article published yes Marko Ljubotina author F75EE9BE-5C90-11EA-905D-16643DDC885E0000-0003-0038-7068 Elena Petrova author 0ac84990-897b-11ed-a09c-f5abb56a4ede Norbert Schuch author Maksym Serbyn author 47809E7E-F248-11E8-B48F-1D18A9856A870000-0002-2399-5827 MaSe department Non-Ergodic Quantum Matter: Universality, Dynamics and Control project The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum. https://research-explorer.ista.ac.at/download/18488/18489/2024_PRXQuantum_Ljubotina.pdf application/pdfno American Physical Society2024 eng 2691-3399 2403.12325 00134619880000110.1103/prxquantum.5.040311 54 Ljubotina M, Petrova E, Schuch N, Serbyn M. 2024. Tangent space generators of matrix product states and exact floquet quantum scars. PRX Quantum. 5(4), 040311. Ljubotina M, Petrova E, Schuch N, Serbyn M. Tangent space generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>. 2024;5(4). doi:<a href="https://doi.org/10.1103/prxquantum.5.040311">10.1103/prxquantum.5.040311</a> M. Ljubotina, E. Petrova, N. Schuch, and M. Serbyn, “Tangent space generators of matrix product states and exact floquet quantum scars,” <i>PRX Quantum</i>, vol. 5, no. 4. American Physical Society, 2024. Ljubotina, Marko, et al. “Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” <i>PRX Quantum</i>, vol. 5, no. 4, 040311, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/prxquantum.5.040311">10.1103/prxquantum.5.040311</a>. M. Ljubotina, E. Petrova, N. Schuch, M. Serbyn, PRX Quantum 5 (2024). Ljubotina, Marko, Elena Petrova, Norbert Schuch, and Maksym Serbyn. “Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” <i>PRX Quantum</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/prxquantum.5.040311">https://doi.org/10.1103/prxquantum.5.040311</a>. Ljubotina, M., Petrova, E., Schuch, N., &#38; Serbyn, M. (2024). Tangent space generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>. American Physical Society. <a href="https://doi.org/10.1103/prxquantum.5.040311">https://doi.org/10.1103/prxquantum.5.040311</a> 184882024-10-29T16:04:05Z2025-09-08T14:26:29Z