Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states using a  limited set of available controls. In this talk I will present a new approach which can be used to find the locally optimal driving protocol for trajectories within an MPS manifold. I will then focus on a specific example, namely the PXP model, where I will compare our approach to
counter-diabatic driving using numerical simulations. Lastly, I will present two use cases. Firstly, I will present how this approach can be used to stabilise quantum scars by constructing a Floquet model with nearly ideal scars and secondly, I will present a step towards full trajectory optimization and demonstrate the entanglement steering capabilites that allow us to construct entangled states with high fidelity.

* Marko Ljubotina, IST Vienna