Description

This course introduces the mathematical and complexity theoretic foundations of quantum computing. Roughly speaking quantum information is the study of information encoded in the state of quantum physical systems.

We will start by studying the simplified formulation of quantum information in terms of tensor products of complex vectors. We'll consider the states of single and multiple systems, and introduce matrix descriptions of quantum circuits.

Having learned the basics of quantum circuits, we will study how they can actually be used as a model of computation. We will cover the notion of quantum advantage motivating quantum computing. We'll start with quantum query algorithms, then move on to more practically interesting problems like integer factorization and unstructured search.

We will conclude by studying a second general formulation of quantum information. This models quantum states as density matrices, and state changes as channels. It has the crucial advantages of being able to model unvertainty and noise. We'll also discuss measures of similarity and distance for quantum states.

Time permitting, we will introduce the idea of quantum error correction.