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Ongoing development of quantum simulators allows for a progressively finerdegree of control of quantum many-body systems. This motivates the developmentof efficient approaches to facilitate the control of such systems and enablethe preparation of non-trivial quantum states. Here we formulate an approach tocontrol quantum systems based on matrix product states~(MPS). We comparecounter-diabatic and leakage minimization approaches to the so-called localsteering problem, that consists in finding the best value of the controlparameters for generating a unitary evolution of the specific MPS state in agiven direction. In order to benchmark the different approaches, we apply themto the generalization of the PXP model known to exhibit coherent quantumdynamics due to quantum many-body scars. We find that the leakage-basedapproach generally outperforms the counter-diabatic framework and use it toconstruct a Floquet model with quantum scars. We perform the first stepstowards global trajectory optimization and demonstrate entanglement steeringcapabilities in the generalized PXP model. Finally we apply our leakageminimization approach to construct quantum scars in the periodically drivennon-integrable Ising model.

Optimal steering of matrix product states and quantum many-body scars