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
| Assignment | Due Date | Problems |
| 0 | 9/6 | II.1 |
| 1 | 9/13 | II.2, II.4-II.12 |
| 2 | 9/27 | II.13-II.28 |
| 3 | 10/11 | II.29-II.34 |
| 4 | 10/18 | II.3 |
| 5 | 11/1 | III.1-III.18 |
| 6 | 11/22 | III.19,III.21-III.27,IV.1-IV.7 |
| 7 | 12/6 | IV.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. |