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

Error-tolerant multiqubit holonomic entangling gates

Jin‐Lei Wu, Yan Wang, Jin‐Xuan Han, Yongyuan Jiang, Jie Song, Yan Xia, Shi‐Lei Su, Weibin Li

Published Dec 5, 2020• 1 citation
OpenAlex

Abstract

Nonadiabatic holonomic quantum computation, focusing mainly on implementing universal single- and two-qubit gates, commonly suffers gate fidelity losses inevitably due to the presence of systematic errors. Here we propose to realize fast holonomic multiqubit controlled~(C$_N$-NOT) Rydberg atom gates. Uniquely, the gate time is independent of the control qubit number $N$. We show that the fast gate is largely immune to laser parameter fluctuations and motional dephasing. The high tolerance of systematic errors can be further enhanced through optimal pulse engineering. The proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade, and moreover can be implemented alternatively with superconducting circuits. Our study paves a new way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or superconducting circuits, and hence contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superdonducting devices.

Related papers

Systematic-Error-Tolerant Multiqubit Holonomic Entangling Gates

Jin‐Lei Wu, Yan Wang, Jin‐Xuan Han +5 more

Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic $(N+1)$-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multibody Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the $N$ control atoms largely remain in the very stable qubit space during the operation. We show that ${C}_{N}$-not gates can reach the same level of fidelity at a given gate time for $N\ensuremath{\le}5$ under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In the case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves an alternative way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts to develop scalable quantum computation with trapped atoms and fabricable superconducting devices.

arXiv:2012.02935•Physical Review Applied•Dec 13, 2021•43 citations

Time-optimal holonomic quantum gates on Rydberg atoms

Jia-Qi Li, Hongxuan Li, P.-Y. 佩瑶 Song 宋 +3 more

Abstract Nonadiabatic holonomic quantum computation (NHQC) has attracted significant interest due to its intrinsic robustness against local parameter fluctuations. However, conventional NHQC schemes are constrained by long evolution times, with all gate operations requiring the same duration regardless of the rotation angle, leading to increased susceptibility to decoherence. In this paper, we propose a time-optima NHQC (TONHQC) scheme in the Rydberg atomic system, which minimizes gate operation time while maintaining geometric robustness. By solving the quantum brachistochrone equation (QBE), we derive an optimal trajectory for state evolution. We demonstrate the feasibility of TONHQC using87Rb atoms by constructing high-fidelity geometric two-qubit gates. Numerical simulations for controlled-Hadamard (C-H), controlled-π/4 (C-S) and controlled-π/8 (C-T) gates confirm that TONHQC outperforms conventional NHQC protocols, achieving higher fidelity and enhanced resilience against spontaneous emission and Rabi frequency fluctuations. These findings suggest that TONHQC as a promising approach for realizing high-fidelity holonomic quantum gates in Rydberg atom systems, paving the way for scalable and fault-tolerant quantum computation.

Physica Scripta•Aug 1, 2025•2 citations

Fast realization of high-fidelity nonadiabatic holonomic quantum gates with a time-optimal-control technique in Rydberg atoms

Pengtao Song, J.-F. Wei, Peng Xu +4 more

The nonadiabatic holonomic quantum computation (NHQC) has received great attention for decades, however, there are many challenges to its implementation in experiments. To further shorten the evolution time is the first challenge to be conquered to realize high-fidelity quantum gates in NHQC. In this paper, we propose a controlled two-qubit model in Rydberg atoms to realize nonadiabatic holonomic quantum gates, where the evolution time is extremely decreased and the influences of several kinds of noises are minimized by utilizing the time-optimal-control technique on the target atom. In addition, we can construct arbitrary geometric gates by selecting the appropriate parameters in our model. Furthermore, numerical simulations for the $\mathrm{C}\ensuremath{-}T$ gate and $\mathrm{C}\ensuremath{-}\sqrt{H}$ gate based on the master equation show that the fidelities of geometric gates obtained in our model are still very high even though noises are considered, which demonstrates the robustness of our protocol. It is worth noting that the controlled two-qubit model may pave the way to realize fault-tolerant quantum computation in the future.

Physical Review A•Feb 20, 2024•25 citations

Nonadiabatic holonomic quantum computation with atom-cavity system

Tonghao Xing, D. M. Tong

Quantum computation is much more effective than classical computation in solving many problems such as factoring large integers and searching unsorted databases. However, such effectiveness relies on the ability to perform universal high-fidelity quantum gates. One main challenge in achieving such high-fidelity gates is to reduce control errors of a quantum system. To overcome this problem, various proposals of fault-tolerant quantum computation are proposed. A promising one of such proposals is nonadiabatic holonomic quantum computation. Nonadiabatic holonomic quantum computation is realized by using a quantum system with a subspace satisfying both the cyclic evolution and parallel transport conditions. For an N dimensional quantum system with Hamiltonian H(t) and evolution operator U(t)=Texp[−i∫0tH(t')dt'] , if there exists a time-dependent L dimensional subspace S(t) spanned by the orthonormal vectors {|ϕk(t)〉=U(t)|ϕk(0)〉}k=1L that satisfy the two conditions: (1) ∑k=1L|ϕk(τ)〉〈ϕk(τ)|= ∑k=1L|ϕk(0)〉〈ϕk(0)| , with τ being the evolution period, and (2) 〈ϕk(t)|H(t)|ϕl(t)〉=0, k,l=1,2,⋯,L, then the unitary transformation U(τ) is a holonomic gate on the L dimensional subspace S(0) spanned by {|ϕk(0)〉}k=1L . The work of realizing nonadiabatic holonomic gate is to build a physical system with a Hamiltonian satisfying both the cyclic evolution condition and the parallel transport condition. Nonadiabatic holonomic quantum computation is based on nonadiabatic non-Abelian geometric phases. Since nonadiabatic non-Abelian geometric phases are only dependent on evolution paths but independent of evolution details, nonadiabatic holonomic gates are robust against control errors. Besides, nonadiabatic holonomic gates do not require the long run-time evolution that is necessary for adiabatic holonomic gates. Due to the merits of both robustness against control errors and high-speed realization, nonadiabatic holonomic quantum computation has received increasing attention in theory and experiment. Various schemes of nonadiabatic holonomic quantum computation have been proposed based on different physical systems, and a number of these schemes have been experimentally demonstrated with nuclear magnetic resonance systems, nitrogen-vacancy center systems, and superconducting systems. The progress of nonadiabatic holonomic quantum computation is also reflected in the improvement of the methods of designing quantum gates. The single-shot scheme, single-loop multiple-pulse scheme and composite gate scheme of nonadiabatic quantum gate are based on the improved methods. In particular, the single-shot scheme simplifies the operation of the one-qubit gate, so that the operation of any one-qubit gate, which needs to be realized by combining two non-commuting π-rotation gate in the original scheme, can be simply realized by a single-shot operation. In this paper, we propose a scheme of nonadiabatic holonomic quantum computation with atom-cavity system. The universal set of quantum gates in our scheme consists of an arbitrary one-qubit nonadiabatic holonomic gate and a two-qubit nonadiabatic holonomic controlled-PHASE gate. To realize the arbitrary one-qubit gate, we use two resonant laser pulses and an off-resonant laser pulse to drive a single four-level atom. With the aid of Stark shifts, the one-qubit gate can be performed in one-step only by changing the Rabi frequencies and the phases of the laser pulses. To realize the two-qubit controlled-PHASE gate, we use two off-resonant laser pulses to drive the two four-level atoms in the cavity. The transitions between the two-atom ground state and the two-atom auxiliary state is facilitated by exchanging virtual photons through a common cavity mode. In this process, the effective two-atom transition is disentangled from the cavity mode and therefore the two-qubit gate is insensitive to the cavity decay.

Chinese Science Bulletin (Chinese Version)•Apr 10, 2020•3 citations

Realization of nonadiabatic holonomic multiqubit controlled gates with Rydberg atoms

Tonghao Xing, P. Z. Zhao, D. M. Tong

Nonadiabatic holonomic gates provide an effective means to perform high-speed and error-resilient manipulation of quantum states. It is practically important to realize nonadiabatic holonomic multiqubit controlled gates since multiqubit controlled gates are widely used in quantum information processing. Rydberg atoms are an appealing physical system for the realization of nonadiabatic holonomic multiqubit controlled gates as the Rydberg-mediated interaction is beneficial to couple two qubits. In this paper, we put forward a scheme for the realization of nonadiabatic holonomic multiqubit controlled gates based on Rydberg atoms, where an $(n+1)$-qubit controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gate can be realized by $(2n\ensuremath{-}1)$ basic operations. Moreover, the effective coupling between two qubits is in the first-order strength of Rabi frequencies, which allows for the implementation of quantum gates within a short duration.

Physical Review A•Jul 29, 2021•12 citations

Nonadiabatic holonomic quantum computation with Rydberg superatoms

P. Z. Zhao, X. Wu, Tonghao Xing +2 more

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.

arXiv:1811.00840•Physical Review A•Sep 11, 2018•43 citations
Nonadiabatic holonomic quantum computation, focusing mainly on implementing universal single- and two-qubit gates, commonly suffers gate fidelity losses inevitably due to the presence of systematic errors. Here we propose to realize fast holonomic multiqubit controlled~(CN_NN​-NOT) Rydberg atom gates. Uniquely, the gate time is independent of the control qubit number NNN. We show that the fast gate is largely immune to laser parameter fluctuations and motional dephasing. The high tolerance of systematic errors can be further enhanced through optimal pulse engineering. The proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade, and moreover can be implemented alternatively with superconducting circuits. Our study paves a new way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or superconducting circuits, and hence contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superdonducting devices.
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic (N+1)(N+1)(N+1)-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multibody Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the NNN control atoms largely remain in the very stable qubit space during the operation. We show that CN{C}_{N}CN​-not gates can reach the same level of fidelity at a given gate time for $N\ensuremath{\le}5$ under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In the case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves an alternative way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts to develop scalable quantum computation with trapped atoms and fabricable superconducting devices.
Abstract Nonadiabatic holonomic quantum computation (NHQC) has attracted significant interest due to its intrinsic robustness against local parameter fluctuations. However, conventional NHQC schemes are constrained by long evolution times, with all gate operations requiring the same duration regardless of the rotation angle, leading to increased susceptibility to decoherence. In this paper, we propose a time-optima NHQC (TONHQC) scheme in the Rydberg atomic system, which minimizes gate operation time while maintaining geometric robustness. By solving the quantum brachistochrone equation (QBE), we derive an optimal trajectory for state evolution. We demonstrate the feasibility of TONHQC using87Rb atoms by constructing high-fidelity geometric two-qubit gates. Numerical simulations for controlled-Hadamard (C-H), controlled-π/4 (C-S) and controlled-π/8 (C-T) gates confirm that TONHQC outperforms conventional NHQC protocols, achieving higher fidelity and enhanced resilience against spontaneous emission and Rabi frequency fluctuations. These findings suggest that TONHQC as a promising approach for realizing high-fidelity holonomic quantum gates in Rydberg atom systems, paving the way for scalable and fault-tolerant quantum computation.
The nonadiabatic holonomic quantum computation (NHQC) has received great attention for decades, however, there are many challenges to its implementation in experiments. To further shorten the evolution time is the first challenge to be conquered to realize high-fidelity quantum gates in NHQC. In this paper, we propose a controlled two-qubit model in Rydberg atoms to realize nonadiabatic holonomic quantum gates, where the evolution time is extremely decreased and the influences of several kinds of noises are minimized by utilizing the time-optimal-control technique on the target atom. In addition, we can construct arbitrary geometric gates by selecting the appropriate parameters in our model. Furthermore, numerical simulations for the $\mathrm{C}\ensuremath{-}T$ gate and $\mathrm{C}\ensuremath{-}\sqrt{H}$ gate based on the master equation show that the fidelities of geometric gates obtained in our model are still very high even though noises are considered, which demonstrates the robustness of our protocol. It is worth noting that the controlled two-qubit model may pave the way to realize fault-tolerant quantum computation in the future.
Quantum computation is much more effective than classical computation in solving many problems such as factoring large integers and searching unsorted databases. However, such effectiveness relies on the ability to perform universal high-fidelity quantum gates. One main challenge in achieving such high-fidelity gates is to reduce control errors of a quantum system. To overcome this problem, various proposals of fault-tolerant quantum computation are proposed. A promising one of such proposals is nonadiabatic holonomic quantum computation. Nonadiabatic holonomic quantum computation is realized by using a quantum system with a subspace satisfying both the cyclic evolution and parallel transport conditions. For an N dimensional quantum system with Hamiltonian H(t) and evolution operator U(t)=Texp[−i∫0tH(t')dt'] , if there exists a time-dependent L dimensional subspace S(t) spanned by the orthonormal vectors {|ϕk(t)〉=U(t)|ϕk(0)〉}k=1L that satisfy the two conditions: (1) ∑k=1L|ϕk(τ)〉〈ϕk(τ)|= ∑k=1L|ϕk(0)〉〈ϕk(0)| , with τ being the evolution period, and (2) 〈ϕk(t)|H(t)|ϕl(t)〉=0, k,l=1,2,⋯,L, then the unitary transformation U(τ) is a holonomic gate on the L dimensional subspace S(0) spanned by {|ϕk(0)〉}k=1L . The work of realizing nonadiabatic holonomic gate is to build a physical system with a Hamiltonian satisfying both the cyclic evolution condition and the parallel transport condition. Nonadiabatic holonomic quantum computation is based on nonadiabatic non-Abelian geometric phases. Since nonadiabatic non-Abelian geometric phases are only dependent on evolution paths but independent of evolution details, nonadiabatic holonomic gates are robust against control errors. Besides, nonadiabatic holonomic gates do not require the long run-time evolution that is necessary for adiabatic holonomic gates. Due to the merits of both robustness against control errors and high-speed realization, nonadiabatic holonomic quantum computation has received increasing attention in theory and experiment. Various schemes of nonadiabatic holonomic quantum computation have been proposed based on different physical systems, and a number of these schemes have been experimentally demonstrated with nuclear magnetic resonance systems, nitrogen-vacancy center systems, and superconducting systems. The progress of nonadiabatic holonomic quantum computation is also reflected in the improvement of the methods of designing quantum gates. The single-shot scheme, single-loop multiple-pulse scheme and composite gate scheme of nonadiabatic quantum gate are based on the improved methods. In particular, the single-shot scheme simplifies the operation of the one-qubit gate, so that the operation of any one-qubit gate, which needs to be realized by combining two non-commuting π-rotation gate in the original scheme, can be simply realized by a single-shot operation. In this paper, we propose a scheme of nonadiabatic holonomic quantum computation with atom-cavity system. The universal set of quantum gates in our scheme consists of an arbitrary one-qubit nonadiabatic holonomic gate and a two-qubit nonadiabatic holonomic controlled-PHASE gate. To realize the arbitrary one-qubit gate, we use two resonant laser pulses and an off-resonant laser pulse to drive a single four-level atom. With the aid of Stark shifts, the one-qubit gate can be performed in one-step only by changing the Rabi frequencies and the phases of the laser pulses. To realize the two-qubit controlled-PHASE gate, we use two off-resonant laser pulses to drive the two four-level atoms in the cavity. The transitions between the two-atom ground state and the two-atom auxiliary state is facilitated by exchanging virtual photons through a common cavity mode. In this process, the effective two-atom transition is disentangled from the cavity mode and therefore the two-qubit gate is insensitive to the cavity decay.
Nonadiabatic holonomic gates provide an effective means to perform high-speed and error-resilient manipulation of quantum states. It is practically important to realize nonadiabatic holonomic multiqubit controlled gates since multiqubit controlled gates are widely used in quantum information processing. Rydberg atoms are an appealing physical system for the realization of nonadiabatic holonomic multiqubit controlled gates as the Rydberg-mediated interaction is beneficial to couple two qubits. In this paper, we put forward a scheme for the realization of nonadiabatic holonomic multiqubit controlled gates based on Rydberg atoms, where an (n+1)(n+1)(n+1)-qubit controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gate can be realized by $(2n\ensuremath{-}1)$ basic operations. Moreover, the effective coupling between two qubits is in the first-order strength of Rabi frequencies, which allows for the implementation of quantum gates within a short duration.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.