Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Continuous-variable quantum error correction I: code comparison

Victor V. Albert, Kasper Duivenvoorden, Kyungjoo Noh, Richard Brierley, Philip Reinhold, Linshu Li, Chao Shen, Robert J. Schoelkopf, S. M. Girvin, Barbara M. Terhal, Liang Jiang

Published Mar 16, 2017• 0 citations
OpenAlex

Related papers

Continuous-variable quantum error correction II: the Gottesman-Kitaev-Preskill code

Kyungjoo Noh, Kasper Duivenvoorden, Victor V. Albert +8 more

Bulletin of the American Physical Society•Mar 16, 2017•0 citations

Discrete-variable assisted error correction of continuous-variable quantum information

Negin Razian, En-Jui Chang, Hoi-Kwan Lau

Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.

quant-pharXiv:2604.06565•Apr 9, 2026•0 citations

Experimental Realization of Continuous-Variable Quantum Error Correction Codes

Mikael Lassen, Lars S. Madsen, Ulrik L. Andersen

•Jan 1, 2011•0 citations

Quantum Error-Correction Codes

Mahn‐Soo Choi

Springer eBooks•Jan 1, 2022•0 citations

A Concatenated Dual Displacement Code for Continuous-Variable Quantum Error Correction

Fucheng Guo, Frank Mueller, Yuan Liu

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors, but when the displacement magnitude becomes large, lattice-crossing events arise beyond the correctable range of the GKP state. To address this issue, we concatenate a Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Unlike conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against both large and small displacement errors, enabling CV error correction within the continuous encoding space and contrasting with earlier approaches that concatenate GKP states with repetition codes for discrete qubit or qudit encodings. Analytical results show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors across all qumodes by up to 50 percent while enabling unbiased correction of lattice-crossing events, with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture continues to provide Gaussian-error suppression together with lattice-crossing correction, and the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides new insight into the design of concatenated CV error-correcting architectures.

quant-pharXiv:2512.00481•Physical Review Research•Dec 2, 2025•0 citations

Stabilizer Codes for Continuous-variable Quantum Error Correction

Barnes, Richard L.

A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable codes presented to date, and can be used to construct new codes based on discrete-variable codes or classical codes. We use it to describe the nine-mode code given by Lloyd and Slotine, and a five-mode code described by Braunstein. In addition, we construct a new continuous-variable code based an code of Gottesman which encodes three logical modes of information into eight physical modes and corrects one error. This generalization is a step toward an independent understanding of continuous-variable quantum information and a theory of fault-tolerant quantum information processing.

arXiv:quant-ph/0405064•May 13, 2004•11 citations
Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.
The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors, but when the displacement magnitude becomes large, lattice-crossing events arise beyond the correctable range of the GKP state. To address this issue, we concatenate a Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Unlike conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against both large and small displacement errors, enabling CV error correction within the continuous encoding space and contrasting with earlier approaches that concatenate GKP states with repetition codes for discrete qubit or qudit encodings. Analytical results show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors across all qumodes by up to 50 percent while enabling unbiased correction of lattice-crossing events, with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture continues to provide Gaussian-error suppression together with lattice-crossing correction, and the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides new insight into the design of concatenated CV error-correcting architectures.
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable codes presented to date, and can be used to construct new codes based on discrete-variable codes or classical codes. We use it to describe the nine-mode code given by Lloyd and Slotine, and a five-mode code described by Braunstein. In addition, we construct a new continuous-variable code based an code of Gottesman which encodes three logical modes of information into eight physical modes and corrects one error. This generalization is a step toward an independent understanding of continuous-variable quantum information and a theory of fault-tolerant quantum information processing.