Overview
Syllabus
Intro
Classical codes
CSS (Calderbank, Shor, Steane) codes A quantum CSS code is given by two orthogonal subspaces
CSS codes as 2-complexes A CSS code given by parity check matrices
Geometric 2-complexes
Boundaries
Towards better complexes
Geometrical approach (II)
LSV (Lubotzky, Samuels, Vishne) complexes (1) These are explicit bounded degree simplicial complexes, which are highly complicated objects (both locally and globally).
Link of a vertex
Decoding LSV complexes (1)
Balancing distances (1) TA
LSV 3-complexes
Final remarks
Taught by
IEEE FOCS: Foundations of Computer Science