Quantum computing
The course will focus on the computer science aspects of quantum computing. Almost all that we do in the class is available in the book by Michael A. Nielsen and Isaac L. Chuang . As the course progress I will be adding pointers to course materials on the web. In this course we will cover the following topics.
A tentative syllabus.
Hilbert spaces (finite dimensional). Axioms of quantum probability. Quantum vs Classical probability.
Turing machines, Boolean circuits, Quantum Circuits, Universality. Simon’s problem, Phase finding, Shor’s algorithm, Grovers algorithm, Probability amplification. Some applications.
Quantum error correction.Knill-Laflamme theorem, Stabiliser codes
Prerequisites
Basic Linear algebra: Finite dimensional vector spaces A first course including Spectral theorem for finite dimensional vector spaces. Tensor products. Basic group theory, Finite fields etc.
I will do a brief review of these topics but do not expect me to go in detail. Above all what is required is Mathematical maturity