quantum-computing

Enlarging the GKP stabilizer group for enhanced noise protection

Quantum Science and Technology (arXiv overlay)

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Researchers Jonathan Pelletier and Baptiste Royer have expanded the stabilizer group of Gottesman-Kitaev-Preskill (GKP) codes to include all operations with trivial action on the code space, enhancing noise protection for bosonic qubits. By identifying the generators of the Gaussian stabilizer group, they enabled the exploration of alternative physical implementations for Clifford operations. The team developed an algorithm to optimize the execution of logical Clifford circuits on GKP codes, minimizing the impact of loss errors during computation. Numerical tests using logical randomized benchmarking showed that this compiler significantly extends the lifetime of square-GKP qubits running Clifford circuits compared to a random walk compiler.

Why it matters

This work advances fault-tolerant quantum computation by offering a systematic way to mitigate loss errors in GKP-encoded qubits, a critical step toward practical, noise-resilient logical circuits in bosonic systems.

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AbstractEncoding a qubit in a larger Hilbert space of an oscillator is an efficient way to protect its quantum information against decoherence. Promising examples of such bosonic encodings are the Gottesman-Kitaev-Preskill (GKP) codes. In this work, we investigate how redefining the stabilizer group of the GKP codes to include all operations with trivial action on the code space can contribute to the search for an optimal implementation of a logical circuit when it is affected by noise. We find the generators of the Gaussian stabilizer group, allowing us to search for different physical implementations of a Clifford operation. We then propose an algorithm that finds the optimal implementation of a given logical Clifford circuit on GKP codes, such that the state is less affected by loss errors during the computation. Finally, we demonstrate numerically, with logical randomized benchmarking, that such a compiler can increase the lifetime of square-GKP qubits while running Clifford circuits, compared to a random walk compiler.► BibTeX data@article{Pelletier2026enlarginggkp, doi = {10.22331/q-2026-07-08-2156}, url = {https://doi.org/10.22331/q-2026-07-08-2156}, title = {Enlarging the {GKP} stabilizer group for enhanced noise protection}, author = {Pelletier, Jonathan and Royer, Baptiste}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2156}, month = jul, year = {2026} }► References [1] V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsioutsios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret. ``Real-time quantum error correction beyond break-even''. Nature 616, 50–55 (2023). arXiv:2211.09116. https://doi.org/10.1038/s41586-023-05782-6 arXiv:2211.09116 [2] Dany Lachance-Quirion, Marc-Antoine Lemonde, Jean Olivier Simoneau, Lucas St-Jean, Pascal Lemieux, Sara Turcotte, Wyatt Wright, Amélie Lacroix, Joëlle Fréchette-Viens, Ross Shillito, Florian Hopfmueller, Maxime Tremblay, Nicholas E. Frattini, Julien Camirand Lemyre, and Philippe St-Jean. ``Autonomous Quantum Error Correction of Gottesman-Kitaev-Preskill States''.

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Springer Berlin Heidelberg. Berlin, Heidelberg (1999). https://doi.org/10.1007/978-3-662-03875-8Cited by[1] Marc-Antoine Roy, Thomas Pousset, and Baptiste Royer, "Decoding Multimode Gottesman-Kitaev-Preskill Codes with Noisy Auxiliary States", arXiv:2510.12677, (2025). The above citations are from SAO/NASA ADS (last updated successfully 2026-07-08 19:13:31). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-07-08 19:13:30: Could not fetch cited-by data for 10.22331/q-2026-07-08-2156 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractEncoding a qubit in a larger Hilbert space of an oscillator is an efficient way to protect its quantum information against decoherence. Promising examples of such bosonic encodings are the Gottesman-Kitaev-Preskill (GKP) codes. In this work, we investigate how redefining the stabilizer group of the GKP codes to include all operations with trivial action on the code space can contribute to the search for an optimal implementation of a logical circuit when it is affected by noise. We find the generators of the Gaussian stabilizer group, allowing us to search for different physical implementations of a Clifford operation. We then propose an algorithm that finds the optimal implementation of a given logical Clifford circuit on GKP codes, such that the state is less affected by loss errors during the computation. Finally, we demonstrate numerically, with logical randomized benchmarking, that such a compiler can increase the lifetime of square-GKP qubits while running Clifford circuits, compared to a random walk compiler.► BibTeX data@article{Pelletier2026enlarginggkp, doi = {10.22331/q-2026-07-08-2156}, url = {https://doi.org/10.22331/q-2026-07-08-2156}, title = {Enlarging the {GKP} stabilizer group for enhanced noise protection}, author = {Pelletier, Jonathan and Royer, Baptiste}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2156}, month = jul, year = {2026} }► References [1] V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsioutsios, S. Ganjam, A. Miano, B. L. Brock, A. Z. Ding, L. Frunzio, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret. ``Real-time quantum error correction beyond break-even''. Nature 616, 50–55 (2023). arXiv:2211.09116. https://doi.org/10.1038/s41586-023-05782-6 arXiv:2211.09116 [2] Dany Lachance-Quirion, Marc-Antoine Lemonde, Jean Olivier Simoneau, Lucas St-Jean, Pascal Lemieux, Sara Turcotte, Wyatt Wright, Amélie Lacroix, Joëlle Fréchette-Viens, Ross Shillito, Florian Hopfmueller, Maxime Tremblay, Nicholas E. Frattini, Julien Camirand Lemyre, and Philippe St-Jean. ``Autonomous Quantum Error Correction of Gottesman-Kitaev-Preskill States''.

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Enlarging the GKP stabilizer group for enhanced noise protection

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