This course aims to teach learners how to go beyond the square root distance barrier in decodable quantum LDPC codes using high-dimensional expanders. The course covers topics such as classical codes, CSS codes, geometric 2-complexes, boundaries, LSV complexes, decoding LSV complexes, and balancing distances. The teaching method involves a geometric approach and explicit bounded degree simplicial complexes. This course is intended for individuals interested in quantum coding theory and advanced error correction techniques.
Decodable Quantum LDPC Codes Beyond the Square Root Distance Barrier Using High Dimensional Expander
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
