Quantum spin models for measurement-based quantum computation

Measurement-based quantum computation is different from other approaches for quantum computation, in that everything needs to be done is only local measurement on a certain entangled state. It thus uses entanglement as the resource that drives computation. We give a pedagogical treatment on the basics, and then review some selected developments beyond graph states, including Affleck–Kennedy–Lieb–Tasaki states and more recent 2D symmetry-protected topological states. We point out some open questions along the way.