Special Seminar by Prof. Gretchen L. Matthews

Error correcting codes protect information from distortion or degradation so that data can be communicated reliably. Classical error correcting codes accomplish this task for digital information by storing it with additional redundancy. The quantum setting provides additional challenges as quantum information cannot be replicated, according to the No Cloning Theorem. Even so, it was shown by Calderbank and Shor and independently by Steane that classical linear codes satisfying a dual-containing condition, meaning vector spaces over finite fields, may be used to define quantum codes. This now famous technique is called the CSS construction. In this talk, we focus on the intersection of a vector space over a finite field and its dual, known as the hull. We share share recent advances in removing the dual-containing condition in the CSS construction and in coding for fault-tolerant quantum computing.