Sparse Blossom: correcting a million errors per core second with minimum-weight matching

Oscar Higgott; Craig Gidney

doi:10.22331/q-2025-01-20-1600

Sparse Blossom: correcting a million errors per core second with minimum-weight matching

Oscar Higgott^1,2 and Craig Gidney¹

¹Google Quantum AI, Santa Barbara, California 93117, USA
²Department of Physics & Astronomy, University College London, WC1E 6BT London, United Kingdom

Published:	2025-01-20, volume 9, page 1600
Editor:	Kishor Bharti
Eprint:	arXiv:2303.15933v2
Doi:	https://doi.org/10.22331/q-2025-01-20-1600
Citation:	Quantum 9, 1600 (2025).

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Abstract

In this work, we introduce a fast implementation of the minimum-weight perfect matching (MWPM) decoder, the most widely used decoder for several important families of quantum error correcting codes, including surface codes. Our algorithm, which we call sparse blossom, is a variant of the blossom algorithm which directly solves the decoding problem relevant to quantum error correction. Sparse blossom avoids the need for all-to-all Dijkstra searches, common amongst MWPM decoder implementations. For 0.1% circuit-level depolarising noise, sparse blossom processes syndrome data in both $X$ and $Z$ bases of distance-17 surface code circuits in less than one microsecond per round of syndrome extraction on a single core, which matches the rate at which syndrome data is generated by superconducting quantum computers. Our implementation is open-source, and has been released in version 2 of the PyMatching library.

Featured image: Decoding time per round for sparse blossom (PyMatching v2), compared to
PyMatching v0.7 and a NetworkX implementation, for surface code circuits with p=0.1% circuit-level noise. All three decoders use a single core of an M1 Max processor.

Popular summary

A key challenge in building a fault-tolerant quantum computer is the development of a decoder fast enough to correct errors produced by the quantum hardware. A decoder is a classical algorithm that uses measurement data from the quantum computer, as well as a model of the noise, to infer which errors have occurred. For scalable quantum computation to be possible, it is crucial that the decoder can process measurement data at least as fast as it is produced by the quantum computer.

In this paper we introduce sparse blossom, a fast decoder for some important families of quantum error correcting codes including the widely-used surface code. Through simulations, we show that sparse blossom can correct over one million errors per second on a single core of a laptop computer – fast enough to decode a 577-qubit superconducting surface code quantum computer.

Sparse blossom is an adaptation of the blossom algorithm for finding a minimum-weight perfect matching (MWPM), developed by Jack Edmonds in 1961. By adapting the blossom algorithm to solve the different (but related) quantum error correction decoding problem directly, sparse blossom avoids the costly quadratic overhead that is often incurred when using a naive reduction from the decoding problem to the MWPM problem.

We release our implementation of sparse blossom in version 2 of the open-source PyMatching Python package. Our open-source implementation reduces the cost of quantum error correction simulations by 100x to 1000x compared to previous open-source software for the same decoding problem. Furthermore, our paper paves the way to real-time CPU decoding of superconducting quantum computers.

► BibTeX data

@article{Higgott2025sparseblossom,
  doi = {10.22331/q-2025-01-20-1600},
  url = {https://doi.org/10.22331/q-2025-01-20-1600},
  title = {Sparse {B}lossom: correcting a million errors per core second with minimum-weight matching},
  author = {Higgott, Oscar and Gidney, Craig},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1600},
  month = jan,
  year = {2025}
}

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