Machine learning assisted zero-area pulse design in an open quantum system

Accurate and precise quantum control is crucial for quantum information processing. Zero-area pulse control, originally developed for closed systems, has played a significant role in driving quantum systems toward desired states. However, its effectiveness is often compromised by environmental noise. Traditional methods can find optimal pulses for fixed environmental parameters, and they need to be recalculated again once the environmental parameters change. Here, we propose a supervised learning (SL)-based protocol to design optimal zero-area pulses in noisy environments. By including environmental parameters as input during training, the neural network (NN) learns to generate effective controls for various environmental parameters. We demonstrate the protocol using quantum state transmission through a spin chain governed by a non-Markovian master equation. The SL-optimized pulses significantly enhance transmission fidelity compared to ideal pulses, with greater improvements observed at higher system-bath coupling and temperature, where more optimization space exists. Interestingly, fidelity first increases and then decreases with stronger Markovianity, suggesting that highly Markovian environments limit control performance. We also compare the SL method with a genetic algorithm, and the similar results confirm the accuracy and generalization ability of the NN-based approach.