MIT Infinite Dimensional Algebra Seminar (Spring 2026)

Stabilizer codes form a distinguished class of exactly solvable quantum lattice models, originally arising in quantum error correction and now central to the study of topological phases. In this lecture, I will explain how abelian anyon theories arise as algebraic invariants of translation-invariant stabilizer codes. Focusing on 2+1-dimensional models, I will describe how bulk excitations and boundary degrees of freedom admit a purely algebraic formulation in terms of finitely generated modules over Laurent polynomial rings equipped with skew-Hermitian forms. In this framework, the abelian anyon content of a stabilizer code is captured by a finite metric group extracted from the lattice Hamiltonian. Viewed this way, abelian anyon theories appear not as emergent topological quantum field theories, but as computable algebraic invariants of quantum lattice models, providing a concrete bridge between stabilizer codes and TQFT. The talk will be largely self-contained.