Quantum codes from classical graphical models

TL;DR

This paper presents a new graphical framework for quantum error correction codes that leverages classical graphical models, making quantum code design more accessible and enabling the derivation of quantum codes from classical ones.

Contribution

It introduces a classical-inspired graphical language for quantum codes, facilitating easier design and understanding of quantum error correction methods.

Findings

Framework closely related to classical factor graphs

Allows design of quantum codes from classical codes

Accessible without quantum mechanics background

Abstract

We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or graphical models in classical information theory and machine learning. It enables us to formulate the description of the recently-introduced `coherent parity check' quantum error correction codes entirely within the language of classical information theory. This makes our construction accessible without requiring background in quantum error correction or even quantum mechanics in general. More importantly, this allows for a collaborative interplay where one can design new quantum error correction codes derived from classical codes.