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

arXiv:2510.04209 · Physical Review Letters

Quantum Error Correction with Superpositions of Squeezed Fock States

Ye‐Xiong Zeng, Fernando Quijandría, Clemens Gneiting, Franco Nori

Published Apr 20, 2026• 1 citation
arXivHTMLPDF

Abstract

Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, a practical continuous-variable bosonic code that can simultaneously correct both photon loss and dephasing errors, while achieving a high level of compliance with the Knill-Laflamme conditions within an experimentally friendly structure, remains elusive. Here, we propose a code based on the superposition of squeezed Fock states with an error-correcting capability that scales as ∝exp(-7r), where r is the squeezing level. The codewords remain orthogonal at all squeezing levels. In particular, this code achieves high-precision error correction for both single-photon loss and dephasing, even at moderate squeezing levels. Building on this code, we develop quantum error correction schemes that exceed the breakeven point, supported by analytical derivations of all necessary quantum gates. Our code offers a competitive alternative to previous encodings for quantum computation using continuous bosonic qubits.

DOI
10.1103/hr5f-lvy7

Related papers

Squeezed-vacuum bosonic codes

Nir Gutman, Eliya Blumenthal, Shay Hacohen-Gourgy +2 more

We introduce a family of bosonic quantum error-correcting codes built as a rotation-symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these "squeezed-vacuum codes" arises from being arranged at evenly spaced angles in phase-space, and simultaneously in evenly spaced photon-number support $n \equiv {2k} \! \pmod {2m}$. We present simple preparation circuits: a two-legged code using a Hadamard-conditional-squeezing-Hadamard sequence on an ancilla qubit, and for general "$m$-legged" codewords using sequences of conditional rotations. The performance of these codes is evaluated against loss and dephasing noises using the Knill-Laflamme violation function and benchmarked against cat codes. As the number $m$ of squeezed-vacuum states in a code increases, the code exhibits improved loss tolerance at the cost of higher dephasing sensitivity. We outline implementations in circuit QED and trapped-ion platforms, where high-fidelity Gaussian operations and conditional controls are available or under active development. These results help establish squeezed-vacuum codes as practical, hardware-ready, members of the bosonic codes class.

quant-pharXiv:2511.06108•Advanced Physics Research•Nov 11, 2025•0 citations

Bosonic quantum error correction using squeezed Fock states

E. N. Bashmakova, S. B. Korolev, T. Yu. Golubeva

In the paper, we develop a bosonic quantum error correction code based on squeezed Fock states. We compare our proposed code with one based on squeezed Schrodinger's cat states using the Knill-Laflamme cost function and the Petz map fidelity. We demonstrate that squeezed Fock states are competitive in protecting information in a channel with particle loss and dephasing.

arXiv:2506.00300•Physical Review A•Sep 5, 2025•5 citations

Quantum error correction using squeezed Schrödinger cat states

David S. Schlegel, Fabrizio Minganti, Vincenzo Savona

Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schr\"odinger cat codes---based on the superposition of two coherent states with opposite displacements---can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e., cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.

arXiv:2201.02570•Physical Review A•Aug 25, 2022•83 citations

Enhancing bosonic qubit protection by squeezing

R. Rousseau, Diego Ruiz, E. Albertinale +38 more

Bosonic qubits implement error correction by harnessing the high-dimensional Hilbert space of a harmonic oscillator to redundantly encode logical quantum information. Squeezing of quantum states — a cornerstone of precision metrology — redistributes uncertainty between conjugate quadratures to enhance sensitivity in one variable at the expense of the other. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. By redistributing uncertainty to that quadrature, squeezing can be leveraged to reduce the environment’s measurement strength, thereby prolonging coherence. Here, we exploit this insight to implement a squeezing deformation of the simplest bosonic code — the cat qubit — extending the bit-flip time with minimal impact on the phase-flip rate. We observe a dramatic reduction in bit-flip errors, achieving a 160-fold improvement over standard cat qubits and bringing multi-cat architectures closer to fault-tolerant quantum computation. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. Here, the authors show how to use squeezing to further protect bosonic codes from noise, extending the bit-flip times of the cat qubit by two orders of magnitude without reducing phase-flip times.

Nature Communications•Oct 22, 2026•0 citations

Quantum capacity and codes for the bosonic loss-dephasing channel

Peter Leviant, Qian Xu, Liang Jiang +1 more

Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.

arXiv:2205.00341•Quantum•Sep 29, 2022•37 citations

Quantum Computation and Communication in Bosonic Systems

Kyungjoo Noh

Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.

arXiv:2103.09445•Mar 17, 2021•2 citations
Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, a practical continuous-variable bosonic code that can simultaneously correct both photon loss and dephasing errors, while achieving a high level of compliance with the Knill-Laflamme conditions within an experimentally friendly structure, remains elusive. Here, we propose a code based on the superposition of squeezed Fock states with an error-correcting capability that scales as ∝exp(-7r), where r is the squeezing level. The codewords remain orthogonal at all squeezing levels. In particular, this code achieves high-precision error correction for both single-photon loss and dephasing, even at moderate squeezing levels. Building on this code, we develop quantum error correction schemes that exceed the breakeven point, supported by analytical derivations of all necessary quantum gates. Our code offers a competitive alternative to previous encodings for quantum computation using continuous bosonic qubits.
We introduce a family of bosonic quantum error-correcting codes built as a rotation-symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these "squeezed-vacuum codes" arises from being arranged at evenly spaced angles in phase-space, and simultaneously in evenly spaced photon-number support n≡2k ⁣(mod2m)n \equiv {2k} \! \pmod {2m}n≡2k(mod2m). We present simple preparation circuits: a two-legged code using a Hadamard-conditional-squeezing-Hadamard sequence on an ancilla qubit, and for general "mmm-legged" codewords using sequences of conditional rotations. The performance of these codes is evaluated against loss and dephasing noises using the Knill-Laflamme violation function and benchmarked against cat codes. As the number mmm of squeezed-vacuum states in a code increases, the code exhibits improved loss tolerance at the cost of higher dephasing sensitivity. We outline implementations in circuit QED and trapped-ion platforms, where high-fidelity Gaussian operations and conditional controls are available or under active development. These results help establish squeezed-vacuum codes as practical, hardware-ready, members of the bosonic codes class.
Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schr\"odinger cat codes---based on the superposition of two coherent states with opposite displacements---can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e., cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.
Bosonic qubits implement error correction by harnessing the high-dimensional Hilbert space of a harmonic oscillator to redundantly encode logical quantum information. Squeezing of quantum states — a cornerstone of precision metrology — redistributes uncertainty between conjugate quadratures to enhance sensitivity in one variable at the expense of the other. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. By redistributing uncertainty to that quadrature, squeezing can be leveraged to reduce the environment’s measurement strength, thereby prolonging coherence. Here, we exploit this insight to implement a squeezing deformation of the simplest bosonic code — the cat qubit — extending the bit-flip time with minimal impact on the phase-flip rate. We observe a dramatic reduction in bit-flip errors, achieving a 160-fold improvement over standard cat qubits and bringing multi-cat architectures closer to fault-tolerant quantum computation. In bosonic codes, decoherence can be seen as the environment performing an unwanted measurement on a noise-sensitive quadrature, collapsing superpositions and inducing errors. Here, the authors show how to use squeezing to further protect bosonic codes from noise, extending the bit-flip times of the cat qubit by two orders of magnitude without reducing phase-flip times.
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.