Infinite Families of Quantum-Classical Hybrid Codes

TL;DR

This paper explores hybrid quantum-classical codes, establishing their properties, error detection capabilities, and constructing infinite families with specific minimum distances, advancing quantum error correction techniques.

Contribution

It introduces general results about hybrid codes, including their impurity and error detection advantages, and constructs new infinite families of such codes with specific parameters.

Findings

Hybrid codes must be impure.

Hybrid codes can detect more errors than quantum codes.

Constructed infinite families of hybrid codes with minimum distances two and three.

Abstract

Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that hybrid codes can always detect more errors than comparable quantum codes. We also introduce the weight enumerators for general hybrid codes, which we then use to derive linear programming bounds. Finally, inspired by the construction of some families of nonadditive codes, we construct several infinite families of genuine hybrid codes with minimum distance two and three.