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We propose a scheme for quantum geometric computation on a fiber-cavity-fiber system, in which two atoms are located in two single-mode cavities, respectively, connected with each other by optical fiber. This scheme not only has the feature of virtual excitation of photons in the cavity quantum electrodynamics (CQED) that can reduce the effect of decay effectively but also has the advantage of geometric phase to withstand noises due to its built-in noise-resilience feature and robust merit. Specifically, our proposal combined with optimized-control-technology (OCT) can reduce gate operation error by adjusting the time-dependent amplitude and phase of the resonant field which further enhances the robustness of the quantum operation. The robustness against decoherence is demonstrated numerically and the scheme may be applied in the remote quantum information processing tasks and quantum computation.

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Single- and two-qubit nonadiabatic noncyclic geometric quantum computation (NNGQC) have been put forward in theory [Phys. Rev. Res. 2, 043130 (2020)]. The features of single-qubit NNGQC have been experimentally verified and the experimental technical route of two-qubit case has been discussed in detail in Ref. [Phys. Rev. Lett. 127, 030502 (2021)]. 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 make 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.

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