Finite groups PGL(Fq) appear in several recent constructions of ground-breaking quantum error-correcting codes. In this talk, I'll discuss how Cayley complexes of these groups appear as quotients of infinite simplicial complexes known as Bruhat-Tits buildings. Historically, these constructions were devised to answer the question of whether optimal (Ramanujan) expander graphs and analogous higher dimensional complexes exist. I'll talk about how simplicial complexes produce quantum LDPC codes and share early results from my experiments in explicitly realizing small examples of codes from affine buildings.
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