  Single-spin measurements on the ground state of an interacting spin lattice
can be used to perform a quantum computation. We show how such measurements can
mimic renormalization group transformations and remove the short-ranged
variations of the state that can reduce the fidelity of a computation. This
suggests that the quantum computational ability of a spin lattice could be a
robust property of a quantum phase. We illustrate our idea with the ground
state of a spin-1 chain, which can serve as a quantum computational wire not
only at the Affleck-Kennedy-Lieb-Tasaki point, but within the
rotationally-invariant Haldane phase.
