2  Introduction

Quantum computers are susceptible to errors caused by decoherence and noise. Quantum error correction (QEC) is essential for building fault-tolerant quantum computers.

This book covers:

• Classical error-correcting codes: Hamming codes, repetition codes
• LDPC codes: Low-density parity-check codes and belief propagation decoding
• Quantum stabilizer codes: CSS codes, Steane code, surface codes
• Decoding algorithms: MWPM, Union-Find, BP, OSD
• Neural decoders: MLP and GNN-based decoders with GPU acceleration

2.1 Prerequisites

• Linear algebra (vector spaces, matrices)
• Basic quantum mechanics (qubits, Pauli operators)
• Programming experience (Python)

2.2 Code Examples

Throughout this book, we provide executable code examples using Python. The code is available in the qec_code/ directory.