Quantum subsystem codes, CFTs and their $\mathbb{Z}_2$-gaugings

TL;DR

This paper constructs and classifies a new class of conformal field theories derived from quantum subsystem codes, revealing novel symmetries, dualities, and supersymmetric structures in the context of quantum error correction and CFTs.

Contribution

It introduces a framework for building Narain CFTs from quantum subsystem codes, extending beyond stabilizer codes, and explores their symmetries and classifications.

Findings

Identification of code CFTs with $ ext{Z}_2$ symmetry

Discovery of self-dual bosonic code CFTs

Construction of new supersymmetric and fermionic code CFTs

Abstract

We construct Narain conformal field theories (CFTs) from quantum subsystem codes, a more comprehensive class of quantum error-correcting codes than quantum stabilizer codes, for qudit systems of prime dimensions. The resulting code CFTs exhibit a global $\mathbb{Z}_2$ symmetry, enabling us to perform the $\mathbb{Z}_2$-gauging to derive their orbifolded and fermionized theories when the symmetry is non-anomalous. We classify a subset of these subsystem code CFTs using weighted oriented graphs and enumerate those with small central charges. Consequently, we identify several bosonic code CFTs self-dual under the $\mathbb{Z}_2$-orbifold, new supersymmetric code CFTs, and a few fermionic code CFTs with spontaneously broken supersymmetry.