Title: Quantum Error Correction Codes
Abstract:
Quantum Information Theory is an exciting new generalization of classical Information Theory. Rather than dealing with states that are elements of a finite set, Quantum Information Theory deals with states that elements of a Hilbert space. Quantum channels can provide provably secure communications, and quantum computers (computers which manipulate quantum states) can factor numbers in polynomial time (as compared to exponential time for classical computers).
I will give an introduction to the mathematical model of quantum states. I will discuss the No-cloning theorem, which states that quantum bits cannot be copied. I will cover the error model on quantum channels, and finally I will give some examples of quantum codes which protect quantum states from errors, and discuss a general recipe for constructing quantum codes from classical codes.