Attention-based neural networks such as transformers have revolutionized various fields such as natural language processing, genomics, and vision. Here, we demonstrate the use of transformers for quantum feedback control through both a supervised and reinforcement learning approach. In particular, due to the transformer's ability to capture long-range temporal correlations and training efficiency, we show that it can surpass some of the limitations of previous control approaches, e.g.~those based on recurrent neural networks trained using a similar approach or policy based reinforcement learning. We numerically show, for the example of state stabilization of a two-level system, that our bespoke transformer architecture can achieve near unit fidelity to a target state in a short time even in the presence of inefficient measurement and Hamiltonian perturbations that were not included in the training set as well as the control of non-Markovian systems. We also demonstrate that our transformer can perform energy minimization of non-integrable many-body quantum systems when trained for reinforcement learning tasks. Our approach can be used for quantum error correction, fast control of quantum states in the presence of colored noise, as well as real-time tuning, and characterization of quantum devices.

翻译：注意力机制神经网络（如Transformer）已在自然语言处理、基因组学及视觉等多个领域引发革命性突破。本文通过监督学习与强化学习两种途径，展示了Transformer在量子反馈控制中的应用。特别地，得益于Transformer捕获长程时间关联的能力及其训练效率，我们证明其能够突破以往控制方法的若干局限——例如采用类似训练方式的循环神经网络或基于策略的强化学习方法。以两能级系统的态稳定为例，我们通过数值模拟表明：即使存在训练集中未包含的低效测量与哈密顿量扰动，且针对非马尔可夫系统进行控制时，我们定制的Transformer架构仍可在短时间内实现接近单位保真度的目标态趋近。此外，我们还验证了该Transformer在强化学习任务训练下能够实现不可积多体量子系统的能量最小化。本方法可应用于量子纠错、有色噪声环境下的量子态快速控制，以及量子器件的实时调谐与表征。