Fast super robust nonadiabatic geometric quantum computation

Jiazhen Li, Yan-Xiong Du, Qing-Xian Lv +3 more

Bao-Jie Liu, Yuan-Sheng Wang, Man‐Hong Yung

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.

Hai Li Xu, Wanchun Li, Tao Chen +2 more

ABSTRACT Nonadiabatic holonomic quantum computation (NHQC) leverages non‐Abelian geometric phases within a nonadiabatic framework to achieve fast and robust quantum gate operations. However, the practical implementation of NHQC is challenged by the imperfect control inherent in experimental environments. Ensuring deep suppression of control error is critical. In this work, we propose a dynamically optimized NHQC scheme to construct universal super‐robust holonomic quantum gates. The proposed scheme is implemented by strategically designing a set of dynamically correcting pulses to achieve cyclic evolution, while ensuring that unwanted and disruptive dynamical phase elements, including previously neglected cross‐coupling terms, are not accumulated. This constructed super‐robust NHQC scheme efficiently safeguards the cyclic evolution process and makes the holonomic gate immune to control error by effectively correcting the error up to the fourth order. Furthermore, when integrated with decoherence‐free subspace (DFS) encoding in superconducting quantum circuits, our scheme can achieve high‐fidelity holonomic gates, and demonstrate robust resilience against both control errors and collective dephasing errors. Consequently, our work offers a promising pathway toward the realization of scalable and fault‐tolerant holonomic quantum computation.

Shi-Liang Zhu, Paolo Zanardi A

Cheng-Yun Ding, Li Chen, Lihua Zhang +1 more

Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a general dynamical-corrected technique, with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies, in terms of resisting the systematic error, i.e., σx error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the σz error caused by the collective dephasing. Notably, our protocol is a general one with simple experimental setups, which can be potentially implemented in different quantum systems, such as Rydberg atoms, trapped ions and superconducting qubits. These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.

Clemens Gneiting