Time-optimal control holds promise across the full spectrum of quantum technologies, where the rapid generation of unitary gates and state transformations is crucial to mitigate decoherence effects. In practical scenarios, quantum systems are always immersed in an external time-dependent field or potential, either owing to the inevitable influence of the environment or as a sought-after effect for enhanced coherence. The challenge then lies in finding the time-optimal approach to navigate quantum systems amidst dynamical ambient Hamiltonians, a pursuit that has proven elusive thus far. We showcase the implementation of arbitrary quantum state transformations and a universal set of single-qubit gates under a background Landau-Zener Hamiltonian. Leveraging the favorable coherence properties of timedomain Rabi oscillations, we achieve velocities surpassing the Mandelstam-Tamm quantum speed limit and significantly lower energy costs than those incurred by conventional quantum control techniques. These findings highlight a promising pathway to expedite and economize high-fidelity quantum operations.

时间最优控制在整个量子技术领域都有希望，其中幺正门的快速生成和状态变换对于减轻退相干效应至关重要。在实际场景中，量子系统总是沉浸在外部时间依赖性的场或势中，要么是由于环境的不可避免的影响，要么是作为增强相干性的热门效应。因此，挑战在于找到时间最优的方法，在动态环境哈密顿量中导航量子系统，到目前为止，这一追求已被证明是难以捉摸的。我们展示了在 Landau-Zener 哈密顿量背景下任意量子态转换和一组通用的单量子比特门的实现。利用时域 Rabi 振荡的良好相干特性，我们实现了超过 Mandelstam-Tamm 量子速度极限的速度，并且比传统量子控制技术产生的能源成本显着降低。这些发现突出了一条有前途的途径，可以加快和节省高保真量子运算。