Quantum feedback control with a transformer neural network architecture

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.