Quantum Codes, CFTs, and Defects

TL;DR

This paper establishes a general framework connecting rational conformal field theories and 3d Chern-Simons theories to quantum stabilizer codes, providing insights into error operations and code subspaces within a CFT context.

Contribution

It introduces a novel construction linking RCFTs and Chern-Simons theories to quantum codes, including orbifold procedures and defect field interpretations.

Findings

Mapped boundary RCFTs to n-qubit quantum codes

Described gauging of RCFTs at the code level when anomalies vanish

Provided CFT interpretations for code subspaces and error operations

Abstract

We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes. Starting from an abelian CS theory with a fusion group consisting of $n$ even-order factors, we map a boundary RCFT to an $n$-qubit quantum code. When the relevant 't Hooft anomalies vanish, we can orbifold our RCFTs and describe this gauging at the level of the code. Along the way, we give CFT interpretations of the code subspace and the Hilbert space of qubits while mapping error operations to CFT defect fields.