---
title: Graphs, Quadratic Forms, and Quantum Codes
url: https://www.emergentmind.com/papers/0703112
type: paper
arxiv_id: '0703112'
arxiv_url: https://arxiv.org/abs/0703112
published: '2007-03-13'
categories:
- quant-ph
- cs.IT
- math.IT
---

# Graphs, Quadratic Forms, and Quantum Codes

## Abstract

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results.