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Physical Review A

Simple construction of Rydberg quantum cloning machines via nonadiabatic geometric quantum operations

Xiaoyu Zhu, Bao‐Long Fang, Y.-H. Li, F.-Q. Guo, Erjun Liang, L.-L. Yan, Shi‐Lei Su

Published Nov 17, 2022• 4 citations
Publisher

Abstract

A theoretical scheme based on the nonadiabatic geometric quantum computation (NGQC) is proposed to realize quantum cloning in the Rydberg atom system. In contrast to previous schemes, the present one utilizes the NGQC to construct the clone machine and thus is more robust against control errors. Meanwhile, to implement the desired cloning framework in the quantum clone machine, the scheme reported by Zhu and Ye [M.-Z. Zhu and L. Ye, Phys. Rev. A 91, 042319 (2015)] based on cavity QED requires a series of single(two)-qubit operations. For the present NGQC-based scheme, through modulating the rotation angle of geometric operations, we can greatly simplify the process of realizing the cloning framework. In addition, through adjusting the relevant parameters, the scheme can perform symmetrical (asymmetrical) universal cloning, optimal symmetrical (asymmetrical) phase-covariant quantum cloning, and optimal symmetrical (asymmetrical) real-state quantum cloning. The present attempt to optimize quantum cloning using geometric quantum control in Rydberg atoms provides a path to robust and simplified quantum cloning, which is meaningful for experiments and has implications for quantum cloning in other quantum systems as well.

DOI
10.1103/physreva.106.052419

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A theoretical scheme based on the nonadiabatic geometric quantum computation (NGQC) is proposed to realize quantum cloning in the Rydberg atom system. In contrast to previous schemes, the present one utilizes the NGQC to construct the clone machine and thus is more robust against control errors. Meanwhile, to implement the desired cloning framework in the quantum clone machine, the scheme reported by Zhu and Ye [M.-Z. Zhu and L. Ye, Phys. Rev. A 91, 042319 (2015)] based on cavity QED requires a series of single(two)-qubit operations. For the present NGQC-based scheme, through modulating the rotation angle of geometric operations, we can greatly simplify the process of realizing the cloning framework. In addition, through adjusting the relevant parameters, the scheme can perform symmetrical (asymmetrical) universal cloning, optimal symmetrical (asymmetrical) phase-covariant quantum cloning, and optimal symmetrical (asymmetrical) real-state quantum cloning. The present attempt to optimize quantum cloning using geometric quantum control in Rydberg atoms provides a path to robust and simplified quantum cloning, which is meaningful for experiments and has implications for quantum cloning in other quantum systems as well.
Quantum gates constructed by geometric phase are naturally robust to control errors due to the global nature of the geometric evolution path. Therefore, how to cope with the inevitable decoherence errors is worthy of serious attention for geometric quantum computation. Different from conventional nonadiabatic geometric quantum computation (NGQC), which needs the same evolution time for any geometric rotation angle, we have proposed and experimentally demonstrated nonadiabatic noncyclic geometric quantum computation (NNGQC) without the requirement of the cyclic evolution condition, which thus reduces decoherence errors due to shortened evolution time [J. W. Zhang et al., Phys. Rev. Lett. 127, 030502 (2021)]. In addition, the use of decoherence-free subspaces (DFS) is another effective strategy to protect quantum gates from dephasing error and has been studied in nonadiabatic holonomic quantum computation [G. F. Xu et al., Phys. Rev. Lett. 109, 170501 (2012)]. Motivated by previous studies, we propose a one-step scheme to implement single-qubit NNGQC operation in DFS constructed by two Rydberg atoms, and then generalize the scheme to the two-logical-qubit case in one step. The numerical results show that our scheme is robust against decoherence in contrast to the NGQC counterparts. The present scheme combines the features of NNGQC and DFS and can further reduce the impact of decoherence on gate infidelity, which may provide an option for the realization of Rydberg-atom-based quantum computation in the future.
Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geomet-ric gate. However, the conventiona NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, wemake simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can berealized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.
Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates.However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases.Here, we give the reasons why nonadiabatic geometric gates are sensitive to the control errors and, further, we propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness of the geometric gate.To illustrate the working mechanism of super-robust geometric quantum gates, we give two simple examples of SR-NGQC and SR-NHQC for two-and three-level quantum systems, respectively.Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance compared to the previous NGQC, NHQC, and standard dynamical schemes.Super-robust geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions.All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.
Abstract Single- and two-qubit nonadiabatic noncyclic geometric quantum computation (NNGQC) have been put forward in theory (Liu B.-J. et al. , Phys. Rev. Res. 2 (2020) 043130). The features of single-qubit NNGQC have been experimentally verified and the experimental technical route of the two-qubit case has been discussed in detail (Zhang J. W. et al. , Phys. Rev. Lett. 127 (2021) 030502). The multiple-qubit quantum logic gate is critical for quantum computation. Although combining a series of single- and two-qubit NNGQC gates can form universal operations and create arbitrary multiple-qubit gates, the created multiple-qubit gate often consumes more quantum resource and requires longer evolution time, which makes it more fragile to systematic error and decoherence. In this article, we propose a scheme to directly construct the multiple-qubit NNGQC gates in Rydberg atoms. The numerical results show that the proposed quantum gates have high fidelity and are robust to systemic error and decoherence. Our scheme may be applied in the future quantum computation and many-body quantum science studies.
Nonadiabatic geometric quantum computation (NGQC) has emerged as an excellent proposal for achieving fast and robust quantum control against control errors. However, previous NGQC protocols could not be strongly resilient against the noise from decay of bare states in a realistic system, which can be equivalently described by a non-Hermitian Hamiltonian. Here we show how to perform NGQC in non-Hermitian quantum systems. By utilizing a geometric phase generated by nonunitary evolution of the system, a universal set of geometric gates can be realized with a high fidelity. Moreover, we demonstrate that the nonadiabatic process does not lead to the loss of fidelity from decay.
Quantum computation has demonstrated advantages over classical computation for special hard problems, where a set of universal quantum gates is essential. Geometric phases, which have built-in resilience to local noise, have been used to construct quantum gates with excellent performance. However, this advantage has been smeared in previous schemes. Here, we propose a state-independent nonadiabatic geometric quantum-gate scheme that is able to realize a more fully geometric gate than previous approaches, allowing for the cancelation of dynamical phases accumulated by an arbitrary state. Numerical simulations demonstrate that our scheme has significantly stronger gate robustness than the previous geometric and dynamical ones. Meanwhile, we give a detailed physical implementation of our scheme with the Rydberg atom system based on the Rydberg blockade effect, specifically for multiqubit control-phase gates, which exceeds the fault-tolerance threshold of multiqubit quantum gates within the considered error range. Therefore, our scheme provides a promising way for fault-tolerant quantum computation in atomic systems.