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Universal robust quantum control is essential for performing complex quantumalgorithms and efficient quantum error correction protocols. Geometric phase,as a key element with intrinsic fault-tolerant feature, can be well integratedinto quantum control processes to enhance control robustness. However, thecurrent geometric quantum control is still controversial in robustuniversality, which leads to the unsatisfactory result that cannot sufficientlyenhance the robustness of arbitrary type of geometric gate. In this study, wefind that the finite choice on geometric evolution trajectory is one of themain roots that constrain the control robustness of previous geometric schemes,as it is unable to optionally avoid some trajectory segments that are seriouslyaffected by systematic errors. In view of this, we here propose a new schemefor universal robust geometric control based on geometric trajectorycorrection, where enough available evolution parameters are introduced toensure that the effective correction against systematic errors can be executed.From the results of our numerical simulation, arbitrary type of geometric gateimplemented by using the corrected geometric trajectory has absolute robustnessadvantages over conventional quantum one. In addition, we also verify thefeasibility of the high-fidelity physical implementation of our scheme insuperconducting quantum circuit, and finally discuss in detail the potentialresearches based on our scheme. Therefore, our theoretical work is expected tooffer an attractive avenue for realizing practical fault-tolerant quantumcomputation in existing experimental platforms.

Universal Robust Geometric Quantum Control via Geometric Trajectory Correction