Witt Groups and Bulk-Boundary Correspondence for Stabilizer States

We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space geometry we associate a boundary operator module. Boundary operator modules provide examples of quasi-symplectic modules, which are objects of independent mathematical interest. In their study, we use ideas from algebraic L-theory in a setting involving non-projective modules and non-unimodular forms. Our results about quasi-symplectic modules in one spatial dimension allow us to resolve the conjecture that every stabilizer state in two dimensions is characterized by a corresponding abelian anyon model with gappable boundary. Our techniques are also applicable beyond two dimensions, such as in the study of fractons.