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On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement

Authors Thiago Bergamaschi , Yunchao Liu

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ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum error correction
  • fault tolerance
  • single-shot error correction
  • logical state preparation

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Abstract

Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state [Raussendorf et al., 2005] offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward [Bravyi et al., 2020]. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman’s clustering-of-errors argument [Gottesman, 2014]. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement.

Cite As Get BibTex

Thiago Bergamaschi and Yunchao Liu. On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 16:1-16:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.16

Author Details

Thiago Bergamaschi
  • University of California Berkeley, CA, USA
Yunchao Liu
  • University of California Berkeley, CA, USA
  • Harvard University, Cambridge, MA, USA

Funding

T.B. acknowledges support by the National Science Foundation under Grant No. DGE 2146752. Y.L. is supported by DOE Grant No. DE-SC0024124, NSF Grant No. 2311733, and DOE Quantum Systems Accelerator.

Acknowledgements

We thank Zhiyang He (Sunny) for helpful discussions. We thank Jong Yeon Lee for helpful discussions and for informing us about an upcoming work with Isaac Kim on single-shot error correction and cluster states. This work was done in part while the authors were visiting the Simons Institute for the Theory of Computing.

References

  1. Dorit Aharonov and Yonathan Touati. Quantum circuit depth lower bounds for homological codes, 2018. URL: https://arxiv.org/abs/1810.03912.
  2. Thiago Bergamaschi and Yunchao Liu. On fault tolerant single-shot logical state preparation and robust long-range entanglement, 2024. URL: https://arxiv.org/abs/2411.04405.
  3. A. Bolt, G. Duclos-Cianci, D. Poulin, and T. M. Stace. Foliated quantum error-correcting codes. Phys. Rev. Lett., 117:070501, August 2016. URL: https://doi.org/10.1103/PhysRevLett.117.070501.
  4. H. Bombin. Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes. New Journal of Physics, 17, 2013. URL: https://api.semanticscholar.org/CorpusID:3355844.
  5. Héctor Bombín. Single-shot fault-tolerant quantum error correction. Phys. Rev. X, 5:031043, September 2015. URL: https://doi.org/10.1103/PhysRevX.5.031043.
  6. S. Bravyi, M. B. Hastings, and F. Verstraete. Lieb-robinson bounds and the generation of correlations and topological quantum order. Phys. Rev. Lett., 97:050401, July 2006. URL: https://doi.org/10.1103/PhysRevLett.97.050401.
  7. Sergey Bravyi, David Gosset, Robert König, and Marco Tomamichel. Quantum advantage with noisy shallow circuits. Nature Physics, 16(10):1040-1045, October 2020. URL: https://doi.org/10.1038/s41567-020-0948-z.
  8. Sergey Bravyi, Isaac Kim, Alexander Kliesch, and Robert Koenig. Adaptive constant-depth circuits for manipulating non-abelian anyons, 2022. URL: https://arxiv.org/abs/2205.01933.
  9. N. P. Breuckmann and Vivien Londe. Single-shot decoding of linear rate ldpc quantum codes with high performance. IEEE Transactions on Information Theory, 68:272-286, 2020. URL: https://api.semanticscholar.org/CorpusID:210157092.
  10. Edward H. Chen, Guo-Yi Zhu, Ruben Verresen, Alireza Seif, Elisa Bäumer, David Layden, Nathanan Tantivasadakarn, Guanyu Zhu, Sarah Sheldon, Ashvin Vishwanath, Simon Trebst, and Abhinav Kandala. Realizing the nishimori transition across the error threshold for constant-depth quantum circuits, 2023. URL: https://arxiv.org/abs/2309.02863.
  11. Omar Fawzi, Antoine Grospellier, and Anthony Leverrier. Efficient decoding of random errors for quantum expander codes. Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2017. URL: https://api.semanticscholar.org/CorpusID:4390794.
  12. Daniel Gottesman. Fault-tolerant quantum computation with constant overhead. Quantum Info. Comput., 14(15–16):1338-1372, November 2014. URL: https://doi.org/10.26421/QIC14.15-16-5.
  13. Shouzhen Gu, Eugene Tang, Libor Caha, Shin Ho Choe, Zhiyang He, and Aleksander Kubica. Single-shot decoding of good quantum ldpc codes. ArXiv, abs/2306.12470, 2023. URL: https://doi.org/10.48550/arXiv.2306.12470.
  14. Jeongwan Haah. An invariant of topologically ordered states under local unitary transformations. Communications in Mathematical Physics, 342(3):771-801, March 2016. URL: https://doi.org/10.1007/s00220-016-2594-y.
  15. Timo Hillmann, Guillaume Dauphinais, Ilan Tzitrin, and Michael Vasmer. Single-shot and measurement-based quantum error correction via fault complexes, 2024. URL: https://arxiv.org/abs/2410.12963.
  16. Mohsin Iqbal, Nathanan Tantivasadakarn, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Aaron Hankin, Nathan Hewitt, Chandler V. Horst, Mitchell Matheny, Tanner Mengle, Brian Neyenhuis, Ashvin Vishwanath, Michael Foss-Feig, Ruben Verresen, and Henrik Dreyer. Topological order from measurements and feed-forward on a trapped ion quantum computer. Communications Physics, 7(1):205, June 2024. URL: https://doi.org/10.1038/s42005-024-01698-3.
  17. Alexey A. Kovalev and Leonid P. Pryadko. Improved quantum hypergraph-product ldpc codes. In 2012 IEEE International Symposium on Information Theory Proceedings, pages 348-352, 2012. URL: https://doi.org/10.1109/ISIT.2012.6284206.
  18. Alexey A. Kovalev and Leonid P. Pryadko. Fault tolerance of quantum low-density parity check codes with sublinear distance scaling. Phys. Rev. A, 87:020304, February 2013. URL: https://doi.org/10.1103/PhysRevA.87.020304.
  19. Aleksander Kubica and Michael Vasmer. Single-shot quantum error correction with the three-dimensional subsystem toric code. Nature Communications, 13, 2021. URL: https://api.semanticscholar.org/CorpusID:235352916.
  20. Jong Yeon Lee, Wenjie Ji, Zhen Bi, and Matthew P. A. Fisher. Decoding measurement-prepared quantum phases and transitions: from ising model to gauge theory, and beyond, 2022. URL: https://arxiv.org/abs/2208.11699.
  21. Jong Yeon Lee, Yi-Zhuang You, and Cenke Xu. Symmetry protected topological phases under decoherence, 2024. URL: https://arxiv.org/abs/2210.16323.
  22. Tsung-Cheng Lu, Leonardo A. Lessa, Isaac H. Kim, and Timothy H. Hsieh. Measurement as a shortcut to long-range entangled quantum matter. PRX Quantum, 3:040337, December 2022. URL: https://doi.org/10.1103/PRXQuantum.3.040337.
  23. Robert Raussendorf, Sergey Bravyi, and Jim Harrington. Long-range quantum entanglement in noisy cluster states. Phys. Rev. A, 71:062313, June 2005. URL: https://doi.org/10.1103/PhysRevA.71.062313.
  24. Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, and Ruben Verresen. Long-range entanglement from measuring symmetry-protected topological phases. Phys. Rev. X, 14:021040, June 2024. URL: https://doi.org/10.1103/PhysRevX.14.021040.
  25. Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen. Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward. PRX Quantum, 4:020339, June 2023. URL: https://doi.org/10.1103/PRXQuantum.4.020339.
  26. Jean-Pierre Tillich and Gilles Zémor. Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength. IEEE Transactions on Information Theory, 60(2):1193-1202, 2014. URL: https://doi.org/10.1109/TIT.2013.2292061.
  27. Hengyun Zhou, Chen Zhao, Madelyn Cain, Dolev Bluvstein, Casey Duckering, Hong-Ye Hu, Sheng-Tao Wang, Aleksander Kubica, and Mikhail D. Lukin. Algorithmic fault tolerance for fast quantum computing, 2024. URL: https://arxiv.org/abs/2406.17653.
  28. Guo-Yi Zhu, Nathanan Tantivasadakarn, Ashvin Vishwanath, Simon Trebst, and Ruben Verresen. Nishimori’s cat: Stable long-range entanglement from finite-depth unitaries and weak measurements. Phys. Rev. Lett., 131:200201, November 2023. URL: https://doi.org/10.1103/PhysRevLett.131.200201.
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