Narain CFTs from nonbinary stabilizer codes

TL;DR

This paper extends the construction of Narain conformal field theories from qudit stabilizer codes to codes over finite fields and rings, resulting in a broader class of rational CFTs and establishing a correspondence between quantum stabilizer codes and Narain CFTs.

Contribution

It generalizes Narain CFT construction to quantum stabilizer codes over finite fields and rings, expanding the set of realizable CFTs and linking codes to specific CFT points.

Findings

Constructs a larger class of rational Narain CFTs

Establishes a correspondence between stabilizer codes and CFTs

Illustrates the correspondence with known codes

Abstract

We generalize the construction of Narain conformal field theories (CFTs) from qudit stabilizer codes to the construction from quantum stabilizer codes over the finite field of prime power order ($\mathbb{F}_{p^m}$ with $p$ prime and $m\geq 1$) or over the ring $\mathbb{Z}_k$ with $k>1$. Our construction results in rational CFTs, which cover a larger set of points in the moduli space of Narain CFTs than the previous one. We also propose a correspondence between a quantum stabilizer code with non-zero logical qubits and a finite set of Narain CFTs. We illustrate the correspondence with well-known stabilizer codes.