Witt Groups and Bulk-Boundary Correspondence for Stabilizer States

• URL: http://arxiv.org/abs/2509.10418v1
• Date: Fri, 12 Sep 2025 17:15:19 GMT
• Title: Witt Groups and Bulk-Boundary Correspondence for Stabilizer States
• Authors: Błażej Ruba, Bowen Yang,
• Abstract summary: Boundary operator modules provide examples of quasi-symplectic modules.<n>We resolve the conjecture that every stabilizer state in two dimensions is characterized by a corresponding abelian anyon model with gappable boundary.
• Score: 8.162672407534899
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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