Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
Open accessAbstract
We introduce a new approach to Gottesman-Kitaev-Preskill (GKP) states that treats their finite-energy version in an exact manner. Based on this analysis, we develop new qubit-oscillator circuits that autonomously stabilize a GKP manifold, correcting errors without relying on qubit measurements. Finally, we show numerically that logical information encoded in GKP states is very robust against typical oscillator noise sources when stabilized by these new circuits.
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The CPd gate is designed for the ideal GKP code and will necessarily incur infidelity when applied to the finite-energy code.
“We emphasize that this CPd gate is designed for the ideal GKP code and will necessarily incur infidelity when applied to the finite-energy code, but it may be possible to adapt this construction to the finite-energy case32,43,55.”
From Quantum error correction of qudits beyond break-even (2025) · cites this paper as [43]
The generalized SBS circuit realizes autonomous QEC of the finite-energy GKP code with respect to the ideal stabilizer.
“The generalized SBS circuit in Fig. 1c realizes autonomous QEC of the finite-energy GKP code with respect to the ideal stabilizer (ref. 43).”
From Quantum error correction of qudits beyond break-even (2025) · cites this paper as [43]
Cites
Experimental issues in coherent quantum-state manipulation of trapped atomic ions
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Encoding a qubit in a trapped-ion mechanical oscillator
Flühmann, C., Nguyen, T. L., Marinelli, M., Negnevitsky, V., Mehta, K., & Home, J. P. (2019) · Nature · doi:10.1038/s41586-019-0960-6 · Cited by 394 · see citing works
Exponential suppression of bit-flips in a qubit encoded in an oscillator
Lescanne, R., Villiers, M., Peronnin, T., Sarlette, A., Delbecq, M., Huard, B., Kontos, T., Mirrahimi, M., & Leghtas, Z. (2020) · Nature Physics · doi:10.1038/s41567-020-0824-x · Cited by 276 · see citing works
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Real-time quantum error correction beyond break-even
Sivak, V. V., Eickbusch, A., Royer, B., Singh, S., Tsioutsios, I., Ganjam, S., Miano, A., Brock, B. L., Ding, A. Z., Frunzio, L., et al. (2023) · Nature · doi:10.1038/s41586-023-05782-6 · Cited by 407 · see citing works
Self-citationFast universal control of an oscillator with weak dispersive coupling to a qubit
Eickbusch, A., Sivak, V., Ding, A. Z., Elder, S. S., Jha, S. R., Venkatraman, J., Royer, B., Girvin, S. M., Schoelkopf, R. J., & Devoret, M. H. (2022) · Nature Physics · doi:10.1038/s41567-022-01776-9 · Cited by 173 · see citing works
Self-citationQuantum error correction of qudits beyond break-even
Brock, B. L., Singh, S., Eickbusch, A., Sivak, V. V., Ding, A. Z., Frunzio, L., Girvin, S. M., & Devoret, M. H. (2025) · Nature · doi:10.1038/s41586-025-08899-y · Cited by 64 · see citing works
Self-citationSchmidt, F., & van Loock, P. (2022) · Physical Review A · doi:10.1103/physreva.105.042427 · Cited by 20 · see citing works
Two-Qubit Operations for Finite-Energy Gottesman-Kitaev-Preskill Encodings
Rojkov, I., Röggla, P. M., Wagener, M., Fontboté-Schmidt, M., Welte, S., Home, J., & Reiter, F. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.100601 · Cited by 12 · see citing works
- Authors
- Royer, B., Singh, S., & Girvin, S. M.
- Affiliations
- Yale University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2020-12-31
- Volume
- 125
- Issue
- 26
- Pages
- 260509-260509
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3085342944
- Cited by
- 88
- References
- 3
- Citations by year
- 2026: 13 · 2025: 22 · 2024: 12 · 2023: 14 · 2022: 16 · 2021: 11
- FWCI
- 4.03
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Army Research Office (W911NF-18-1-0212)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Gottesman-Kitaev-Preskill states, oscillator noise, continuous-variable quantum information
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