Decoding quantum low density parity check codes with diffusion

D. Deutsch, Quantum theory, the church–turing principle and the universal quantum computer, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400

1985

Earlier work this paper cites.

P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52

1995

Earlier work this paper cites.

E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43

2002

Earlier work this paper cites.

D. J. MacKay, G. Mitchison, and P. L. McFadden, Sparse-graph codes for quantum error correction, IEEE Transactions on Information Theory 50

2004

Earlier work this paper cites.

J.-P. Tillich and G. Zémor, Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory 60

2013

Earlier work this paper cites.

B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87

Original

2015

Earlier work this paper cites.

S. Bravyi, G. Smith, and J. A. Smolin, Trading classical and quantum computational resources, Phys. Rev. X 6

2016

Earlier work this paper cites.

A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, Attention is all you need, Advances in neural information processing systems 30

2017

Earlier work this paper cites.

I. Loshchilov and F. Hutter, Decoupled weight decay regularization, arXiv preprint arXiv:1711.05101 (2017)

Original

2017

Earlier work this paper cites.

J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: composable transformations of Python+NumPy programs (2018)

2018

Earlier work this paper cites.

Y.-H. Liu and D. Poulin, Neural belief-propagation decoders for quantum error-correcting codes, Physical review letters 122

2019

Earlier work this paper cites.

J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, Bert: Pre-training of deep bidirectional transformers for language understanding, in Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, volume 1 (long and short papers) (2019) pp. 4171–4186

2019

Earlier work this paper cites.

J. Ho, X. Chen, A. Srinivas, Y. Duan, and P. Abbeel, Flow++: Improving flow-based generative models with variational dequantization and architecture design, in International conference on machine learning (PMLR, 2019) pp. 2722–2730

2019

Earlier work this paper cites.

J. Roffe, D. R. White, S. Burton, and E. Campbell, Decoding across the quantum low-density parity-check code landscape, Physical Review Research 2

2020

Earlier work this paper cites.

J. Ho, A. Jain, and P. Abbeel, Denoising diffusion probabilistic models, Advances in neural information processing systems 33

2020

Earlier work this paper cites.

J. Song, C. Meng, and S. Ermon, Denoising diffusion implicit models, arXiv preprint arXiv:2010.02502 (2020)

Original

2020

Earlier work this paper cites.

J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and R. Van Den Berg, Structured denoising diffusion models in discrete state-spaces, Advances in neural information processing systems 34

2021

Earlier work this paper cites.

C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5

2021

Earlier work this paper cites.

T. Chen, R. Zhang, and G. Hinton, Analog bits: Generating discrete data using diffusion models with self-conditioning, arXiv preprint arXiv:2208.04202 (2022)

Original

2022

Cited alongside, same era.

J. Ho and T. Salimans, Classifier-free diffusion guidance, arXiv preprint arXiv:2207.12598 (2022)

Original

2022

Cited alongside, same era.

Y. Lipman, R. T. Chen, H. Ben-Hamu, M. Nickel, and M. Le, Flow matching for generative modeling, arXiv preprint arXiv:2210.02747 (2022)

Original

2022

Cited alongside, same era.

C. Luo, Understanding diffusion models: A unified perspective, arXiv preprint arXiv:2208.11970 (2022)

Original

2022

Cited alongside, same era.

Suppressing quantum errors by scaling a surface code logical qubit, Nature 614

S. Sahoo, M. Arriola, Y. Schiff, A. Gokaslan, E. Marroquin, J. Chiu, A. Rush, and V. Kuleshov, Simple and effective masked diffusion language models, Advances in Neural Information Processing Systems 37

2024

Later among the works it cites.

J. Shi, K. Han, Z. Wang, A. Doucet, and M. Titsias, Simplified and generalized masked diffusion for discrete data, Advances in neural information processing systems 37

2024

Later among the works it cites.

Quantum error correction below the surface code threshold, Nature 638

2025

Closest in time.

K. Wang, Z. Lu, C. Zhang, G. Liu, J. Chen, Y. Wang, Y. Wu, S. Xu, X. Zhu, F. Jin, et al. , Demonstration of low-overhead quantum error correction codes, arXiv preprint arXiv:2505.09684 (2025)

Original

2025

Closest in time.

T. Müller, T. Alexander, M. E. Beverland, M. Bühler, B. R. Johnson, T. Maurer, and D. Vandeth, Improved belief propagation is sufficient for real-time decoding of quantum memory, arXiv preprint arXiv:2506.01779 (2025)