Yan Liang

Nonadiabatic holonomic quantum computation provides a promising approach toward fault-tolerant quantum control, due to its simple requirements for energy level structure and intrinsic robustness stemming from non-Abelian geometric phases. However, conventional nonadiabatic holonomic quantum computation relies on segmented evolution along a specific trajectory, which not only complicates experimental control but also exacerbates decoherence effects. Meanwhile, minor deviations in systematic parameters can directly disrupt the cyclic evolution process necessary to construct holonomic gates, leading to degraded gate robustness. To address these disadvantages, we here propose a general strategy to incorporate cyclic evolution protection into the holonomic gate construction. The aim is to design on-demand trajectories by modulating pulse shapes, thereby circumventing the detrimental impact of systematic errors on cyclic evolution. Consequently, universal holonomic gates implemented through a stable cyclic evolution process can maintain lower error sensitivity. Meanwhile, in our scheme, compressing the state population in the ancillary state ensures less energy consumption, resulting in higher gate fidelity. Therefore, our work serves as a practical solution for achieving high-fidelity and robust universal quantum gates, paving the way for large-scale quantum computation.

A nonadiabatic geometric quantum gate is realized by integrating nonadiabatic geometric phases with global geometric features into the unitary quantum control, thereby removing the limitation of a long evolution time in the adiabatic case. However, systematic errors are inevitable in practical quantum control; these lead to the deviation of the evolution from target conditions to inducing geometric phases, smearing the robustness of the induced geometric quantum gates. Here, we present a general theoretical framework with enhanced robustness for geometric quantum gates by preserving fundamental geometric conditions. We first analytically evaluate the influence of systematic errors on geometric gates and then propose an optimized approach to mitigate this influence. Numerical simulations indicate that, as the geometric conditions are still maintained in the presence of systematic errors in our scheme, the constructed geometric quantum gates exhibit strong robustness, far superior to that of conventional schemes. Furthermore, we propose implementing the scheme in superconducting quantum circuits, where geometric quantum gates can achieve high fidelity with current experimental parameters. Therefore, the enhanced gate performance highlights the promise of our scheme for large-scale quantum computations.

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single‐qubit gate and nontrivial two‐qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high‐fidelity quantum gates are promising for large‐scale fault‐tolerant quantum computation.

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.