---
title: Quantum LDPC Codes
url: https://www.emergentmind.com/topics/quantum-ldpc-codes
type: topic
---

# Quantum LDPC Codes

Quantum low-density parity-check (LDPC) codes are quantum stabilizer codes characterized by sparse, constant-weight parity-check matrices—each stabilizer generator involves only O(1) qubits and each qubit appears in O(1) stabilizers. The advent of quantum LDPC codes marks a milestone in quantum error correction, promising the potential for constant overhead, efficient decoding, and scalability well beyond topological codes such as the surface code. Modern constructions of quantum LDPC codes rely on sophisticated algebraic, combinatorial, and homological techniques to reconcile the conflicting requirements of commutativity, sparsity, and large minimum distance.

## 1. Fundamental Definitions and Constraints

Quantum LDPC codes are instances of stabilizer codes defined over $n$ qubits by an abelian subgroup $\mathcal S \subset \mathcal P_n$, where the code space $\

Source: https://www.emergentmind.com/topics/quantum-ldpc-codes