The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering¹. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems^2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback⁴. Successful implementations thus far include experiments on the level of optical and atomic systems^5,6,7. Here we demonstrate real-time optimal control of the quantum trajectory⁸ of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

通过测量和反馈准确控制物理系统动力学的能力是现代工程学的支柱¹。如今，对应用量子技术的需求不断增加，需要将这种控制水平适应于单个量子系统^2,3。以最佳方式实现这一点是一项具有挑战性的任务，它依赖于量子限制测量和专门定制的状态估计和反馈算法⁴。迄今为止成功的实施包括光学和原子系统^5,6,7级别的实验。^{在这里，我们演示了量子轨迹8}的实时最优控制光学捕获的纳米粒子。我们将接近海森堡极限的共焦位置传感与通过卡尔曼滤波进行的最优状态估计相结合，以实时跟踪相空间中的粒子运动，位置不确定性为零点波动的 1.3 倍。最佳反馈使我们能够将量子谐振子稳定到 0.56 ± 0.02 量子的平均占用，实现从室温到量子基态的冷却。我们的工作将量子卡尔曼滤波确立为一种实现机械运动量子控制的方法，对所有尺度的传感具有潜在影响。结合悬浮，这为全面控制线性和非线性系统中固态宏观量子物体的波包动力学铺平了道路。