Adiabatic quantum computation requires the system to be always maintained in its ground state. However, environmental noise readily disrupts this adiabatic process. Adiabatic speedup via leakage elimination operator (LEO) control, as one of the effective strategies, has been proposed to achieve adiabatic evolution in a shorter time frame, thus mitigating the detrimental effects of environmental noise. The LEO Hamiltonian can be realized by a sequence of pulses. While the pulse design via a traditional optimal algorithm is feasible for time-independent noise, it becomes more challenging for time-dependent cases. To ensure robust performance under time-dependent noise, we employ the neural network (NN)-based supervised learning algorithm for the pulse design. Our strategy is to incorporate the environmental parameters into the training process, then the resulting network can effectively accommodate a wide range of arbitrary parameters, including time-dependent cases. Specifically, the NN can learn the optimal total evolution time $T_{\text{tot}}$, without the need to set it as a known value a priori. Taking the adiabatic speedup of an open quantum qutrit system under time-dependent noise as an example, we identify a noise-insensitive path by adapting the ideal pulse shape originally designed for closed systems. Fidelity improvement has been obtained compared to the ideal pulses. Our approach offers an effective strategy to enhance the performance of various quantum information processing tasks under time-dependent noise, such as adiabatic quantum computation, quantum state transfer, or quantum state preparation.

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• Adiabatic quantum optimization
• Open quantum systems
• Quantum control
• Quantum information processing