Circular-path holonomic quantum gates with multiple degrees of freedom

Holonomic quantum gates offer a promising approach for achieving high fidelity and robustness in quantum computation by leveraging geometric phases to suppress the influence of noise. However, existing schemes often suffer from limitations such as complex segmented evolution paths and an inability to implement certain gates, including those with a geometric phase of 𝜋𝜋. In this work, we propose a circular-path holonomic quantum gate scheme with multiple degrees of freedom, which enables the realization of any single-qubit gate, including gates with a geometric phase of 𝜋𝜋. The scheme allows for the optimization of pulse performance, effectively mitigating control errors in both the addressing frequency and Rabi frequency. Applied to a Rydberg-atoms system, numerical simulations demonstrate high fidelity and robustness against control errors, with fidelities exceeding 99.97% under various conditions. This work addresses the limitations of previous schemes and provides a flexible framework for implementing robust quantum gates in three-level quantum systems.