IQI Weekly Seminar

Abstract: In the iid noise model, error correction crucially depends on the existence of good codes. In this context, "good" relates to an as-large-as-possible coherent information under the action of various noisy channels, such as depolarizing, dephrasure, or BB84. Each of these channels has a noise parameter p, which allows us to ask which codes are optimal for a particular choice of p. Existing upper bounds on the quantum capacity of the above channels are not known to be tight, and in certain noise regimes there is a large gap between upper and lower bounds on the quantum capacity.

Our goal is to find optimal codes under a family of states called "graph states". Such states often feature large symmetries, which together with a Pauli channel's properties (e.g. covariance) can be exploited to vastly reduce the numerical complexity of exhaustive search. We present a few prelimiary results.

This is a work-in-progress project jointly with Felix Leditzky (University of Colorado Boulder/JILA).