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:2110.01933 · Physical Review Research

Nonadiabatic geometric quantum computation with cat-state qubits via invariant-based reverse engineering

Yi‐Hao Kang, Ye‐Hong Chen, Xin Wang, Jie Song, Yan Xia, Adam Miranowicz, Shi‐Biao Zheng, Franco Nori

Published Mar 28, 2022• 77 citations
arXivHTMLPDF

Abstract

We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schr\"odinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, $1/f$ noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.

DOI
10.1103/physrevresearch.4.013233

Related papers

Nonadiabatic geometric quantum computation of W-state codes using invariant-based reverse engineering

Sheng Wang, Wen-Shu Ni, Zewen Chen +4 more

Abstract In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.

Laser Physics Letters•Dec 8, 2022•1 citation

Error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering

Yi‐Hao Kang, Jie Song, Yan Xia

We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.

Optics Letters•Jul 19, 2022•22 citations

Effective implementation of nonadiabatic geometric quantum gates of cat-state qubits using an auxiliary qutrit

Yi‐Hao Kang, Yang Xiao, Zhi‐Cheng Shi +4 more

Abstract We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.

New Journal of Physics•Mar 1, 2023•22 citations

Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering

Meng-Yun Mao, Zheng Cheng, Yan Xia +2 more

Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity $(>99.99%)$ phase gates, such as the $\ensuremath{\pi}/8$ gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.

arXiv:2309.16470•Physical Review A•Sep 27, 2023•9 citations

Generalized Kerr-Cat Qubit Codes

Alonso Viladomat, Shahram Dehdashti, Amin Kargarian +2 more

We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between $\mathfrak{su}(2)$, $\mathfrak{su}(1,1)$ coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.

quant-pharXiv:2606.14901•Jun 16, 2026•0 citations

Noise-resilient nonadiabatic geometric quantum computation for bosonic binomial codes

Dong-Sheng Li, Yang Xiao, Yu Wang +5 more

The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.

quant-pharXiv:2603.17250•Science China Physics Mechanics and Astronomy•Mar 19, 2026•1 citation
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schr"odinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, 1/f1/f1/f noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.
Abstract In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.
We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.
Abstract We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.
Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity (>99.99(>99.99%)(>99.99 phase gates, such as the $\ensuremath{\pi}/8$ gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.
We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between su(2)\mathfrak{su}(2)su(2), su(1,1)\mathfrak{su}(1,1)su(1,1) coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.
The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.