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:2010.02064 · Physical Review A

Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations

Jian-Jian Cheng, Lin Zhang

Published Mar 29, 2021• 6 citations
arXivHTMLPDF

Abstract

We propose a simple but versatile protocol to engineer time-dependent Hamiltonians inversely for geometric quantum computation. By utilizing SU(2) transformation, a speedup goal on gate operation is achieved with more freedom to design the control parameters. As an application, this protocol enables the conventional and unconventional nonadiabatic geometric quantum gates with desired evolution paths by controlling the microwave pulses in the diamond nitrogen-vacancy center system. We show that the inversely designed Hamiltonian can fulfill the geometric gate with more economical evolution time and further reduces the influence of the environment noise on gate fidelity.

DOI
10.1103/physreva.103.032616

Related papers

Fast quantum state engineering via universal SU(2) transformation

Bi‐Hua Huang, Yi‐Hao Kang, Ye‐Hong Chen +3 more

We introduce a simple yet versatile protocol to inverse engineer the time-dependent Hamiltonian in two- and three-level systems. In the protocol, by utilizing a universal SU(2) transformation, a given speedup goal can be obtained with large freedom to select the control parameters. As an illustration example, the protocol is applied to perform population transfer between nitrogen-vacancy (NV) centers in diamond. Numerical simulation shows that the speed of the present protocol is fast compared with that of the adiabatic process. Moreover, the protocol is also tolerant to decoherence and experimental parameter fluctuations. Therefore, the protocol may be useful for designing an experimental feasible Hamiltonian to engineer a quantum system.

arXiv:1708.03433•Physical Review A•Aug 15, 2017•51 citations

Invariant-based inverse engineering for fast nonadiabatic geometric quantum computation

Wei Li

Abstract In this paper, based on first given Lewis–Riesenfeld invariant depicted by a unit vector in parameter space, we inverse engineering the time-dependent Hamiltonian of a system with su(2) Lie algebraic structure. The introduced method is then applied to investigate nonadiabatic Abelian geometric quantum computation. We demonstrate that, by employing the nonadiabatic Berry phase generated through nonadiabatic periodic evolution, a driven two-level system which undergoes a single cyclic evolution along a loop path in Bloch space can realize a universal set of one-qubit gates. Subsequently, under consideration of the influence of the systematic error and dissipation on nonadiabatic process, the result reveals arbitrary one-qubit gate can be implemented with a high fidelity. Moreover, to complete the universal set, arbitrary controlled-U gate is designed by utilizing a driven system consisted of a pair of coupled spin subsystems.

New Journal of Physics•Jul 1, 2021•10 citations

Parallel-path implementation of nonadiabatic geometric quantum gates in a decoherence-free subspace with nitrogen-vacancy centers

M.-R. Yun, F.-Q. Guo, L.-L. Yan +5 more

We propose a scheme for nonadiabatic noncyclic geometric quantum computation in a decoherence-free subspace (DFS). The physical system we used is a cavity quantum electrodynamics system consisting of nitrogen-vacancy (NV) centers in diamond and a whispering-gallery-mode (WGM) microresonator. This scheme not only has the feature of DFSs insensitive to decoherence, but also has the advantage of nonadiabatic noncyclic geometric quantum computation which has the built-in noise-resilience geometric feature and further enhances the robustness due to the ability beyond the limitation of the cyclic condition. An unconventional two-qubit phase gate in DFS has been realized in one step with our parallel protocol, which can largely shorten the computation time and the system error caused by decoherence. In addition, a scheme to realize a parallel process of two evolution paths is put forward to achieve the distribution quantum computation of two WGM microresonators containing a NV center in each. Our scheme may provide a promising way towards the practical realization of high-fidelity geometric quantum computation with the features of a DFS, geometric phase, and parallel implementation process.

Physical Review A•Jan 24, 2022•16 citations

A universal set of geometric quantum gates through dressed-states assisted shortcuts to adiabaticity

María E. Rus, Alejandro Ferrón, Omar Osenda +1 more

Abstract Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution times, making the system vulnerable to decoherence. In this work, we propose a scheme to realize fast and high-fidelity geometric quantum gates by applying the superadiabatic transitionless driving protocol within the dressed-state framework. We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field, focusing in particular on the nitrogen-vacancy center in diamond. We show how the dynamical phase can be canceled to obtain purely geometric operations. The robustness of the gates is assessed under systematic errors and environmental decoherence, demonstrating high fidelity even in regimes with strong fluctuations. Finally, we extend the protocol to construct nontrivial two-qubit gates, highlighting its feasibility for scalable quantum information processing.

arXiv:2509.08723•Journal of Physics B Atomic Molecular and Optical Physics•Feb 2, 2026•1 citation

Approach to realizing nonadiabatic geometric gates with prescribed evolution paths

K. Z. Li, P. Z. Zhao, D. M. Tong

The authors put forward an approach to the realization of nonadiabatic geometric quantum computation, by which a universal set of nonadiabatic geometric gates can be realized with any desired evolution paths. This approach makes it possible to realize geometric quantum computation with an economical evolution time, so that the influence of environment noises on the quantum gates can be minimized further

arXiv:2006.03837•Physical Review Research•Jun 5, 2020•44 citations

Nonadiabatic geometric quantum gates with on-demand trajectories

Yan Liang, Zheng‐Yuan Xue

High-fidelity quantum gates are an essential prerequisite for large-scale quantum computation. When manipulating practical quantum systems, environmentally and operationally induced errors are inevitable, and thus, in addition to being fast, it is preferable that operations should be intrinsically robust against different errors. Here, we propose a general protocol for constructing geometric quantum gates with on-demand trajectories by modulating the applied pulse shapes that define the system's evolution trajectory. Our scheme adopts reverse engineering of the target Hamiltonian using smooth pulses, which also eliminates the difficulty of calculating geometric phases for an arbitrary trajectory. Furthermore, because a particular geometric gate can be induced by various different trajectories, we can further optimize the gate performance under different scenarios; the results of numerical simulations indicate that this optimization can greatly enhance the quality of the gate. In addition, we present an implementation of our proposal using superconducting circuits, showcasing substantial enhancements in gate performance compared with conventional schemes. Our protocol thus presents a promising approach for high-fidelity and strong-robust geometric quantum gates for large-scale quantum computation.

arXiv:2401.11147•Physical Review Applied•Jun 20, 2024•11 citations
We propose a simple but versatile protocol to engineer time-dependent Hamiltonians inversely for geometric quantum computation. By utilizing SU(2) transformation, a speedup goal on gate operation is achieved with more freedom to design the control parameters. As an application, this protocol enables the conventional and unconventional nonadiabatic geometric quantum gates with desired evolution paths by controlling the microwave pulses in the diamond nitrogen-vacancy center system. We show that the inversely designed Hamiltonian can fulfill the geometric gate with more economical evolution time and further reduces the influence of the environment noise on gate fidelity.
We introduce a simple yet versatile protocol to inverse engineer the time-dependent Hamiltonian in two- and three-level systems. In the protocol, by utilizing a universal SU(2) transformation, a given speedup goal can be obtained with large freedom to select the control parameters. As an illustration example, the protocol is applied to perform population transfer between nitrogen-vacancy (NV) centers in diamond. Numerical simulation shows that the speed of the present protocol is fast compared with that of the adiabatic process. Moreover, the protocol is also tolerant to decoherence and experimental parameter fluctuations. Therefore, the protocol may be useful for designing an experimental feasible Hamiltonian to engineer a quantum system.
Abstract In this paper, based on first given Lewis–Riesenfeld invariant depicted by a unit vector in parameter space, we inverse engineering the time-dependent Hamiltonian of a system with su(2) Lie algebraic structure. The introduced method is then applied to investigate nonadiabatic Abelian geometric quantum computation. We demonstrate that, by employing the nonadiabatic Berry phase generated through nonadiabatic periodic evolution, a driven two-level system which undergoes a single cyclic evolution along a loop path in Bloch space can realize a universal set of one-qubit gates. Subsequently, under consideration of the influence of the systematic error and dissipation on nonadiabatic process, the result reveals arbitrary one-qubit gate can be implemented with a high fidelity. Moreover, to complete the universal set, arbitrary controlled-U gate is designed by utilizing a driven system consisted of a pair of coupled spin subsystems.
We propose a scheme for nonadiabatic noncyclic geometric quantum computation in a decoherence-free subspace (DFS). The physical system we used is a cavity quantum electrodynamics system consisting of nitrogen-vacancy (NV) centers in diamond and a whispering-gallery-mode (WGM) microresonator. This scheme not only has the feature of DFSs insensitive to decoherence, but also has the advantage of nonadiabatic noncyclic geometric quantum computation which has the built-in noise-resilience geometric feature and further enhances the robustness due to the ability beyond the limitation of the cyclic condition. An unconventional two-qubit phase gate in DFS has been realized in one step with our parallel protocol, which can largely shorten the computation time and the system error caused by decoherence. In addition, a scheme to realize a parallel process of two evolution paths is put forward to achieve the distribution quantum computation of two WGM microresonators containing a NV center in each. Our scheme may provide a promising way towards the practical realization of high-fidelity geometric quantum computation with the features of a DFS, geometric phase, and parallel implementation process.
Abstract Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution times, making the system vulnerable to decoherence. In this work, we propose a scheme to realize fast and high-fidelity geometric quantum gates by applying the superadiabatic transitionless driving protocol within the dressed-state framework. We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field, focusing in particular on the nitrogen-vacancy center in diamond. We show how the dynamical phase can be canceled to obtain purely geometric operations. The robustness of the gates is assessed under systematic errors and environmental decoherence, demonstrating high fidelity even in regimes with strong fluctuations. Finally, we extend the protocol to construct nontrivial two-qubit gates, highlighting its feasibility for scalable quantum information processing.
High-fidelity quantum gates are an essential prerequisite for large-scale quantum computation. When manipulating practical quantum systems, environmentally and operationally induced errors are inevitable, and thus, in addition to being fast, it is preferable that operations should be intrinsically robust against different errors. Here, we propose a general protocol for constructing geometric quantum gates with on-demand trajectories by modulating the applied pulse shapes that define the system's evolution trajectory. Our scheme adopts reverse engineering of the target Hamiltonian using smooth pulses, which also eliminates the difficulty of calculating geometric phases for an arbitrary trajectory. Furthermore, because a particular geometric gate can be induced by various different trajectories, we can further optimize the gate performance under different scenarios; the results of numerical simulations indicate that this optimization can greatly enhance the quality of the gate. In addition, we present an implementation of our proposal using superconducting circuits, showcasing substantial enhancements in gate performance compared with conventional schemes. Our protocol thus presents a promising approach for high-fidelity and strong-robust geometric quantum gates for large-scale quantum computation.