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The Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code has emerged as a key technique in achieving fault-tolerant quantum computation using photonic systems. Whereas [Baragiola et al., Phys. Rev. Lett. 123, 200502 (2019)] showed…

Quantum Physics · Physics 2020-11-10 Hayata Yamasaki , Takaya Matsuura , Masato Koashi

Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus…

Quantum Physics · Physics 2019-08-02 Yang Wang

Quantum error correction is essential for achieving fault-tolerant quantum computing. Gottesman-Kitaev-Preskill (GKP) codes are particularly effective at correcting continuous noise, such as Gaussian noise and loss, and can significantly…

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum…

Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental…

Quantum Physics · Physics 2019-09-06 Yunong Shi , Christopher Chamberland , Andrew W. Cross

Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator…

Quantum Physics · Physics 2025-05-13 Anthony J. Brady , Alec Eickbusch , Shraddha Singh , Jing Wu , Quntao Zhuang

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic candidate for realizing fault-tolerant quantum computation. Among existing error-correction protocols for GKP code, the Steane-type scheme is a canonical and widely adopted…

Quantum Physics · Physics 2026-04-10 Xiang-Jiang Chen , Hao-Miao Jiang , Liu-Jun Wang , Qing Chen

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous…

The realisation of a universal quantum computer at scale promises to deliver a paradigm shift in information processing, providing the capability to solve problems that are intractable with conventional computers. A key limiting factor of…

Quantum Physics · Physics 2024-09-10 V. G. Matsos , C. H. Valahu , M. J. Millican , T. Navickas , X. C. Kolesnikow , M. J. Biercuk , T. R. Tan

Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond…

Quantum Physics · Physics 2024-09-20 Anthony J. Brady , Jing Wu , Quntao Zhuang

With the significance of continuous-variable quantum computing increasing thanks to the achievements of light-based quantum hardware, making it available to learner audiences outside physics has been an important yet seldom-tackled…

Quantum Physics · Physics 2025-07-10 Richard A. Wolf , Pavithran Iyer

To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available…

Decoherence errors arising from noisy environments remain a central obstacle to progress in quantum computation and information processing. Quantum error correction (QEC) based on the Gottesman-Kitaev-Preskill (GKP) protocol offers a…

We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors…

Quantum Physics · Physics 2020-11-18 Lisa Hänggli , Margret Heinze , Robert Koenig

Straightforward logical operations contrasting with complex state preparation are the hallmarks of the bosonic encoding proposed by Gottesman, Kitaev and Preskill (GKP). The recently reported generation and error-correction of GKP qubits in…

Quantum Physics · Physics 2023-09-20 Christian Siegele , Philippe Campagne-Ibarcq

Continuous-variable measurement-based quantum computation, which requires deterministically generated large-scale cluster state, is a promising candidate for practical, scalable, universal, and fault-tolerant quantum computation. In this…

Quantum Physics · Physics 2025-06-03 Peilin Du , Jing Zhang , Tiancai Zhang , Rongguo Yang , Jiangrui Gao

The Gottesman-Kitaev-Preskill (GKP) quantum error correcting code attracts much attention in continuous variable (CV) quantum computation and CV quantum communication due to the simplicity of error correcting routines and the high tolerance…

Quantum Physics · Physics 2020-09-23 Takaya Matsuura , Hayata Yamasaki , Masato Koashi

Quantum error correction is an essential ingredient in the development of quantum technologies. Its subject is to investigate ways to embed quantum Hilbert spaces into a physical system such that this subspace is robust against small…

Quantum Physics · Physics 2024-12-04 Jonathan Conrad

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic quantum error-correcting code, encoding logical qubits into a bosonic mode in such a way that many physically relevant noise types can be corrected effectively. A particularly…

Quantum Physics · Physics 2023-11-17 Jacob Hastrup , Ulrik L. Andersen

We review some of the recent efforts in devising and engineering bosonic qubits for superconducting devices, with emphasis on the Gottesman-Kitaev-Preskill (GKP) qubit. We present some new results on decoding repeated GKP error correction…

Quantum Physics · Physics 2020-06-08 Barbara M. Terhal , Jonathan Conrad , Christophe Vuillot