Dynamical-corrected nonadiabatic geometric quantum computation

Abstract

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., {\sigma }_x error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the {\sigma }_z 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.

Graphical abstract

Keywords

geometric phases / dynamical-corrected gates / fault-tolerant quantum computation

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This work was supported by the Key-Area Research and Development Program of Guangdong Province (Grant No. 2018B030326001), the National Natural Science Foundation of China (Grant No. 12275090), Guangdong Provincial Key Laboratory (Grant No. 2020B1212060066), the Quality Engineering Project of the Education Department of Anhui Province (No.2021cyxy046), the key Scientific Research Foundation of Anhui Provincial Education Department (KJ2021A0649), Outstanding Young Talents in College of Anhui Province (Grant No. gxyq2022059), and the High-Level Talent Scientific Research Starting foundation (Grant No. 2020rcjj14).

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