State engineering of quantum objects is a central requirement for precision sensing and quantum computing implementations. When the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have been theoretically proposed and experimentally realized. For more complex systems such as interacting quantum gases, simplifying assumptions do not apply anymore and the optimization techniques become computationally impractical. Here, we propose Bayesian optimization based on multi-output Gaussian processes to learn the physical properties of a Bose–Einstein condensate within few simulations only. We evaluate its performance on an optimization study case of diabatically transporting the quantum gas while keeping it in its ground state. Within a few hundred executions, we reach a competitive performance to other protocols. While restricting this benchmark to the well known Thomas–Fermi approximation for straightforward comparisons, we expect a similar performance when employing more complex theoretical models, which would be computationally more challenging, rendering standard optimal control theory protocols impractical. This paves the way for efficient state engineering of complex quantum systems including mixtures of interacting gases or cold molecules.

中文翻译：

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量子气体状态工程的贝叶斯优化


量子对象的状态工程是精确传感和量子计算实现的核心要求。当量子动力学可以用解析解或简单的近似模型来描述时，最优状态准备方案已经在理论上被提出并通过实验实现。对于更复杂的系统，例如相互作用的量子气体，简化假设不再适用，优化技术在计算上变得不切实际。在这里，我们提出了基于多输出高斯过程的贝叶斯优化，以仅在少数模拟中学习玻色-爱因斯坦凝聚态的物理性质。我们在一个优化研究案例中评估了它的性能，该案例在保持量子气体处于基态的同时绝热传输量子气体。在几百次执行中，我们达到了与其他协议相比具有竞争力的性能。虽然将此基准限制为众所周知的 Thomas-Fermi 近似以进行直接比较，但我们预计在采用更复杂的理论模型时会有类似的性能，这在计算上更具挑战性，使标准最优控制理论协议不切实际。这为复杂量子系统的高效状态工程铺平了道路，包括相互作用气体或冷分子的混合物。