Speaker: Itamar Vigdorovich (Weizmann)

Title: Complexes, Lie groups, lattices and quantum homological codes

Abstract: 
Google's recent announcement of the first demonstration of quantum supremacy drew much of attention and excitement, and yet, the road towards building a universal quantum computer still seems long. The main issue concerns the noisy nature of quantum systems, and it remains a major challenge to find an error correcting procedure to overcome this hurdle - if such even exists. Out of all such procedures the class of homological codes seems rather promising. Putting aside its physical importance, it allows one to study this information theoretic problem in a purely combinatorial manner. In this talk we will discuss what a classical/quantum code is, and explain how it can be understood in terms of simplicial complexes, Riemannian manifolds, lattices in Lie groups, and even arithmetic. Using these interpretations, we will show concrete constructions to obtain some pretty effective quantum codes: precisely, LDPC codes with constant rate and with distance that is a fractional power of the codes length.