  Quantum many-body control is among most challenging problems in quantum
science, due to computational complexity of related underlying problems. We
propose an efficient approach for solving a class of control problems for
many-body quantum systems, where time-dependent controls are applied to a
sufficiently small subsystem. The approach is based on a tensor-networks-based
scheme to build a low-dimensional reduced-order model of the subsystem's
non-Markovian dynamics. Simulating dynamics of such a reduced-order model,
viewed as a ``digital twin" of the original subsystem, is significantly more
efficient, which enables the use of gradient-based optimization toolbox in the
control parameter space. We validate the proposed method by solving control
problems for quantum spin chains. In particular, the approach automatically
identifies sequences for exciting the quasiparticles and guiding their dynamics
to recover and transmit information. Additionally, when disorder is induced and
the system is in the many body localized phase, we find generalized spin-echo
sequences for dynamics inversion, which show improved performance compared to
standard ones. Our approach by design takes advantage of non-Markovian dynamics
of a subsystem to make control protocols more efficient, and, under certain
conditions can store information in the rest of the many-body system and
subsequently retrieve it at a desired moment of time. We expect that our
results will find direct applications in the study of many-body systems, in
probing non-trivial quasiparticle properties, as well as in development control
tools for quantum computing devices.
