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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…

Quantum Physics · Physics 2026-04-21 Fucheng Guo , Frank Mueller , Yuan Liu

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For…

We initiate the study of state complexity for continuous-variable quantum systems. Concretely, we consider a setup with bosonic modes and auxiliary qubits, where available operations include Gaussian one- and two-mode operations, single-…

Quantum Physics · Physics 2025-11-06 Lukas Brenner , Libor Caha , Xavier Coiteux-Roy , Robert Koenig

The Gottesman-Kitaev-Preskill (GKP) coding is proven to be a good candidate for encoding a qubit on continuous variables (CV) since it is robust under random-shift disturbance. Its preparation in optical systems, however, is challenging to…

Quantum Physics · Physics 2024-12-24 Fattah Sakuldee

Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation…

Quantum Physics · Physics 2008-07-04 Mitsuyoshi Yukawa , Ryuji Ukai , Peter van Loock , Akira Furusawa

We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of…

Quantum Physics · Physics 2022-02-14 Jonathan Conrad , Jens Eisert , Francesco Arzani

Quantum repeaters that incorporate quantum error correction codes have been shown to be a promising alternative compared with the original quantum repeaters that rely upon probabilistic quantum error detection depending on classical…

Quantum Physics · Physics 2024-06-12 Stefan Häussler , Peter van Loock

The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum…

Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space…

Quantum Physics · Physics 2026-05-01 Zi-Xu Lu , Gang Liu , Matteo Fadel , Jie Li

A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model…

We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs,…

Quantum Physics · Physics 2007-12-23 Nicolas C. Menicucci , Steven T. Flammia , Hussain Zaidi , Olivier Pfister

We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states…

Quantum Physics · Physics 2026-01-14 Jonathan Conrad , Joseph T. Iosue , Ansgar G. Burchards , Victor V. Albert

Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…

Quantum Physics · Physics 2021-03-26 Jing Wu , Quntao Zhuang

Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate because one can achieve fault-tolerance with a probabilistic supply of GKP states and…

Quantum Physics · Physics 2024-02-07 Matthew P. Stafford , Nicolas C. Menicucci

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode is a promising bosonic code for quantum computation due to its tolerance for noise and all-Gaussian gate set. We present a toolkit for phase-space description and…

Quantum Physics · Physics 2021-08-26 Lucas J. Mensen , Ben Q. Baragiola , Nicolas C. Menicucci

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

Hybrid continuous-variable--discrete-variable (CV--DV) architectures process quantum information in bosonic modes and qubits, but noise limits their performance. To reduce the noise, existing DV error correction must be complemented by CV…

Quantum Physics · Physics 2026-04-22 Mohammad Nobakht , Ivan Kassal

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

Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively…

Quantum Physics · Physics 2025-09-17 A. Govindarajan , M. Mazzei , H. Wang , L. Tian

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by taking the advantages of both…

Quantum Physics · Physics 2025-03-19 Jaehak Lee , Nuri Kang , Seok-Hyung Lee , Hyunseok Jeong , Liang Jiang , Seung-Woo Lee