorithm, the Deutsch-Jozsa Algorithm, and Grover's Algorithm.

CSE 439 Course Information

Instructor: Matthew G. Knepley

Class times: 11:00am to 12:20pm on Tuesday & Thursday

Location: Capen 108

Office Hours: Instructor 12:30pm to 1:30pm Tuesday Capen 211A


A course overview and grading policy are available in accordance with Buffalo academic policy.

Required and Recommended Reading

The texts for the course are Quantum Algorithms via Linear Algebra: A Primer by Richard J. Lipton and Kenneth W. Regan and Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III. Class notes have been prepared for each class, and the lecture will follow the notes. All homework problems are given in the class notes.

John Preskill has an excellent course at Caltech on quantum computing which is quite technical.

Syllabus

Homework

AssignmentDue DateProblems
09/6II.1
19/13II.2, II.4-II.12
29/27II.13-II.28
310/11II.29-II.34
410/18II.3
511/1III.1-III.18
611/22III.19,III.21-III.27,IV.1-IV.7
712/6IV.8-IV.13

Class Videos

Video 1: Linear Algebra
Video 2: Unitary Operators and the Tensor Product
Video 3: Vector and Matrix Norms
Video 4: The Singular Value Decomposition
Video 6: Gram-Schmidt Orthogonalization
Video 7: Strings and Boolean Functions
Video 8: Special Matrices
Video 9: Quantum Tricks
Video 10: Deutsch's Algorithm
Video 11: The Deutsch-Jozsa Algorithm
Video 12: Grover's Algorithm
Video 14: Implementing Grover's Algorithm

External Videos

Great explanation of Bell's results, given by Tim Maudlin.
Excellent introduction to the connection between entanglement and wormholes, given by Leonard Susskind.
Overview talk on the state of Quantum Computing, given by Artur Ekert and Harry Buhrman.
Overview talk on the physics of Quantum Computing, given by John Preskill.
Good talk on current work in Quantum Computing, given by Jarrod McClean.