Abstract
We present a high-rate projective measurement-based approach for controlling non-unitary evolution of a quantum chain of interacting spins. In this approach, we demonstrate that local measurement of a single external spin coupled to the chain can produce a spin polaron, which remains stable after the end of the measurement. This stability results from the fact that the Hilbert space of the chain contains a subspace of non-decaying states, stable during the nonunitary evolution. These states determine the resulting final state of the chain and long-term shape of the polaron. In addition to formation of the spin polarons, the presented measurement protocol can be used for distillation of non-decaying states from an initial superposition or mixture.