Weight Enumerators and Magic State Distillation by Dr. Amolak Kalra

In this talk I will start by describing a protocol called magic state distillation, which was first introduced by Bravyi and Kitaev in 2005. This protocol uses quantum error-correcting codes and noisy magic states to perform universal fault-tolerant quantum computation.

I will then explain how the performance of a certain class of magic state distillation protocols can be determined by the weight enumerator of the quantum error-correcting code used for distillation. Using this connection, I will show how one can derive new constraints on certain families of classical and quantum weight enumerators that are stronger than those previously known.

These stronger constraints lead to tighter distance bounds for quantum codes and, rather surprisingly, to a proof of the non-existence of certain families of classical codes.