- Spring 2009 - Independent study, Materials:

- AMS
Course by
Lomonaco, Lomonaco
Lecture Notes, http://arxiv.org/abs/quant-ph/0007045,

- N. S. Yanofsky, Introduction to Quantum Computing, arXiv:0708:0261

- Wikipedia.

Brief Description

This independent study under the supervision of
Lucian Ionescu
aims to introduce the student to the modern applications of mathematics
to
quantum computing. The list of topics depends on the level and
background of
the student taking the course.

__List of Topics for
Spring 2009: __

- Part I (Preliminaries): Recall on operator theory and spectral theory, applications to quantum mechanics, classical algebraic groups and symmetries (transformations preserving the algebraic or analytic structure);
- Part II (Classical computing): Boolean algebras and functions, classical logic and circuits;
- Part III (Quantum Computing): Qubits (SU2/quaternions), unitary operators as quantum gates, universal gates, quantum algorithms (Schor’s algorithm and cryptography);
- Research & Development Project: Quantum Computing from theory to experiment: building your first quantum computer, The Max-Zender Interferometer.

Lecture Outlines