Universal robust geometric quantum control via geometric trajectory correction

Universal robust quantum control is essential for large-scale quantum computation. The geometric phase, as a key element with intrinsic error-resilient features, can be well integrated into a quantum control process to enhance control robustness. However, due to the inability to optionally avoid some trajectory segments seriously affected by systematic errors, the robust universality of current geometric quantum control based on some special geometric evolution trajectories is still lacking, resulting in unsatisfactory performance of arbitrary geometric gate. Here, we propose another scheme for universal robust geometric control based on geometric trajectory correction, where enough available evolution parameters are introduced, without more experimental demands, to ensure the effective reduction of sensitivity to systematic errors. Numerical simulation shows that our implemented arbitrary geometric gates have error-resilient features better than conventional ones. In addition, we also verify the feasibility of the high-fidelity physical implementation of our scheme on superconducting quantum circuits. Therefore, our theoretical work is expected to offer an attractive avenue for realizing practical quantum computation in existing experimental platforms.