Narain CFTs from qudit stabilizer codes

TL;DR

This paper constructs a discrete subset of Narain conformal field theories from qudit stabilizer codes, revealing deep connections between quantum codes, classical codes, Lorentzian lattices, and CFTs, with implications for holography.

Contribution

It introduces a novel method to derive Narain CFTs from qudit stabilizer codes, especially CSS codes, and analyzes their averaged partition functions.

Findings

Exact averaged partition functions for Narain code CFT ensembles.

Establishment of relations between quantum stabilizer codes and Lorentzian lattices.

Implications for holographic duality from the constructed CFT ensembles.

Abstract

We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is a prime number. Our construction exploits three important relations. The first relation is between qudit stabilizer codes and classical codes. The second is between classical codes and Lorentzian lattices. The third is between Lorentzian lattices and Narain CFTs. In particular, we study qudit Calderbank-Shor-Steane (CSS) codes as a special class of qudit stabilizer codes and the ensembles of the Narain code CFTs constructed from CSS codes. We obtain exact results for the averaged partition functions over the ensembles and discuss their implications for holographic duality.