BPDecoderPlus

Quantum Error Correction with Belief Propagation

Work in Progress

This WIP project is for AI + Quantum winter school training.

A winter school project on circuit-level decoding of surface codes using belief propagation and integer programming decoders, with extensions for atom loss in neutral atom quantum computers.

Project Goals

Level	Task	Description
Basic	MLE Decoder	Reproduce the integer programming (MLE) decoder as the baseline
Challenge	Atom Loss	Handle atom loss errors in neutral atom systems
Extension	QEC Visualization	https://github.com/nzy1997/qec-thrust

Info

We also want to explore the boundary of vibe coding, which may lead to a scipost paper.

Learning Objectives

After completing this project, students will:

• Understand surface code structure and syndrome extraction
• Implement and compare different decoding algorithms
• Analyze decoder performance through threshold plots
• Learn about practical QEC challenges (atom loss, circuit-level noise)

Prerequisites

• Programming: Julia basics, familiarity with Python for plotting
• Mathematics: Linear algebra, probability theory
• QEC Background: Stabilizer formalism, surface codes (helpful but not required)

Quick Start

Install the package:

# Clone the repository
git clone https://github.com/TensorBFS/BPDecoderPlus.git
cd BPDecoderPlus

# Install dependencies
make setup

# Run tests
make test

Generate a dataset:

python -m bpdecoderplus.cli \
  --distance 3 \
  --p 0.01 \
  --rounds 3 5 7 \
  --generate-dem \
  --generate-syndromes 1000

Features

Python Module (bpdecoderplus)

• Noisy Circuit Generation: Create surface code circuits with realistic noise models
• Detector Error Model (DEM): Extract error models for belief propagation
• UAI Format Support: Export to UAI format for probabilistic inference with TensorInference.jl
• Syndrome Database: Generate training datasets from circuit simulations
• PyTorch BP Implementation: Belief propagation solver for factor graphs

Julia Module (TensorQEC.jl Integration)

• Multiple decoder implementations (IP, BP, BP+OSD, Matching)
• Comprehensive benchmarking tools
• Performance visualization

Documentation

• Getting Started - Quick start guide and pipeline overview
• Usage Guide - Detailed usage examples
• API Reference - Complete API documentation
• Mathematical Description - Mathematical background

Available Decoders

Decoder	Symbol	Description
IP (MLE)	:IP	Integer programming decoder - finds minimum weight error
BP	:BP	Belief propagation without post-processing
BP+OSD	:BPOSD	BP with Ordered Statistics Decoding post-processing
Matching	:Matching	Minimum weight perfect matching (via TensorQEC)

Resources

Core Library

• TensorQEC.jl - QEC library we build on

Reference Implementations

• bp_osd - Python BP+OSD implementation
• ldpc - LDPC decoder library

Documentation

• TensorQEC Documentation
• Error Correction Zoo

License

MIT License - See LICENSE file for details.

Acknowledgments

This project is built on TensorQEC.jl by nzy1997.