Clifford Code Constructions of Operator Quantum Error Correcting Codes

TL;DR

This paper introduces a new construction method for operator quantum error-correcting codes using Clifford codes, unifying various quantum error correction approaches with classical additive codes.

Contribution

It presents a natural Clifford code-based construction for operator quantum error-correcting codes, extending stabilizer code concepts with character-theoretic methods.

Findings

Provides a simple method to construct operator codes from classical additive codes

Unifies decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes

Generalizes stabilizer codes through Clifford code framework

Abstract

Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabilizer codes due to Knill. Character-theoretic methods are used to derive a simple method to construct operator quantum error-correcting codes from any classical additive code over a finite field.