Computer Science/Discrete Mathematics Seminar I

A CSS quantum code $\mathcal{C} = (W_1, W_2)$ is a pair of orthogonal subspaces in $\mathbb{F}_2^n$. The distance of $\mathcal{C}$ is the smallest hamming weight of a vector in $W_1^{\perp}-W_2$ or $W_2^{\perp}-W_1$. A large distance roughly means that the quantum code can correct many errors that affect the information stored in it.  

In this talk we show how to construct a CSS quantum code that can be implemented in a 3-dimensional lattice and has near optimal distance. Along the way we will discuss a connection between quantum codes and systolic geometry made by Freedman and Hastings, as well as a probabilistic embedding result of Gromov and Guth.