# Fusion Blossom: Fast MWPM Decoders for QEC

arXiv: https://arxiv.org/abs/2305.08307 · HTML: https://mlsanity.com/paper/2305.08307/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2023.

## Built on by (most cited first, 6 of 6)

- [Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers](https://mlsanity.com/paper/2311.16082/) (2023)
- [DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting](https://mlsanity.com/paper/2311.16214/) (2023)
- [Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction](https://mlsanity.com/paper/2601.09921/) (2026)
- [Neural Minimum Weight Perfect Matching for Quantum Error Codes](https://mlsanity.com/paper/2601.00242/) (2026)
- [Maximum Likelihood Decoding of Quantum Error Correction Codes](https://mlsanity.com/paper/2605.17230/) (2026)
- [Efficient foundation decoders for fault-tolerant quantum computing](https://mlsanity.com/paper/2606.27119/) (2026)

## Abstract (arXiv)

The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds.