Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation (GQC) on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric phase, π/8 and Hadamard gates can be obtained as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for GQC, making it more promising in the application of large-scale fault-tolerant quantum computation.

基于非绝热几何相位的量子计算由于其快速操作和固有的抗噪性而引起了广泛的兴趣。然而，它仅限于一些特殊的进化路径，门时间通常比传统的动态门更长，导致鲁棒性减弱，实现的几何门更不保真。在这里，我们提出了一种路径优化的几何量子计算（GQC）方案，用于基于传统实验设置的超导传输量子位，其中可以实现高保真和鲁棒的通用非绝热几何门。具体来说，我们发现，通过选择合适的演化路径，构建的几何门可以在不同的局部误差下优于相应的动力学门。π /8 和 Hadamard 门分别可以达到 99.93%、99.95% 和 99.95%。值得注意的是，双量子位控制相位门的保真度高达 99.87%。因此，我们的方案为 GQC 提供了一个新的视角，使其在大规模容错量子计算的应用中更有前景。