This paper explores the preparation of tensor network states using a single round of measurements and on-site unitary feedback. The authors identify criteria for local tensors that enable deterministic state preparation and use these to construct families of measurement-preparable states in one and two dimensions. These states span distinct symmetry-breaking, symmetry-protected, and intrinsic topological phases of matter. For example, in one dimension, they chart a three-parameter family of states that interpolate between the AKLT, cluster, GHZ, and other states. The protocol allows for engineering quantum states with desired correlation lengths and entanglement properties. The authors also present diagnostics for verifying whether a given tensor network state is preparable using measurements. They discuss generalizations such as multiple rounds of measurements, matrix product operators, and incomplete basis measurements. The paper also highlights the rich phase diagram of preparable matrix product states with bond dimension χ=2, showing how different states can be prepared by tuning parameters. The authors demonstrate how these ideas can be extended to higher dimensions, showing how to prepare states such as the toric code. The paper concludes with a discussion of open questions and future directions, including the experimental realization of these states in quantum devices with mid-circuit measurement capabilities.This paper explores the preparation of tensor network states using a single round of measurements and on-site unitary feedback. The authors identify criteria for local tensors that enable deterministic state preparation and use these to construct families of measurement-preparable states in one and two dimensions. These states span distinct symmetry-breaking, symmetry-protected, and intrinsic topological phases of matter. For example, in one dimension, they chart a three-parameter family of states that interpolate between the AKLT, cluster, GHZ, and other states. The protocol allows for engineering quantum states with desired correlation lengths and entanglement properties. The authors also present diagnostics for verifying whether a given tensor network state is preparable using measurements. They discuss generalizations such as multiple rounds of measurements, matrix product operators, and incomplete basis measurements. The paper also highlights the rich phase diagram of preparable matrix product states with bond dimension χ=2, showing how different states can be prepared by tuning parameters. The authors demonstrate how these ideas can be extended to higher dimensions, showing how to prepare states such as the toric code. The paper concludes with a discussion of open questions and future directions, including the experimental realization of these states in quantum devices with mid-circuit measurement capabilities.