Encoding Classical Information in Gauge Subsystems of Quantum Codes

TL;DR

This paper introduces a method to encode classical information into gauge subsystems of quantum codes, enabling hybrid quantum-classical codes with distinct minimum distances for quantum and classical data, using Bacon-Casaccino subsystem codes.

Contribution

It presents a novel construction of hybrid quantum-classical codes from subsystem codes with separate minimum distances, expanding the capabilities of quantum error correction.

Findings

Explicit construction of hybrid codes from classical linear codes

New examples of high-performance hybrid codes

Demonstration of encoding classical info into gauge qudits

Abstract

We show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon-Casaccino subsystem codes, as well as several new examples of good hybrid code.