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Nonadiabatic Noncyclic Geometric Quantum Computation via unconventional Rydberg blockade

Bao-Jie Liu, Shi‐Lei Su, Man‐Hong Yung

Published May 14, 2020• 0 citations
OpenAlex

Abstract

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.

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•Feb 1, 2021•2 citations
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.
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.
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.
Arrays of neutral atoms have emerged as promising platforms for quantum computing. Realization of high-fidelity two-qubit gates with robustness is currently a significant important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate using Rydberg blockade. We achieve the noncyclic geometric control with a single modulated pulse. As compared with the control scheme by cyclic evolution that determined by dynamical parameters, the robustness of the proposal against systematic errors will be remarkably improved due to the geometric characteristic. Importantly, the noncyclic geometric control reduces the gate time for small rotation angles and will be more insensitive to the decoherence effect. We accelerate the adiabatic control with the aid of shortcuts to adiabaticity to further shorten the operation time. We apply our protocol to the algorithm of quantum Fourier transformation to show the actual acceleration. Therefore, the proposed scheme will provide an analytical waveforms for arbitrary two-qubit gates and may have important use in the experiments of atomic arrays.
Arrays of neutral atoms have emerged as promising platforms for quantum computing. The realization of high-fidelity two-qubit gates with robustness is currently a significantly important task for large-scale operations. In this paper, we present a convenient approach for implementing a two-qubit controlled-phase gate with Rydberg blockade. We achieve noncyclic and geometric control within a single modulated pulse. Compared with the control scheme by cyclic evolution determined by dynamical parameters, the robustness of our proposal against systematic errors will be remarkably improved due to its geometric characteristics. Importantly, the noncyclic geometric control reduces the gate time for small rotation angles and is more insensitive to decoherence effects. Furthermore, we accelerate the adiabatic control with the aid of shortcuts to adiabaticity to further shorten the operation time. We apply our protocol to the quantum Fourier transformation algorithm to demonstrate the actual acceleration. Therefore, the proposed scheme provides analytical wave forms for arbitrary two-qubit gates and may play an important role in experiments involving atomic arrays.
Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which is the necessity of fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate-time and abrupt pulse control, and thus weaken the gate performance. Here, we propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolutions, which effectively shorten the gate duration, and universal quantum gates can be realized in one step without path mutation. Our numerical simulation shows that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistant not only to noise but also to decoherence effect. In addition, our scheme can also be implemented on a superconducting circuit platform, with the fidelities of single-qubit and two-qubit gates higher than 99.97%\%% and 99.84%\%%, respectively. Therefore, our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.