# Nested Quantum Error Correction Codes

## TL;DR

This paper introduces a general and efficient method for constructing new quantum error correction codes by nesting existing codes, simplifying the search for long and high-quality codes in quantum information processing.

## Contribution

The authors present a novel nesting approach that unifies and extends existing methods like concatenation and pasting for quantum error correction code construction.

## Key findings

- The nesting method applies to all code lengths and distances.
- It enables construction of optimal or near-optimal codes.
- The approach simplifies the search for long quantum codes.

## Abstract

The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are available in constructing new quantum error correction codes from old codes. Here we exhibit a simple and general method to construct new quantum error correction codes by nesting certain quantum codes together. The problem of finding long quantum error correction codes is reduced to that of searching several short length quantum codes with certain properties. Our method works for all length and all distance codes, and is quite efficient to construct optimal or near optimal codes. Two main known methods in constructing new codes from old codes in quantum error-correction theory, the concatenating and pasting, can be understood in the framework of nested quantum error correction codes.