Error-mitigated geometric quantum control over an oscillator

Quantum information is very fragile to environmentally and operationally induced imperfections. Therefore, the construction of practical quantum computers requires quantum error-correction techniques to protect quantum information. In particular, encoding a logical qubit into the large Hilbert space of an oscillator is a hardware-efficient way of correcting quantum errors. In this strategy, selective number-dependent arbitrary phase (SNAP) gates are vital for universal quantum control. However, the quality of SNAP gates is considerably limited by the small coupling-induced nonlinearity of the oscillator. Here, to resolve this limitation, we propose a robust scheme based on quantum optimal control via functional theory, by designing an appropriate trajectory for a target operation. Besides, we combine the geometric phase approach with our trajectory design scheme to minimize the decoherence effect, by shortening the gate time. Numerical simulation shows that both errors can be significantly mitigated and that the robustness of the geometric gate against both $X$ and $Z$ errors can be maintained. Therefore, our scheme provides a promising alternative for fault-tolerant quantum computation.