CMSA Member Seminar: Poincaré Duality in Quantum Error-Correcting Codes

Quantum information is fragile, and one of the main tools for protecting it is a family of error-correcting codes called stabilizer codes. These codes have a second life as exactly solvable models of quantum matter: the code space is the vacuum state and the “syndromes” behave like excitations that can move freely, get stuck in place, or wind around one another. I will show how a little homological algebra packages these excitations into clean mathematical objects, which we call charge modules. Moreover, there are natural pairing between different charge modules of complementary degrees sometimes called “braiding”. They actually came from the Poincare duality of the sphere. This is joint work with Błażej Ruba.

Lunch will be provided.